A Review of Quadruped Robots: Structure, Control, and Autonomous Motion

With their unique point‐contact ability with the ground and exceptional adaptability to complex terrains, quadruped robots have become a focal point in the fields of automation and robotic engineering. Significant research progress has been made in aspects such as structural design, motion planning, and balance control of these robots. However, a primary challenge in current research lies in further enhancing the dynamic performance, environmental adaptability, and payload capacity. In this article, research achievements in key technical areas of quadruped robots, encompassing structural design, gait planning, traditional control strategies, intelligent control strategies, and autonomous movement, are comprehensively discussed. The focus of the article is on analyzing trends in intelligence and technological innovation within the aforementioned areas, aiming to provide robust theoretical support and forward‐looking technical guidance for quadruped robots research. Additionally, it offers valuable references for scholars engaged in this field.


Introduction
Mobile robots are paying increasing attention due to their ability to substitute for humans in complex or hazardous working environments, including nuclear power plants, antiterrorism operations, warfare, and underground coal mines.Generally, these robots can be categorized into three types: wheeled, tracked, and legged. [1]Wheeled and tracked robots excel in smooth and rapid movement on flat surfaces, and their control systems are relatively straightforward.However, their efficiency significantly diminishes or they may even become immobile when traversing soft or uneven terrain.In contrast, legged robots, with discrete footholds, demonstrate superior adaptability, they can navigate through complex terrains, including obstacles, swamps, deserts, and uneven surfaces, while maintaining body stability.
Additionally, a quadruped robot has the advantage of unrestricted lateral movement, allowing it to achieve omnidirectional motion. [2]This capability is observed in nature, where animals like antelopes navigate freely on steep cliffs, cheetahs sprint at high speeds across grasslands, and sled dogs move effortlessly through snow.Legged robots possess the potential to operate effectively in natural off-road conditions, as they have lower requirements for specific walking surfaces.Consequently, legged robots have been extensively researched by scholars.However, the structure, movement speed, load capacity, and environmental adaptability of biomimetic legged robots still lag behind those of their animal counterparts.
Research on legged robots has primarily focused on bipedal, quadrupedal, and hexapodal robots, with comparatively less attention given to monopodal and octopodal robots.The appropriate number of legs plays a crucial role in ensuring efficient movement and stable performance of the robot. [3]In comparison to biped robots, quadruped robots exhibit a stronger carrying capacity and superior stability.Furthermore, quadruped robots have simpler structures and control systems when compared to hexapod and octopod robots, making them an essential branch within the realm of legged robots.The torso of a quadruped robot is a floating base, with its legs operating independently of the torso.This design enables the robot to traverse complex terrains smoothly, even when bearing a load. [4]In recent years, numerous research teams have concentrated on investigating dynamic gaits, motion stability, balance ability, and the high-load characteristics of quadruped robots, aiming to enhance their dynamic stability, motion speed, and transportation capacity. [5]he adaptability of quadruped robots to various complex terrains expands their range of applications across different scenarios.In natural environments where existing wheeled and tracked transportation tools face challenges, quadruped robots demonstrate greater flexibility and efficiency in handling heavy load transportation tasks.The Boston Dynamics' Big Dog, which is the world's first quadruped robot with the ability to walk in the wild and carry heavy loads, is an excellent example of this application.It can be used for material transportation tasks on the battlefield. [6]Quadruped robots exhibit more robust movement capabilities than humans, making them valuable in exploring dangerous or hard-to-reach areas, such as earthquakestricken zones, narrow pipelines, and nuclear power plant inspection sites. [7]Notably, the quadruped robot developed by Unitree Technology Company has found utility in factory production bases, substations, and the construction industry, successfully completing inspection tasks. [8]In mineral exploration, robots can assist workers and replace humans in hightemperature and high-pressure environments, ensuring human safety. [9]Furthermore, quadruped robots have widespread applications in the service industry.With the rapid economic development, these robots can accompany humans to alleviate loneliness and anxiety.They engage in emotional communication, bringing happiness, and enhancing people's satisfaction with their spiritual needs.Moreover, there is no need to worry about pet birth, aging, illness, or death. [10]

Structure of Quadruped Robots
A quadruped robot, a form of biomimetic automation, is meticulously designed to faithfully replicate the walking patterns of animals and adeptly navigate through intricate environments.The foundational task in achieving motion for quadruped robots lies in structural design.A well-conceived structure plays a pivotal role in augmenting the robot's stability, speed, and agility.Presently, prevalent structural variations of quadruped robots encompass bioinspired dogs, [11] bioinspired sheep, [12] bioinspired rats, [13] bioinspired cats, [14] and bioinspired cheetahs, [15] among other examples.The fundamental structure of a quadruped robot typically comprises a body, thighs, shanks, and feet, as illustrated in Figure 1.Quadruped robots are characterized by multiple degrees of freedom (DoF), and the power sources for motion can be categorized into hydraulic drives, electric drives, pneumatic drives, and more.

Hydraulic Drive
Hydraulic actuation employs a fluid, typically hydraulic oil, to transfer energy, regulating the flow and pressure of the liquid through hydraulic cylinders and valves to facilitate joint movement.The underlying principle of a hydraulic system relies on a sealed pipeline filled with liquid, utilizing pressure differentials to generate force and motion.Controlling hydraulicdriven robots entails overseeing liquid flow, pressure, valve operations, and adjusting the fluid's flow and pressure based on feedback information to attain the desired movement.
Hydraulic-driven quadruped robots possess a higher power density, which allows them to generate substantial driving force and torque.Consequently, quadruped robots can bear heavier loads and traverse more complex terrains.Representative hydraulic-driven quadruped robots include Big Dog, LS3, [16] and Wild Cat, developed by Boston Dynamics, as well as the HyQ series of electrohydraulic hybrid-driven quadruped robots manufactured by the Italian Institute of Technology (IIT).The characteristics of these robots are shown in Table 1.
In 2008, with the support of China's National 863 Program's "12th Five-Year" major project, the development of hydraulicdriven quadruped robots was initiated in China.These quadruped robots exhibit unique features and capabilities.For instance, Shandong University's SCalf quadruped robot [17] was the first hydraulic-driven quadruped robot in China capable of high-speed trot gait.It can traverse obstacles approximately 150 mm high.Shanghai Jiao Tong University's Baby Elephant quadruped robot [18] can walk on various types of terrain with a maximum load of 100 kg.The Beijing Institute of Technology has developed a 16 DoF hydraulic bionic quadruped robot, [19] which is capable of performing a wide range of flexible movements.The Chinese version of the "Big Dog" quadruped robot, developed by the Northern Vehicle Research Institute, can navigate across different types of terrain, including walking up slopes with a 30°i ncline, and a maximum speed of 6 km h À1 .
Hydraulically driven quadruped robots can be applied in military, exploration, industrial, and other fields.However, due to the drawbacks of hydraulic drive systems, such as their heavy weight, large size, and high noise levels, their application in military fields is still relatively limited.Efforts are underway to develop lightweight and highly efficient hydraulically driven quadruped robots.In the future, more intelligent and flexible hydraulically driven quadruped robots that can adapt to a wide range of scenarios and task requirements may emerge.

Motor Drive
Motor-driven motion is achieved by regulating the speed and torque of the motor to manipulate joint movements.Typically, a battery or alternative power source is necessary for operation.The control of motor-driven robots involves managing the speed, position, and current of the motor.Adjustments to the motor's output are implemented based on feedback information to accomplish the desired movement.
In comparison to hydraulically driven quadruped robots, electrically driven quadruped robots offer advantages, including smaller size, lower noise levels, and more convenient control.Noteworthy examples of motor-driven quadruped robots include the MiniCheetah from the Massachusetts Institute of Technology, the ANYmal from ETH Zurich, and the SpotMini from Boston Dynamics.Additionally, Laikago from Unitree Technology, as well as "Red Rabbit" and "Jueying" from Zhejiang University in China, exhibit impressive motion capabilities.The performance parameters of these quadruped robots are compared in Table 2.  Reproduced with permission. [6]Copyright 2024, Elsevier.b) LS3, [213] and c) Wild Cat. [213]ble   [6] cargo transportation

Figure 2a
LS3 [213] 2009 Hydraulic drive Load capacity up to 181 kg.Completing tasks lasting 24 h and covering 32 km [46] Military scenarios Figure 2b Wild Cat 2013 Hydraulic drive High speed, with outdoor laboratory speed reaching up to 32 km hÀ1 [46] Various gaits such as trotting, jumping, and running High dynamic characteristics, [203] adaptability Performing movements like running, single-foot hopping, and jumping Good robustness, compact structure [218] Complex terrains Figure 3d HyQ2 Real 2015 Hydraulic drive High-performance hydraulic system, superior load characteristics, dynamic properties, integrated structure [4] Complex terrains Figure 3e (a Figure 3. HyQ series quadruped robots: a) HyQ V1.0.Reproduced with permission. [214]Copyright 2010, Claudio Semini; b) HyQ V1.1.Reproduced with permission. [203]Copyright 2011, SAGE Publications; c) HyQ V1.2; [215] d) HyQ-blue; [216] and e) HyQ2 Real. [217]ach of these quadruped robots has its own unique advantages.The MiniCheetah, characterized by its relatively light body weight and limbs with flexible bending capabilities, notably became the first quadruped robot to achieve backflips without visual assistance. [20]Designed for autonomous operation in challenging environments, the ANYmal exhibits exceptional compliance and precise torque-controlled actuator-driving devices, enabling dynamic movement and high maneuverability, including climbing capabilities. [21]A notable distinction for ANYmal lies in its legs' ability to rotate 360°and change configuration freely.The most outstanding feature of SpotMini for urban and industrial environments is its ability to climb stairs.Employing a comprehensive visual scheme, it creates a global map and identifies appropriate foothold points, thereby avoiding abrupt changes in terrain and unsafe areas for footholds. [22]It is also the world's first quadruped robot with a mounted robotic arm, achieving stable control.In terms of mechanical design, Laikago draws inspiration from Boston Dynamics' SpotMini.The key to Laikago's high-frequency responsive motion performance lies in its gearbox-free driver, characterized by its small size, lightweight construction, simplicity, and reliable torque control.This design approach significantly reduces the actuator's cost.With 12 lightweight and compact direct-drive motors, the entire robot can be controlled within the dimensions of a suitcase and a total weight of 22 kg. [23]Red Rabbit" excels in high adaptability to various complex terrains, possesses a strong load capacity, and operates quietly during running.Jueying has mastered diverse abilities, including running, jumping, climbing ladders, walking on gravel roads, and autonomously squatting and standing up.When individuals are about to lose balance, they will make a decision and quickly adjust their posture through a series of actions to maintain stability.[8]

Pneumatic Drive
Pneumatically driven quadruped robots utilize compressed air or gas to drive actuators, such as pneumatic cylinders or pneumatic muscles, achieving motion by controlling the pressure of the gas.The control of pneumatic-driven robots involves managing the gas pressure and monitoring the position or force of the actuators.Control algorithms for pneumatic systems need to consider the dynamic response of the gas.
The pneumatic drive offers advantages such as low manufacturing cost, lightweight design, and good flexibility.However, it faces challenges related to low control accuracy, making it difficult to achieve high-precision control and low energy consumption.Given the complex application scenarios of quadruped robots and the demand for high dynamic response and precision, the use of pneumatic drive has not been widespread.Pneumatic quadruped robots, characterized by low impedance, are prone to unnecessary oscillatory behavior during walking.Wait et al. [24] introduced a small pneumatic quadruped robot (depicted in Figure 4a) and developed a gain scheduling walking controller.During the standing phase, the pneumatic drive system displays high-impedance characteristics, whereas in the swinging phase, it exhibits low-impedance characteristics, enabling the robot to achieve a walking gait.Kim et al. [25] proposed a pneumatic system coupling an origami pump actuator and a soft pneumatic actuator (illustrated in Figure 4b).The inherent flexibility of the pneumatic drive system allows the robot to perform more realistic tasks, though suitable materials and manufacturing equipment pose challenges.Furthermore, the scalability of the pneumatically driven quadruped robot structure is limited.Considering these drawbacks of pneumatic quadruped robots, Park et al. [26] designed a quadruped robot with bidirectional motion and soft inflatable joints (as shown in Figure 4c).This design facilitates easy assembly and disassembly while minimizing the number of components and materials.

Body Structure
The body of a quadruped robot is the primary supporting structure, analogous to the torso of a quadruped animal.It is commonly constructed using materials such as aluminum alloys and carbon fibers chosen for their specific strength and stiffness Pneumatically driven quadruped robot: a) Pneumatic quadruped robot model.Reproduced with permission. [24]Copyright 2014, IEEE; b) the origami pump actuator based pneumatic quadruped robot.Reproduced with permission. [25]Copyright 2021, IEEE; and c) quadruped robot of scalable soft actuation.Reproduced with permission. [26]Copyright 2022, IEEE.
properties.Various sensors and control devices are typically installed on the body to enable functions such as autonomous walking and obstacle avoidance.The body of a quadruped robot is divided into rigid and flexible structures, as illustrated in Figure 5.

Rigid Torso
Current research on quadruped robots has predominantly focused on rigid torso designs.Rigid torsos, characterized by a lower number of DoFs and a relatively straightforward structural design, exhibit reduced flexibility and stability.Therefore, it is crucial to enhance the speed, stability, and energy efficiency of such rigid torso quadruped robots to optimize their locomotive performance.Recent advancements primarily concentrate on the optimization of the drive system, leg design, and the selection of control algorithms to achieve these objectives.Byeonghun Na et al. [27] based on the principles of brushed DC motors, designed a high-speed linear drive system that achieved high-speed movement in robots, with a maximum speed of 1.07 m s À1 .Iqbal et al. [28] proposed a continuous control method utilizing a hybrid time-varying dynamics model, which achieved stable movement on dynamic rigid platforms.Valsecchi et al. [29] introduced a new high-efficiency actuator and low-inertia leg design to limit energy consumption and enable fast, agile movement.Although these methods can improve certain aspects, such as the speed, stability, and energy efficiency of rigid torso quadruped robots, they are not as effective as robots with flexible torsos in dispersing or absorbing impact forces.The combination of advanced perception systems and intelligent control strategies [30] has the potential to enhance a robot's terrain adaptability, load capacity, and energy efficiency.However, it also increases the system's complexity and power consumption.

Flexible Torso
The spine of a quadruped robot significantly contributes to enhancing its flexibility, stability, and environmental adaptability.Previous studies have primarily focused on rigid torsos for quadruped robots, as shown in Figure 5a.In the locomotion of quadruped mammals, the spine plays a crucial role in body contraction and extension, thereby improving running speed, stability, and energy utilization to a certain extent.
In the field of biomimetic quadruped robots, flexibility and movement speed can be enhanced by increasing the DoFs of the torso or using flexible materials, as shown in Figure 5b-d.Khoramshahi et al. [31] introduced a quadruped robot named Bobcat, where the torso is connected to the front and rear parts of the robot through a single motor rotating in the sagittal plane.This design increases the effective length of the hind legs, enhancing stride and movement speed while minimizing ground friction.In comparison, the increased DoF in the torso in passive mode, as seen in Bobcat, requires no additional control or computing resources, simplifying the overall structural design and enhancing dynamic stability and motion speed. [32]To optimize mobility in confined spaces and limited dimensions, Shi et al. [13] devised the SQuRo bionic rat quadruped robot with 12 active DoFs, including two at the waist.This design allows flexible body bending for tight turns with a small radius (0.48 BL) in narrow spaces.Another approach involves incorporating springs into the torso, which is a common method for achieving flexibility.A flexible torso effectively reduces ground force, increases stride length, and enhances movement speed. [33]onversely, designing the torso with flexible materials, while enhancing terrain adaptability and expanding the range of motion, introduces complexity to robot modeling.Practical applications may encounter issues such as wear and aging in flexible materials, necessitating regular maintenance and replacement, thereby increasing maintenance and time costs for robots.

Structure of Legs
The leg structure is an essential component of quadruped robots, and its design profoundly influences their motion performance.A good structural design can reduce problems such as leg drive impact and large leg inertia, and improve the stability and maneuverability of the robot.According to the different forms of leg structures, the leg structures of quadruped robots can broadly be categorized into two types: linkage legs and scaled legs.

Linkage Leg Structure
The linkage leg structure comprises multiple hinged connecting rods, which can be categorized into series, parallel, and hybrid types based on their modes of connection.The series type offers advantages such as a simple structure, a large range of motion, and straightforward control.In contrast, the parallel type provides advantages such as high stiffness, strong load-bearing capacity, high precision, and low inertia.The hybrid type combines the strengths of both series and parallel structures.As is well known, MIT's MiniCheetah [34] and Unitree Technology's A1 [35] adopt a series leg structure.ANYmal from ETH Zürich employs direct motor-driven joints, where the joint drive units integrate the driver, sensors, and bearings of the joint axis.There is bias at the knee joint of each leg to ensure that all joints can rotate 360°, achieving high maneuverability in the quadruped robot. [36]he Stanford Student Robotics club developed the Stanford Doggo, a low-cost, open-source quadruped robot.Comprising a planar four-link mechanism (depicted in Figure 6a), this robot exhibits remarkable jumping capabilities. [37]Qi et al. [38] analyzed the kinematic performance of the 3-universal-prismatic-universal (3-UPU) and 6-spherical-prismatic-universal (6-SPU) parallel leg mechanisms of quadruped robots (as shown in Figure 6b,c).The utilization of parallel legs demonstrated reduced energy consumption and enhanced load capacity. Park et al. [39] inspired by the physiological structure of cats' hind leg bones and muscles, designed a single DoF leg mechanism consisting of nine links and a spring, as shown in Figure 6d.The robot equipped with this innovative leg mechanism can run at an average speed of 0.75 m s À1 on flat ground.The cat-like link mechanism achieves a 360°continuous motor drive.

Scaled Leg Structure
The scaled leg structure amplifies the displacement of the driving element to the end effector, thereby increasing the overall displacement of the mechanism and greater efficiency compared to other structures.Inspired by the characteristics of animal motion, the Cheetah Cub [40] and Oncilla robots [40] utilize spring-loaded pantographs (SLP) for their leg structures (as depicted in Figure 7a).The SLP mechanism effectively reduces leg mass and inertia, but the large extension range of the knee joint adds weight of the robot.This may impact the robot's ability to navigate uneven terrain and resist ground interference.To enhance the efficiency of the output motion in quadruped robots, Nizami et al. [41] proposed a variant of the SLP mechanism called the elastic load scissor mechanism (shown in Figure 7b).This mechanism amplifies the input angle to generate a greater output displacement of the knee joint.In summary, an analysis of various leg structures indicates that a link-type leg structure with multiple bars and numerous optimizable parameters is conducive to achieving diverse foot trajectories.This design effectively simulates biological motion patterns and is commonly employed.However, its limited range of motion imposes higher demands on control algorithms.The scaled leg structure, dynamically adjusting leg length to adapt to varying terrains and tasks, represents an innovative trend in recent robot design.This structure relies on precise mechanical scaling mechanisms, which increase the overall cost and maintenance difficulty of the system.The additional mechanical components required for scaling may increase the weight and volume of a robot, thereby influencing its overall performance and energy efficiency to some extent.

Leg Topology Structure
The mobility, traversability, and singularity of quadruped robots are determined by their topology structure.A suitable topology structure forms the basis for achieving stable and flexible movement in complex environments.The joints in quadruped robots can be classified into two structural forms: knee joints and elbow joints.Knee joints are characterized by apex points that face the direction of forward motion (pitch), akin to human knees.In contrast, elbow joints pertain to joints where the apex is opposite to the direction of forward motion, similar to human elbows.The distinct configurations of these joints give rise to variations in the application scenarios and motion capabilities of quadruped robots.
The leg topology structures of quadruped robots can be broadly classified into three types: insect-like structure, reptilelike structure, and mammal-like structure, [42] as illustrated in Figure 8-10.Insect-like and reptile-like quadruped robots have a large single-leg workspace, minimizing interference and contact between legs.However, their locomotion capabilities are often limited and characterized by static gaits.Compared to mammal-like robots, they have better static stability, but maintaining body balance requires relatively larger joint torques. [43]iomimetic robots that emulate quadruped mammals possess a large working space and strong obstacle avoidance capabilities, (a) (b) Figure 7.The spring-loaded pantograph: a) spring-loaded pantograph (SLP) for leg structures.Reproduced with permission. [40]Copyright 2013, SAGE Publications; b) the elastic load scissor mechanism.Reproduced with permission. [41]Copyright 2020, IEEE.
and excel in speed and dynamic performance.The leg structures are primarily oriented in the vertical plane, providing strong loadbearing capacity and adaptability to varying loads.Therefore, for quadruped robots requiring heavy load capacity and rapid movement, this topology structure is more suitable.Common mammal-like walking leg topology structures encompass four main types: all-elbow, all-knee, front knee and back elbow, and front elbow and back knee.When encountering steep slopes, stairs, or other intricate terrains, the forward-facing knee of the front-knee-back-elbow configuration often encounters interference with the terrain ahead, leading to a reduction in the space below the abdomen and compromising movement stability. [44]In contrast, the all-elbow configuration addresses this issue, making it suitable for indoor or urban environments with low vertical obstacles or continuous stairs.As a result, it is widely used in most small and medium-sized electric quadruped robots. [45]Conversely, the all-knee configuration, mirroring the all-elbow configuration, is rarely used in practice.The front-knee-back-elbow configuration adopts a fully symmetrical arrangement.The forward leg's knee is more suitable for climbing vertical obstacles, avoiding interference with obstacles, and is suitable for outdoor environments. [46]he front-elbow-back-knee configuration, contrasting the front-knee-back-elbow configuration, features a symmetrical formation that effectively reduces fluctuations in the trunk's center of mass resulting from joint control errors.In addition, its compact structure allows sensors to be more easily installed on feet to detect ground obstacles.It is widely used in quadruped robots such as Big Dog and HyQ.

Foot Structure
The foot design of quadruped robots usually adopts cylindrical feet (including semicylindrical feet) [47] and spherical feet (including semispherical feet). [48]A cylindrical (or semicylindrical) foot is the foot of a quadruped robot that has a horizontal cylindrical or semicylindrical shape.When in contact with the ground, a rectangular plane is formed. [49]Currently, the circular foot end is the most prevalent design for quadruped robots, with a spherical or hemispherical shape.This design allows the robot's foot to make contact with the ground from all directions, enhancing its adaptability to different environments.However, when faced with obstacles, slopes, or uneven terrain, quadruped robots with flat or ball feet may risk falling or encountering difficulties in traversing the terrain.Furthermore, traditional foot structures often lack sensing systems that can provide information about  the environment and the interaction between the foot and the surroundings.This further limits the adaptability of quadruped robots in complex environments.Catalano et al. [50] proposed an articulated adaptive foot and conducted tests and experiments on the ANYmal quadruped robot.Real quadruped animals have irregular feet with structures like claws and flesh pads, providing a firm grip when in contact with the ground.However, research on bionic foot structures remains insufficient.It is well known that lizards have very flexible and soft bodies, and can move agilely on vertical walls.Inspired by lizards, Nishad et al. [51] designed a bionic lizard quadruped robot with adhesion and peeling mechanisms on each leg, imitating the toes and claws of real lizards.Some quadruped robots are designed with unique foot structures to fulfill specific tasks.Hooks et al. [52] installed an end effector with a passive DoF at the foot of the robot to complete the picking task.The foot end of the quadruped robot magnetically adhesive robot for versatile and expeditious locomotion (MARVEL) integrates electropermanents and magnetorheological elastomers, which provide enhanced adhesion and traction.This allows the robot to move quickly on various surfaces, including walls, floors, and ceilings. [53]Quadruped robot feet are typically made of elastic materials, like rubber and sponges.However, traditional materials often struggle to meet the demands of a high friction coefficient, strong shock absorption, and robust flexibility simultaneously.Therefore, the application of new materials in the design of quadruped robot feet will enhance environmental adaptability of these robots.The use of special materials, such as biomimetic gecko foot end materials, can enable quadruped robots to navigate through more intricate environments.

Motion Planning
The motion planning of quadruped robots encompasses the selection of suitable ground contact points and the planning of leg trajectories to prevent the robot from tipping over.By generating suitable leg trajectories, the impact between the robot and the ground can be minimized.

Gait Generation Method
The motion planning for a quadruped robot includes the gait generation method and the execution of gait.The commonly used gait generation methods include the central pattern generator (CPG), spring-loaded inverted pendulum (SLIP), zero moment point (ZMP), and Bezier curve.
The CPG generates stable periodic oscillation signals by simulating the low-level neurons of organisms, allowing for gait planning in robots.This method utilizes mathematical techniques to generate oscillation curves, which serve as inputs for determining the position and velocity of leg joints.With specific self-stabilizing abilities, the phase relationship between a quadruped robot's legs can be easily adjusted using these oscillation curves.The CPG structure is relatively simple and has a low computational load.Since it relies on known oscillators, although this method has a certain self-stabilizing ability, it is no longer applicable when facing complex terrains due to the enormous environmental disturbances on the robot. [54]Fukuoka et al. [55] utilized neural oscillators to generate torque control or phase modulation signals in the joint space, achieving motion stability control of quadruped robots on uneven terrain.To ensure stability in quadruped robots, it is necessary to adjust the parameters of CPGs to generate appropriate control signals for the joints.For robots with multiple DoFs, multiple CPG units are required to meet the control requirements, thereby increasing the complexity of parameter adjustment.Liu et al. [56] studied the trajectory generation method for quadruped robots in workspace.They developed a method that maps the output signals of the CPG network to the trajectory of the quadruped robot in the 3D workspace.This approach enables the artificial intelligence robot (AIBO) robot to adaptively move on irregular surfaces like slopes and stairs.It can achieve gait transitions and change walking modes by modifying a few CPG network parameters.Recently, reinforcement learning (RL) has been widely and successfully applied in the field of robotics.Wang et al. [57] combined DRL with the CPG method to generate rhythmic motion in robots.This method enables the robot to walk blindly and resist external interference.
The SLIP model simplifies the leg to a massless spring with a load, achieving jumping control of the robot through the three-component method. [58]Due to its simple principles and practicality, this technology has been widely adopted by various institutions and universities, including Boston Dynamics, Hangzhou Unitree Technology Co., Ltd., and Shandong University.Gong et al. [3] planned the dynamic gait trajectory for a robot's foot when contacting the ground with zero velocity and acceleration.Based on the 3D-SLIP model, they verified the effectiveness of dynamic gait through simulation on a complex robot system with 20 DoFs.The SLIP model can explain the dynamics of leg movement during various gaits.Based on this, Hayati et al. [59] used the SLIP model to investigate the impact of compliant terrain on fast leg movement.However, the SLIP model cannot directly adjust time-related parameters such as the step frequency and cycle, which restricts its ability to achieve asymmetrical gaits like galloping and gait conversion.
ZMP control assumes a point within the support polygon of the robot where the ground reaction force acting on the robot is balanced with gravity and inertial forces.Based on this stability criterion, the robot's trajectory is planned, exhibiting excellent performance in controlling low-speed motion. [60]Vukobratovi et al. [61] applied the ZMP method to generate robot motion.This method relies on predefined foothold points.Although decoupling the planning of footholds and body motion trajectories reduces complexity, the design of foothold points is intended to assist the body in achieving the desired motion, potentially leading to unnatural movements.Winkler et al. [62] introduced vertex-based ZMP constraints, which can handle point contacts, line contacts, and surface contacts in any direction.This gait generation method empowers quadruped robots with walking, trotting, jumping, and more.However, the ZMP method requires accurate dynamic and environmental models and may not respond swiftly to disturbances.The process of trajectory planning is time-consuming.Additionally, this method may be not suitable for objects with flexible links that require precise control.
In the field of quadruped robots, Bezier curves are widely used for generating foot trajectories.These curves exhibit continuity and differentiability at all points, making them suitable for modeling animal foot trajectories.The foot trajectory of the Cheetah Cub quadruped robot is generated by four quadratic Bezier curves, and the stability of the robot is improved by adjusting the leg angles at the moment of takeoff and landing. [63]anoonpong et al. [64] achieved various motion modes by replaying parameterized foot trajectories derived from four cubic Bezier curves fitted to dog foot trajectory data.The foot trajectory of the MIT Cheetah 2 robot during the swing phase is based on three fifth-order Bezier curves. [65]Zhu et al. [66] applied highorder Bezier curves to design the foot trajectory of a quadruped robot during the swing phase, ensuring stable motion on unfamiliar incline.Currently, Bezier curves are extensively employed for foot trajectory planning.Compared with previous elliptical curves [67] and cycloidal trajectories, [68] the derivative of the Bezier curve is also a Bezier curve.This property simplifies the determination of the velocity at the starting and ending positions.Additionally, the curve is smooth and differentiable at every point, allowing for smooth motion.

Gait
The lifting and landing sequence of the four limbs in quadruped mammals follows a specific pattern known as gait.Quadruped animals demonstrate the ability to employ different gaits by coordinating the movements of their limbs, leading to superior movement efficiency and adaptability in complex terrains.Through bionic experiments and gait analysis, researchers have identified various gaits of quadruped robots.Usually, gaits can be divided into symmetrical gaits, such as walk, trot, and pace, [69] and asymmetrical gaits, such as flying trot, bound, and gallop. [70]The phase relationship diagrams of different gaits are shown in Figure 11.
In these gaits, the quadruped robot undergoes diverse speeds and intensities, resulting in significant variations in configuration.In the walk gait, three legs are on the ground at any time, forming a stable triangular support structure.Hence, it is also denoted as a static gait. [71]Trot is a low to medium-speed gait commonly used during the transition from walking to running to achieve higher speed.It is characterized by the alternating movements of the four legs in a diagonal pattern within the sagittal plane.As the speed increases, the four legs may also be in the air. [72]uadruped animals exhibit a diverse range of running gaits.To date, numerous studies have demonstrated that trot and pace gaits are preferred by quadruped robots due to their speed, stability, efficiency, and adaptability. [73]The pace gait is widely used in robot motion control.In this gait, the left front leg and left hind leg have the same motion, while the right front leg and right hind leg exhibit identical movements.
Flying trot is a unique type of trot characterized by a ballistic movement of the torso.In this gait, one pair of diagonal legs move simultaneously and alternate with the other pair, resulting in a period where none of the legs make contact with the ground.However, quadruped robots rarely achieve this dynamic gait. [17]ased on the active compliance control method, the HyQ robot first achieved trotting movement without the use of springs in its mechanical structure. [74]The ANYmal robot, developed by ETH Zurich, can perform dynamic gaits, including flying trot, jump, and pronk. [75]MIT Cheetah 3 and MiniCheetah [76] have simplified the motion control problem by converting it into a convex optimization problem based on model predictive control (MPC) for ground reaction force.Various gait movements such as standing, trotting, galloping, jumping, and walking can be achieved.These implementation methods have high requirements for the structural design and dynamic modeling of robots, especially considering size and light in weight (weighing less than 100 kg).There is little research on flying trotting for large and heavy quadruped robots. [77]The bound gait consists of four phases: flight, front-leg standing, back-leg standing, and four-leg standing. [78]As a high-speed gait, bounding not only increases the robot's speed but also aids in overcoming obstacles and ravines, thus enhancing environmental adaptability.The gallop gait is a form of rapid running where the four legs move cyclically, allowing for maximum movement speed. [79]Quadruped animals exhibit a variety of gaits, and the choice of locomotion gait depends on the required traversal speed of the robot while minimizing energy consumption.

Motion Control
Motion control refers to the implementation of sophisticated algorithms to regulate a robot's position and joint torque during dynamic motion, aiming to achieve dynamic stability and enhance overall robustness.Unlike conventional fixed-base robots, quadruped robots heavily depend on the interaction between their feet and the ground for controlling motion speed and posture stability.Therefore, in addition to the dynamics of the robot itself, the control of a quadruped robot also needs to consider the contact between the robot's feet and the ground, including the contact reaction force and friction force.The motion control strategies for quadruped robots can be broadly divided into two categories: model-based control methods and model-independent control methods.The commonly used methods are shown in Figure 12.

Model-Independent Control Methods
A quadruped robot is a relatively complex underactuated system.In general, for a quadruped robot to achieve omnidirectional movement, it necessitates one DoF for rolling and two DoFs for pitching for each leg.This implies that there are 12 active DoFs for the four legs coupled with an additional 6 passive DoFs for the torso, resulting in a total of 18 DoFs.The control method for an independent model does not require precise dynamic models.This allows the robot to adapt to complex and uncertain environments, enhancing its autonomy in motion.
The concept of the CPG involves the creation of multiple periodic oscillators that emulate the structure of the central nervous system in simpler organisms.These oscillators are interconnected to generate rhythmic motion trajectories for joints of a robot. [80,81]The proposed CPG model exhibits excellent characteristics, including high parameterization, low feedback influence, self-correction, and self-stability. [82]CPG models are commonly divided into two categories, nonlinear oscillator models and neural oscillator models.Wasista et al. [83] proposed a CPG controller architecture based on the neural principles of CPGs.By configuring the parameters of the CPG controller using the neural state output model, it is possible to obtain effective gait control signals for quadruped robots.Xie et al. [84] utilized the Hopf nonlinear oscillator model to enable quadruped robots to adapt to slopes, execute smooth transitions, and seamlessly traverse from flat ground to slopes.Since the neural oscillator equation is generally linear, multiparameter, and multidimensional, tuning parameters and dynamic analysis can be complex. [85]Nonlinear oscillators are often challenging to analyze because of their nonlinear and chaotic characteristics. [86]ue to their exceptional capability in addressing nonlinear problems, neural networks are an ideal control method for complex nonlinear control problems in robotics. [87]Jin et al. [88] implemented a new trotting gait for quadruped robots based on neural networks.The proposed control system demonstrates remarkable accuracy and significant anti-interference to both internal and external random disturbances induced by irregular terrain.RL, as an unsupervised learning algorithm, has been widely used in motion control and kinematics of robots in recent years. [89,90]eng et al. [91] introduced a novel RL control architecture composed of RG and PF networks, which addresses the issue of RL's sensitivity to reward functions and improves training speed.Pei et al. [92] utilized the emerging technology of deep reinforcement learning (DRL) to investigate the locomotion challenges faced by quadruped robots in unfamiliar and unstructured terrains.DRL combines the advantages of RL and deep learning (DL).Therefore, DRL has the ability to handle complex tasks in high-dimensional control spaces with minimal prior knowledge. [93]

Model-Based Control Methods
The model-based control method follows the concept of "modelplanning-control".In this approach, the robot and the environment are initially modeled, then the ideal motion trajectory of the robot is planned, and finally, the robot's motion is approximated to the ideal trajectory through feedback control.The mainstream ideas of model-based control methods include those based on simplified models, like SLIP and virtual model control (VMC), those based on complete dynamic models, such as ZMP, MPC, and WBC, and those based on inverse dynamic modeling, including proportion integration differenttiation (PID), adaptive control, and backstepping control.
The SLIP model is a commonly used approximate modeling method in the motion control of legged robots.The single-leg support configuration is referred to as the spring-inverted pendulum model, where the motion process is equivalent to the swinging and extending process of the inverted pendulum. [94]he spring-inverted pendulum algorithm for quadruped robots decouples base position and attitude control through an approximate equivalent method. [3]Based on the amphibious spherical quadruped robot platform, He et al. [73] achieved trot gait and pace gait by using the SLIP model.Yu et al. [95] designed a 12 DoFs quadruped robot with a flexible spine, based on task-space dual-SLIP model control.The expected trajectory of the robot's center of mass is generated based on two uncoupled SLIP models.A suitable controller is then designed to enable the quadruped robot to track the desired trajectory, thereby achieving a stable galloping gait.The motion control method based on the inverted pendulum model has a simple modeling approach without demanding high modeling accuracy, the strong inherent nonlinearity of the SLIP model poses challenges in obtaining precise analytical solutions. [96]he VMC method was first proposed by Jerry E. Pratt and applied to the motion control of bipedal robots. [97]Through the use of VMC, all of the robot system's spatial movements are roughly represented as the position and attitude motion of a single rigid floating body.The interaction between the base and the ground can be roughly represented as a virtual spring-damping model to regulate the movement of the base body when the support effects of all legs are disregarded.Regardless of the influence of the acceleration of the base body, the control force is distributed to the foot end of the supporting leg as the ground reaction force.The control force of each joint can be calculated based on the force Jacobian matrix of each leg. [98]When calculating the control force of the robot, it is possible to achieve different tracking effects and anti-interference capabilities by adjusting the virtual spring stiffness and damping coefficient.A hierarchical controller is not needed for VMC, and the speed and height control of the quadruped robot can be achieved using only joint torque.This method considers the generalized coordinates of the body and feet, including their configuration, position, and velocity, without requiring tedious dynamic calculations. [99]This control method has been effectively implemented on both the springy tetrapod with articulated robottic legs (StarlETH) robot [100] and the HyQ robot. [99]MC is a relatively intuitive-model-based control algorithm that decouples the motion variables of a robot through the adjustment of control parameters.This approach can achieve good force control characteristics without considering the complex calculation relationship of dynamics.This method has the obvious advantages of simplicity and high computational efficiency. [101]he stiffness and damping coefficients of the virtual spring are equivalent to the proportional and derivative control parameters in PID control.Therefore, when there is a significant deviation in the robot's configuration, a larger control torque is needed.Under the constraint of the friction cone at the foot, the torque quickly reaches saturation, which affects the stability and duration of the robot's stability.
The disadvantage of VMC is that virtual physical components cannot adequately describe the dynamic characteristics of the system, particularly in terms of fast dynamic motion capabilities.The VMC has significant limitations. [102]Inertia and sensor noise can further exacerbate this limitation.Moreover, VMC only considers the system's control at the current moment, in contrast to other predictive control methods.Consequently, its dynamic and robustness on complex terrains, such as stairs, will be significantly worse. [103]he theory of the ZMP ensures that the combined force direction of gravity and the inertial force acting on the body during motion intersect with the ground within the foot's support area, thereby achieving stable motion.Initially, the ZMP method was applied to analyze the stability of humanoid robots, specifically bipedal robots. [104]Subsequently, this approach was also introduced for ensuring stability control in quadruped robots.
This control method relies on the stability domain of the foot to provide control torque for the robot.Therefore, the foot needs to establish a supporting polygon, which is commonly used for walking. [105]The motion based on ZMP proves to be overly restrictive for quadruped robots, leading to relatively slow robot motion. [106]With the recent development of quadruped robots, there has been growing interest toward achieving high dynamic performance.To meet the demands for high speed and flexibility in quadruped robots, a popular approach is to combine the ZMP method with other techniques.For example, Bellicoso C et al. [75] combined the sequential quadratic programming (QP) framework to solve nonlinear ZMP constraints.Although this method increases the computational complexity, it enables quadruped robots to perform online motion planning and execute tasks in a manner similar to MPC.Consequently, they can achieve dynamic gaits such as trotting, pacing, and dynamic lateral walking.Additionally, it allows them to perform gaits with complete flight phases, such as jumping, pushing up, and flying trot.To address the challenge of quadruped robots' flexibility in walking gaits when faced with unperceived interference, Xu et al. [107] proposed a compliance control strategy.This strategy is based on ZMP preview control, aiming to establish soft contact between the foot and the ground.The objective is to minimize the impact on the robot's body and enable it to walk robustly and flexibly even in the presence of interference.Meng et al. [108] achieved stable control of the trotting gait for small quadruped robots by combining the ZMP method and the MPC method.
The locomotion of quadruped robots depends on the contact force between their feet and the ground.However, due to the nature of pushing forces exerted by the feet, their movement and ability to accurately follow a predetermined trajectory are restricted, especially in the presence of disturbances. [109]hen walking on flat ground, the stability of robot movement requires the center of pressure to remain within the support polygon. [110]MPC [111] is a class of control laws specifically designed to handle such constraints effectively and generate stable motion.This control scheme involves minimizing an objective function, [112] constraining the system state at the end of the predictive range, [113] or a combination of both. [114]MPC is essentially an optimal control method, [112] with modern methods commonly addressing it through linear, [113] quadratic, [76] or nonlinear optimization problems. [21]These problems determine the control sequence for the future backward prediction window.While the computational power and the efficiency of optimization algorithms have been significant advancements, the computational requirements for high dynamic motion remain a significant obstacle that limits the widespread application of MPC.
When considering the quadruped robot system as a spacefloating multi-body system, research has primarily focused on determining the position and attitude of the base as well as each leg.The state variables include the configuration of the body and the joint angles of the legs.The control force within the system includes the joint torques and ground reaction forces. [115,116]The desired trajectory of the body and each leg can be generated through preplanning or constraints.In addition to constraints related to ground contact and friction, [117] tasks can be described as equations or inequality constraint equations that involve state variables or joint torque.To address the issue of conflicting task constraints, it is essential to employ appropriate optimization equations in the design of hierarchical control.This hierarchical controller, known as a whole-body controller (WBC), [118] integrates tasks for all robot systems.WBC can be broadly categorized into the following types: 1) the WBC method based on QP [119] does not prioritize tasks and treats each task equally; 2) the WBC method based on null space projection (NSP) [120] maps low-priority tasks to the null space of high-priority tasks to accomplish multitask motions with prioritization.However, this method represents contact as an equality constraint, which may not be suitable for fast-moving robots; 3) the QP (hierarchical quadratic programming [HQP]) method with task priority weights [121] addresses low-priority tasks while ensuring highpriority tasks, taking into account various task constraints such as equality and inequality constraints; this method can incorporate multiple constraints and tasks, but the computational cost for real-time applications is high; and 4) the WBC method that combines QP and NSP [122] offers higher computational efficiency compared to other WBC methods.
Unlike simplified approaches in VMC and MPC, a WBC demands higher model accuracy and control precision for robots.Consequently, WBC has become a powerful candidate for highly dynamic motion.WBC is based on full multibody dynamics to enable the system to track desired trajectories of the torso and foot tips. [123,124]Moreover, the growing number of optimization variables and task constraint equations has increased the demand for faster hardware computing speeds. [122]This method has been successfully applied to quadruped robots such as StarlETH, [125] ANYmal, [124] and HyQ. [118]Based on this control method, significant improvements have been made in gait planning and switching, [75] coping with external force disturbances, [126] as well as navigating smooth surfaces [127] or soft terrains [128] during robot locomotion.
To achieve high dynamic motion control in quadruped robots, joint torque control is usually required to meet performance requirements.However, this method has to solve inverse kinematics. [129]The dynamic modeling method in inverse dynamics control generally establishes an overall dynamic equation based on multi-rigid body dynamics algorithms, instead of being limited to simplified dynamic models.Hence, the model accuracy achieved through inverse dynamics control methods is higher.For quadruped robots, commonly used control methods based on inverse dynamics include force control, [130] force/position hybrid control, [131] impedance control, [132] and robust control. [133,134]However, control systems based on overall dynamic equations also have shortcomings.Due to the complexity of the structure and the variability of the motion process, the calculation required for the overall dynamic equation is enormous.This poses a challenge for the practical application of these systems. [134]Apart from contact reaction forces, quadruped robots can also encounter unknown forces during motion, which makes overall dynamic modeling very difficult and poses great challenges to the control of quadruped robots. [135]The control method of inverse dynamics is commonly used in motion control of robots with fixed bases, such as manipulators [136,137] and parallel platforms. [138]In recent years, notable advancements have been made in control methods based on inverse dynamics for robots with floating bases, including biped and quadruped robots.These advancements are attributed to the optimization of modeling techniques and the enhancement of computational efficiency. [139]

Autonomous Motion
Autonomous movement of quadruped robots is a crucial technical approach for independently assessing the external environment and aiding humans in accomplishing tasks within complex environments.The key to realizing autonomous movement lies in path planning and terrain recognition technologies.

Path Planning
Path planning is a fundamental strategy for robots to navigate from a starting point to a destination while avoiding collisions with both static and dynamic obstacles in the environment.According to the characteristics of path planning methods, they can be categorized into traditional path planning methods, intelligent biomimetic path planning methods, and learning-based path planning methods.The specific path-planning methods and their advantages and disadvantages are shown in Table 3.

Traditional Algorithms
The artificial potential field method is based on the principle of balancing gravitation and repulsion to calculate feasible paths for robots in an environment.This method approximates the force balance among different objects at various positions.It enables real-time motion control in dynamic environments with short planning time and high execution efficiency.However, sometimes it may become trapped in local optimal solutions, resulting in the failure of path planning.Ge et al. [140] proposed a potential field method for robot path planning in dynamic environments, where both targets and obstacles are in motion.They successfully addressed the issue of local optimal values.Igarashi et al. [141] utilized the artificial potential field method to enhance the maneuverability of quadruped robots, enabling them to smoothly pass through uneven and irregular terrains, including overhead obstacles, narrow passages, and steps.Lee et al. [142] extended the artificial potential field method by introducing an artificial thermal field, which considers not only obstacle avoidance and collision but also obstacle traversal.In addition, gait constraints are taken into consideration to ensure the feasibility of the planned path.Dijkstra algorithm systematically searches for the optimal route between nodes, starting from a central point, iteratively expanding toward the destination until the shortest path is found. [143]However, this method is not suitable for real-time control, and will consume a significant amount of time and resources when dealing with problems with a large number of elements.Noto et al. [144] extended the traditional Dijkstra method to obtain a path (optimal path) that closely approximates the optimal path within a specified time.This approach aims to balance computational efficiency and path optimality.To address the shortest path problem in uncertain environments, Deng et al. [145] proposed the fuzzy Dijkstra algorithm, which handles the shortest path problem with fuzzy arc lengths.By representing arc lengths with fuzzy numbers, finding the shortest path becomes more easier. [145]Liu et al. [143] proposed a path planning method based on the Dijkstra algorithm for global terrain autonomous navigation in quadruped robots.They also implemented a local map autonomous obstacle avoidance strategy using artificial potential field theory.This approach enables accurate global path planning, autonomous obstacle avoidance within the local map, and autonomous navigation of quadruped robots in challenging environments [143] The A* algorithm can be considered as an extension of the Dijkstra algorithm, which is a path search method that improves search efficiency through the use of heuristic functions.A heuristic search utilizes heuristic search rules to evaluate the distance between the current search position and the target position.By prioritizing search directions toward the target location, the algorithm improves the search efficiency.Boston Dynamics has conducted research on the autonomous movement of quadruped robots in complex environments using the Big Dog platform.Path planning for these robots utilizes the A* algorithm. [146]This method is the most effective direct search method for solving the shortest path in a static road network, but it faces challenges when applied in dynamic environments with moving obstacles.Although it has the ability to capture complete solutions, the algorithm complexity is relatively high.Therefore, the improved A* algorithm has been widely studied.Li et al. [147] proposed the adaptive dynamic firefly algorithm, which optimizes existing route search results instead of conducting a new search from the starting point.This approach reduces computational burden and improves path search efficiency in dynamic map environments. [147]Fu et al. [148] proposed an improved A * algorithm that achieves a higher search success compared to the original A* algorithm, resulting in shorter and smoother paths.This improved A* algorithm effectively enhances the success rate of robot path planning and expands the optimal range of robot paths.
An rapidly exploring random tree (RRT) is a random search method that utilizes a tree-like structure.This approach starts at the root node in a non-convex high-dimensional space and iteratively samples new states by creating branches in the space.It then connects existing nodes that are closer to each sample, ultimately creating an optimal route map from the starting point to the target. [149]Aguilar et al. [150] based on the RRT method, determined the path between the initial position and the final position in the detected obstacle environment through morphological segmentation, thereby achieving autonomous motion of a spider robot.However, the path generated by the RRT algorithm may lack smoothness, leading to increased convergence time in environments with narrow passages or numerous obstacles.Consequently, many researchers have worked on improving the RRT algorithm.Classic methods for improving RRT include RRT-connect and RRT*. [151,152]The RRT-connected method allows the random tree to rapidly expand toward the vicinity of the goal, improving the algorithm's optimization efficiency. [153]In contrast, the RRT* algorithm evaluates nodes near new nodes in the tree to find better paths, addressing the issue of generating unnecessarily detoured paths. [149]

Intelligent Biomimetic Algorithms
With the extensive research conducted by scholars on intelligent optimization algorithms, various algorithms have become widely employed in solving path planning problems for robots.These algorithms are designed to obtain optimal paths that satisfy specific evaluation criteria.Common intelligent optimization algorithms include neural network algorithms, genetic algorithms (GAs), and ant colony algorithms.
The neural network algorithm takes inspiration from the neural networks in the human brain and simulates brain mechanisms for modeling purposes.Therefore, this approach is flexible and can handle input information regardless of its continuity. [154]While neural networks possess good learning ability and robustness, they struggle to effectively utilize existing prior knowledge.Moreover, as the number of neurons increases, the computational and time costs with the neural activity values in biomimetic neural networks increase dramatically.To address these limitations, Wang et al. [155] proposed a fuzzy neural network algorithm for mobile robot path planning.By combining the advantages of fuzzy theory and neural networks, the algorithm effectively determines the optimal path from the initial point to the destination point.Even in entirely unknown and static environmental conditions, this algorithm exhibits high efficient and fast convergence speed, thereby enhancing the intelligence of mobile robots.Luo et al. [156] improved traditional neural network algorithms by introducing a multi-scale map approach to robot path planning.This approach significantly reduces the time and complexity of the path planning algorithm.To adapt to various application scenarios, neural network algorithms are often integrated with traditional algorithms, [157] swarm intelligence algorithms, [158,159] and learning algorithms [160,161] to fulfill performance requirements such as convergence speed and computational cost.
A GA is an adaptive algorithm developed based on the principles of natural genetic evolution.The optimization process of a GA is illustrated in Figure 13.The population evolution starts with random individuals and generates new individuals with different genes and fitness through multiple crossovers and mutations.As the population reaches a satisfactory level of fitness, the algorithm converges to an optimal solution.The GA incorporates randomness and an exhaustive search range, making it well suited for solving complex path planning problems.Consequently, it is widely used in robot path planning.Ismail et al. [162] described the use of the GA to solve path planning problems in nondynamic environments.Their experimental results demonstrated the effectiveness of this method in different static domains.Tuncer et al. [163] used the GA to solve path planning problems in dynamic environments.They also proposed new mutation operators to overcome the limitations of traditional random mutation operators, which can produce infeasible paths.The GA is widely recognized as one of the most powerful search techniques for complex and ill-behaved objective functions.Its inherent parallel search technique allows for the simultaneous exploration of multiple potential solutions, leading to faster identification of the optimal path. [162]To achieve better results in robot path planning, researchers have made improvements to the GA [164,165] or combined it with other intelligent algorithm, resulting in hybrid approaches.Examples of these hybrid approaches include the fuzzy GA, [166] neural GA, [167,168] and GA-particle swarm optimization. [169]he ant colony algorithm is derived from the foraging behavior of ants.Ants are able to find efficient paths from the nest to food sources, even without knowing the exact location of the food.The algorithm has been applied in various scientific and engineering fields, such as workshop scheduling, traveling salesman problems, and image coloring.It is also being used to address robot navigation problems, with the goal of achieving obstacle avoidance and efficient path planning.The optimization process is depicted in Figure 14. Brand et al. [170] explored the application of the ant colony optimization (ACO) algorithm in finding the shortest and collision-free paths in a grid network for robot path planning.They used various obstacle shapes and sizes to simulate dynamic environments and validated the feasibility of this approach through simulations.Path planning for robots on unknown dynamic terrains mainly relies on heuristic methods.Rajput et al. [171] improved the traditional ant colony algorithm by merging the robot's directional movement history on a grid into a vector as a probability multiplier factor, which helps to improve the convergence speed and avoid unnecessary movements.
To overcome the drawbacks of the traditional ACO algorithm in indoor mobile robot path planning, such as a lengthy planning time, slow convergence speed, nonoptimal paths, and local optima, Miao et al. [172] proposed an improved adaptive ACO algorithm.In their approach, they introduced the angle guidance factor and obstacle exclusion factor into the transition probability of ACO to enhance the exploration and exploitation capabilities of the algorithm.Furthermore, they incorporated heuristic information, an adaptive adjustment factor, and an adaptive pheromone evaporation factor into the information update rule of ACO.By considering indicators such as path length, safety, and energy consumption, they transformed the path planning problem into a multi-objective optimization problem, enabling the robot to achieve global path optimization.The ant colony algorithm is a population-based method that involves self-organization and positive feedback. [173]It provides a unique approach to solving pathplanning problems in complex environments.

Learning-Based Algorithms
Classical path planning algorithms reached a relatively mature stage of development.However, they rely on establishing an  environment model and lack the ability to perceive the environment and learn automatically.RL enables robots to acquire environmental information through autonomous exploration, allowing them to adapt to various geographical environments and achieve path planning in multiple scenarios.The primary methods for solving path planning problems in RL include Q-learning, state-action-reward-state-action (SARSA), Q (λ)learning, and SARSA (λ).Among these, Q-learning is the most commonly used and effective RL algorithm in the field of path planning. [174]It does not require modeling and can guarantee convergence.Maoudj A et al. [175] proposed improvements to the Q-learning algorithm by introducing a new reward function.This function is used to initialize the Q-table and provide prior knowledge of the environment to the robot.They also proposed a new, efficient selection strategy to accelerate the learning process.This strategy reduces the search space while ensuring rapid convergence to an optimized solution.Q-values in the Q-learning algorithm are calculated based on state, action, and reward values.Similar to Q-learning, the SARSA approach is closely related but differs in that it is a policy-based learning algorithm. [176]ARSA learns Q-table values based on the current policy, rather than using a greedy strategy.This means that SARSA has limitations in terms of exploring alternative actions. [177]-learning is a model-free approach, meaning that it does not require an explicit environment model and can be widely applied to solve path planning problems.The Q (λ) algorithm is an extension of Q-learning that incorporates eligibility traces, which store traces of recent actions as a form of short-term memory. [178]y storing traces of state-action pairs, multiple steps can be taken simultaneously, enabling more efficient learning and faster convergence to a near-optimal path compared to Q-learning. [179]L plays a crucial role in solving sequential decision-making problems and excels in self-learning through interactions with the environment.Combining the SARSA (λ) algorithm, a local path planning algorithm based on RL, with the RRT algorithm helps reduce the randomness of sampling, thereby improving real-time performance and reliability. [180]RL has also been extensively utilized for path planning tasks.DL excels in perception tasks, while RL excels in decisionmaking.The combination of these two learning methods can yield remarkable results in path planning.Lei et al. [181] applied DeepMind's Double Q-Network, a DRL algorithm proposed in 2016, to dynamic path planning in unknown environments.
Yang et al. [182] addressed the issues of slow convergence and excessive randomness in robot path planning by combining the deep Q-network algorithm with the Q-learning algorithm.Yu et al. [161] proposed a mobile robot path planning algorithm based on neural networks and hierarchical reinforcement learning (HRL).This algorithm utilizes neural networks to enable the robot to perceive the environment and extract relevant features.The HRL maps the current state to specific actions.Compared to the Q-learning algorithm, this approach reduces the convergence time and improves the smoothness of the planned path.Furthermore, it demonstrates good generalization performance across different scenarios.

Terrain Recognition
Terrain recognition refers to the ability of a robot to identify and classify unknown terrain environments using sensors mounted on its platform.The interaction between quadruped robots and their environment is complex, and terrain features have a significant impact on robot locomotion performance.Therefore, the robot needs accurate perception and classification capabilities for the terrain to make appropriate path and trajectory planning and design suitable motion control strategies.This ensures that the robot can traverse the terrain effectively, achieve the desired motion trajectory, and maintain motion stability.The robot acquires terrain information through hardware devices it carries.Based on the distinct developmental stages of terrain recognition algorithms, they can be categorized into traditional terrain recognition algorithms and terrain recognition algorithms based on DL.The detailed classification is illustrated in Figure 15.
Terrain recognition algorithms that rely on nonvisual features are typically equipped with sensors such as light detection and ranging (LiDAR), infrared sensors, inertial measurement sensors, and vibration sensors.Based on the characteristics of these sensors, nonvisual terrain recognition algorithms can be further divided into two categories: terrain recognition algorithms based on point cloud information and terrain recognition algorithms based on vibration.
The terrain recognition algorithm based on point cloud features involves scanning the contour of the terrain environment using laser radar to obtain point cloud data and construct a grid map.Subsequently, the algorithm calculates the maximum and minimum values of the point cloud data in the grid map to create an accessibility map.Jung et al. [183] utilized a single laser range scanner to track a running person and avoid dynamically moving obstacles in unstructured outdoor environments.Leigh et al. [184] designed the Smart Wheeler robot, which utilizes a 2D laser scanner to assist individuals with mobility impairments in person tracking and following under different conditions.Meng et al. [185] introduced a slope detection method based on 3D LiDAR () point cloud data.By continuously adjusting the gait of a quadruped robot based on varying slope angles, the robot can avoid potential hazards and maintain stability during locomotion.Compared to 2D LiDAR point cloud data, 3D LiDAR data has evolved from perceiving a single plane to perceiving 3D space.Saputra et al. [186] proposed a multi-behavior generation model that is capable of generating suitable behaviors based on 3D point clouds, ground touch sensors, and inertial measurement units.This model was designed for navigating from the lower to the upper stairs in a ladder environment without handrails.The accuracy of the acquired point cloud feature data is influenced by the detection range of the radar, resulting in a higher point cloud density at close distances and higher accuracy in the generated traversability map.However, the accuracy of point clouds at far distances is lower.In practice, it is often necessary to correct the data to achieve a more balanced representation.
Vibration-based terrain recognition algorithms utilize vibration sensors integrated into a robot to collect and analyze the vibrations generated when the robot traverses unknown terrain environments, thereby realizing terrain recognition.Brooks et al. [187] proposed a more comprehensive method for classifying terrain based on vibrations.The classifier is trained offline using labeled vibration data and performs online linear classification recognition for terrains.Weiss et al. [188] proposed a terrain classification method based on vehicle body vibrations.They used support vector machines (SVMs) to perform vibration-based terrain classification, employing radial basis function (RBF) kernels and feature extraction techniques.Based on the identified terrain, the vehicle can adjust its driving mode.Hoepflinger et al. [189] proposed an algorithm for terrain shape and attribute recognition.The algorithm extracts features from the joint motor current data and ground vibration contact force measurements generated during robot locomotion.The algorithm achieves a terrain shape recognition rate of 94% and a terrain attribute recognition rate of 73%.Bai et al. [190] proposed a 3D vibration terrain recognition algorithm based on the interaction between wheels and terrain.They used fast Fourier transform spectroscopy to convert the three-axis vibration vector into the frequency domain.By normalizing the transformed data, the researchers obtained training feature vectors and conducted algorithm classification tests in five different terrain environments.
The working environment for quadruped robots is characterized by complexity, dynamics, and high uncertainty, which poses challenges for sensor reliability.Additionally, the constraints of volume, weight, and cost make it impractical to carry a full set of sensors on the robot.In this context, vision sensors offer several advantages.They are versatile and capable of providing valuable terrain information, which is crucial for preventing unexpected robot falls.
Autonomous robot motion relies on perceiving and interpreting the surrounding environment.Visual-based terrain recognition methods, compared to nonvisual methods, provide abundant information and are not influenced by the robot itself, making them a preferred choice for robot terrain recognition.To further categorize visual-based terrain recognition methods, they can be divided into two subcategories: structured visual features and abstract visual features.
Structured visual features, such as color and texture, are precisely quantified through clear mathematical or algorithmic definitions.These features not only provide consistent and reliable information in computer vision tasks but also are primarily applied in the selection and extraction of specific visual elements captured by sensors.Subsequently, these features are inputted into classifiers for precise categorization, as shown in Figure 16.Cortes et al. [191] evaluated texture descriptors and combined texture with color descriptors.They selected an SVM with an RBF as the kernel function and combined it with Gabor wavelet filters.This approach achieved a recognition accuracy of over 91%.Filitchkin et al. [192] proposed a terrain recognition algorithm based on the fusion of bag of visual words created by speeded up robust features (SURF) and support vector machine (SVM) classifiers.The algorithm was implemented on the LittleDog platform for real-time terrain classification.This led to enhanced accuracy and gait speed in the robot's terrain recognition.Wu et al. [193] combined the stacked denoising sparse automatic encoder and fisher vector techniques to achieve parameter self-tuning through unsupervised machine learning.They conducted outdoor experiments on a quadruped robot with curved legs and obtained promising results in terrain recognition using datasets from various terrains.
Structured visual feature algorithms involve feature extraction and classification using classifiers.The recognition process occurs in discrete steps, which prevents end-to-end training.This limitation hampers the ability to globally backpropagate the algorithm's parameters, making parameter updates more challenging.Consequently, training the algorithm becomes significantly more difficult, impeding effective optimization.Furthermore, the design of classifier often relies on human expertise for determination.This reliance on human intervention diminishes the efficiency and accuracy of terrain recognition.
A convolutional neural network (CNN) is a biomimetic representation of the neural network in the human brain; it simulates the brain's multilayer receptive fields and processes visual information.By constructing a multilayer convolutional network structure, CNNs can extract and convolve structured visual features such as color, structure, and texture of images layer by layer.During the layer-wise convolution process, these structured visual features interweave and integrate with each other, eventually forming abstract visual features with semantic content.Terrain recognition algorithms based on DL primarily utilize CNNs to extract these abstract visual features, which are then transformed into identifiable labels using classifiers, such as fully connected layers.This method allows for an end-to-end processing of sensor-extracted features within the network.By employing this end-to-end approach, results can be obtained at the output end without the need for feature design and classifier selection.The primary process is illustrated in Figure 17.Abou-Nasr et al. [194] proposed a method for gray scale image terrain recognition based on recursive neural networks.This method classifies grass, trees, and fallen leaves on the road.As the pixels of the image are scanned from the top to the bottom, the classifier identifies the terrain class.Liu et al. [195] proposed a terrain recognition method based on the deep sparse filtering network (DSFN).They employed a groundbreaking DL network that autonomously learns features from the raw input data.Unlike traditional deep networks, the DSFN requires adjusting only a few parameters during pretraining and fine-tuning.Borijindakul et al. [196] proposed a recursive neural network to classify soft terrains to expand the locomotion range of quadruped robots.This approach successfully classified six different terrains.
Sun et al. [197] proposed a semantic segmentation model using a fully convolutional network [198] for terrain perception of legged robots in outdoor environments.They utilized deep neural networks to identify ground textures, enabling perception of the terrain environment.Kong et al. [199] formulated the problem of visual traversability analysis as an image classification task.They trained a CNN to classify different terrain patches and dynamically adjusted the leg configuration in real time.This adaptation ensured that the robot traversed the terrain accurately and robustly, adapting to the environmental conditions.Junaid et al. [200] proposed multi-feature view-based shallow convolutional neural network (MVS-CNN) that extracts abstract features from explicit representations of input images.The gradient information of the input images is used as an additional channel to enhance the learning process of the proposed DL architecture.Multiple feature views are fed into a fully connected neural network to accurately segment road areas.Compared with the popular semantic segmentation network (SegNet), [201] the proposed approach performs better during training and evaluation, while also being more efficient.
In robot terrain recognition, whether based on nonvisual features or visual features, it is crucial to select a fast and efficient method for terrain classification.The accuracy of terrain recognition and the efficiency of the algorithm are key factors in improving the practicality of classification methods.However, both nonvisual feature-based terrain recognition algorithms and visual feature-based terrain recognition algorithms have their shortcomings.For example, visual feature-based terrain recognition algorithms may be unsuitable for strong lighting conditions, [190] while terrain recognition algorithms based on nonvisual features struggle to differentiate between different terrains that have similar geometric characteristics.The combination of the two methods is a trend in future research on terrain recognition methods. [202] Key Technologies of Quadruped Robots

Structural Design of Quadruped Robots
The structural design of a quadruped robot plays a crucial role in its locomotion capabilities and consists primarily of the body, legs, and feet.The main objective of torso design is to maximize the flexibility of the quadruped robot while ensuring controllability.In design of quadruped robot's legs, joint movements are simulated by incorporating DoFs.Generally, quadruped robots have three DoFs in each leg and two DoFs in their hip joints.These hip joints are used to achieve lateral crossing and forward/backward swinging of the robot. [4]The circular foot design is the most prevalent foot design among quadruped robots. [203]This design allows the robot's feet to make contact with the ground in all directions, providing remarkable environmental adaptability.However, compared to real quadrupedal animals, the current structure of quadruped robots still has a significant gap.Real quadruped animals possess bones and muscles, granting them much greater flexible than biomimetic quadruped robots.Their feet have irregular shapes, like claws and pads, which provide strong gripping when in contact with the ground.Additionally, real quadruped animals demonstrate exceptional balance capabilities and exhibit low energy consumption during movement.Therefore, efforts in structural innovation and the utilization of novel materials are of great significance in enhancing robot flexibility, locomotion capabilities, and environmental adaptability. [36]

Motion Control of Quadruped Robots
Motion control is a critical technology for quadruped robots as it directly influences their stability, speed, and agility.In motion control for quadruped robots, gait planning is used to determine the motion trajectory and posture of each leg.Gait planning considers factors such as the morphology and mechanical structure of the quadruped robot, as well as the complexity and uncertainty of the environment. [35]However, the current gait of quadruped robots is not as elegant and natural as that of quadrupedal animals.The goal of motion control in quadruped robots is to achieve dynamic stability and robustness by utilizing control algorithms to regulate the robot's position and joint torques. [204]In the development of quadruped robots for complex environments, it is essential to employ controllers that ensure accurate tracking performance and adaptability to the environment.Inaccurate, non-real-time, or poorly robust control can lead to unstable states of the robot or hinder normal movement.For high-speed and high-performance quadruped robots, the computational complexity of control algorithms necessitates further research and improvement.By utilizing highly accurate sensors and advanced computational units, robots can achieve real-time perception of their surrounding environment.Based on the perceived data, intelligent decisions can be made, facilitating higher levels of intelligence and autonomy in the robots.

Autonomous Locomotion of Quadruped Robots
Autonomous locomotion technology is important for achieving intelligence in quadruped robots.It empowers robots to autonomously perceive the environment, plan paths, avoid obstacles, and localize themselves.Path planning and terrain recognition are the core components of autonomous locomotion technology for quadruped robots. [205]By utilizing terrain recognition technology and path planning algorithms, an optimal route can be generated based on information such as the starting point, destination, and obstacles.This path can then be transformed into a motion trajectory that the robot can follow to achieve autonomous locomotion.At present, quadruped robots generally lack sufficient intelligence and autonomy, relying on operators for control. [206]However, to accomplish complex tasks, quadruped robots must possess the ability to interact with their environment.With the advancements in artificial neural networks [202] and RL, [207] these technologies can be applied to quadruped robots to enhance their adaptability in unstructured environments.This enables quadruped robots to autonomously plan their behavior based on task objectives and environmental conditions, allowing them to efficiently and accurately complete a wide range of tasks.In the future, quadruped robots are expected to become more autonomous and intelligent.

Conclusion
This article focuses on cutting-edge research in the field of quadruped robots, paying attention to three critical areas: structural design, motion control, and autonomous movement.Quadruped robots, as advanced autonomous intelligent systems, have garnered widespread interest due to their potential in autonomous navigation, task execution, and environmental adaptability.The objective of this article is to conduct an in-depth study and summarize the currently available structural forms of quadruped robots, as well as to explore methods of motion control, path planning techniques, and terrain recognition technologies that propel their intelligence and high degree of autonomy.
With respect to the structural design of quadruped robots, current research has focused on enhancing their flexibility and adaptability, such as through the addition of ankles, [208] tails, [209] heads, [13] etc.There is also a growing trend toward equipping quadruped robots with reconfigurable [210,211] and multimodal [207,212] locomotion capabilities to adapt to various environments and perform multiple tasks.In the future, quadruped robots could adopt a modular design approach, allowing components such as legs, bodies, and heads to be interchangeable and reconfigurable as needed, thereby facilitating the reconfigurability and expandability of the robot.A modular design approach enhances the robot's flexibility and universality, while reducing costs and maintenance complexity.
In the domain of motion control, research on quadruped robots has made significant strides.By integrating advanced sensing technologies with real-time control algorithms, robots can adapt to unstable or complex terrains better, maintain balance, and achieve more natural and efficient gaits.Future research could further explore cooperative control technologies for quadruped robots, including integration with robotic arms to expand operational capabilities such as grasping, carrying, and assembling.Collaboration with unmanned aerial vehicles could enhance task efficiency and safety, offering ground-air synergy.Such integration is particularly impactful in specialized scenarios like disaster response, military reconnaissance, and environmental monitoring.Additionally, incorporating artificial skin could augment tactile and sensory abilities, such as touch sensing, temperature perception, and pain detection.

Figure 1 .
Figure 1.Structure of a quadruped robot.

Figure 5 .
Figure 5.The types of body: a) rigid torso; b) torso with a revolute joint; c) torso with spring; and d) flexible material torso.

Figure 11 .
Figure 11.Structure of a quadruped robot.

Figure 12 .
Figure 12.Common control methods and flowcharts.

Figure 16 .
Figure 16.Flowchart of the terrain classification process using structured features.

Figure 17 .
Figure 17.Flowchart of deep learning terrain classification.

Qinghua
Liu received his M.S. degree from the Department of Mechanical and Materials Engineering, North China University of Technology, Beijing, China.Currently he is a doctor at the School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China.His research interests focus on intelligent robot system and intelligent manufacturing.

Table 2 .
Performance comparison of electrically driven quadruped robots.

Table 3 .
Standard path planning algorithms and their advantages and disadvantages.