In Situ Reconfigurable Continuum Robot with Varying Curvature Enabled by Programmable Tensegrity Building Blocks

Reconfigurable continuum robots exhibit programmable interaction capability, enabling them to cope with challenges poorly addressed by conventional rigid robots. However, the regulation of the module type and/or sequence may result in time‐consuming and labor‐intensive problems. Therefore, in situ reconfiguration schemes are required to develop in a simple yet robust solution for continuum robot design. Herein, inspired by the structure characteristics of the seahorse tail, an original template based on a tensegrity building block (TBB) for creating an in situ reconfigurable continuum robotic paradigm is proposed. As the length of the stretchable struts in the TBB could be programmed, five typical homologous types from the template are derived. Then, ten TBBs into a continuum robot are assembled and the multi‐body dynamic framework is employed to develop a mechanical model for predicting the profile after deformation. Theoretical predictions demonstrate that the robotic shape can be customized in situ by switching the type of TBBs, without disassembling the robot. Furthermore, the tailored continuum robotic configurations are applied to conformally interact with the varying‐curvature objects. The experimental results suggest that the proposed programmable template offers a facile and rapid reconfiguration scheme for the continuum robots, which greatly improves the robotic interaction capability.

Reconfigurable continuum robots exhibit programmable interaction capability, enabling them to cope with challenges poorly addressed by conventional rigid robots. However, the regulation of the module type and/or sequence may result in time-consuming and labor-intensive problems. Therefore, in situ reconfiguration schemes are required to develop in a simple yet robust solution for continuum robot design. Herein, inspired by the structure characteristics of the seahorse tail, an original template based on a tensegrity building block (TBB) for creating an in situ reconfigurable continuum robotic paradigm is proposed. As the length of the stretchable struts in the TBB could be programmed, five typical homologous types from the template are derived. Then, ten TBBs into a continuum robot are assembled and the multi-body dynamic framework is employed to develop a mechanical model for predicting the profile after deformation. Theoretical predictions demonstrate that the robotic shape can be customized in situ by switching the type of TBBs, without disassembling the robot. Furthermore, the tailored continuum robotic configurations are applied to conformally interact with the varying-curvature objects. The experimental results suggest that the proposed programmable template offers a facile and rapid reconfiguration scheme for the continuum robots, which greatly improves the robotic interaction capability.
utilization of elastic materials, this robot is able to exhibit a compliant circle-shaped profile while actuating cables. [12] However, as these cable-driven continuum robots always demonstrate relatively homogeneous deformation behaviors, the invariant robotic curvature may result in mismatching during the interaction, hindering the highly efficient interaction in varying scenarios. [13] To enhance the interaction efficiency in unstructured environments, programming the robotic curvature has become a promising solution for continuum robots. [14] These tailored configurations are generally constructed by combining graduated material properties and/or structures. [15] For example, Zhang et al. developed a bio-inspired continuum robot by integrating springs with varying stiffness into a modular tensegrity structure. [16] As the structural stiffness significantly varies between the modules, the robotic curvature can be programmed to conformally interact with varying environments. In addition, Ke et al. presented a programmable robotic paradigm that was constructed by discretely presetting graded structural properties to enhance the interaction efficiency. [13] However, these configurations are of great difficulty to be changed ad tunned once generated. [17] Hence, each continuum robot has its unique shape and can perform specific tasks only. [18] Introducing a simple reconstruction strategy into continuum robotic design can help to overcome this challenge. [19] Reconfigurable robotic profile enables continuum robots to adjust their physical properties depending on the requirements of each application. [20] For example, Santoso et al. proposed a modular continuum robot that is capable of both deployable extension and bending deformation achieved through an origami-inspired design. [21] This continuum robot can be scaled up by optionally adding robotic modules on-demand because each module can be controlled independently, without modification to the system architecture, demonstrating a more robust interaction capability to adapt to varying scenarios. However, the embedded actuators installed in each module would result in uneven mass distribution, which may reduce the control accuracy. [22] Therefore, continuum robots are often equipped with a remotely centralized actuation system. [23] An example of this was underactuated modular continuum robot developed by Bishop et al [24] . As the configuration is constructed by an identical module, the robot can merely reconfigure a limited number of profiles, which may hinder the continuum robot to interact with complex and changeable scenarios. To overcome this limitation, Atia et al. proposed a design method to create diverse building blocks for enriching the robotic module type. [6] Therefore, the robotic configuration can be preprogrammed on-demand by assembling varying building blocks. These building blocks can also be disassembled and reconfigured to facilitate the reconfigurability from one assembled robot to another. However, this reconfigurable route may result in time-consuming and labor-intensive problems during regulating the type/sequence of the modules.
Herein, inspired by the structural characteristics of the seahorse tail, we proposed an original template for constructing an in situ reconfigurable continuum robot based on a tensegrity building block (TBB) which consists of transverse, longitudinal, and stretchable struts ( Figure 1). The components of the TBB are fabricated by 3D printing, which not only simplifies the robotic production but also reduces the costs, facilitating future community uptakes. By programming the length of the stretchable struts, we derived five typical homologous types from the TBB template. To elaborate on the effects of this programmable TBB for enhancing the interaction capability of the continuum robot, we first assembled ten TBBs into a continuum robot and formulated a mechanical model using multi-body dynamic framework to predict the profiles after deformation. Theoretical predictions demonstrate that our continuum robotic profile can be programmed in situ by switching the types of the TBBs, without disassembling the continuum robot. Then, we utilized the tailored continuum robotic configurations to interact with the varying-curvature objects conformally. The experimental results suggest that our proposed programmable TBB offers a facile and rapid reconstruction paradigm for the development of continuum robots, which can improve the robotic interaction capability.

Structural Characteristics of Seahorse Tail
A seahorse is featured by its unique morphology and special swimming style, enabling it to become one of the most remarkable sea creatures ( Figure 2A). [25] We focused on the seahorse tail because this agile appendage enables the slow-moving seahorse to survive in complex marine environments. The tail is composed of several subdermal bony plates arranged in articulated ring-like segments. [26] By measuring the dimension of the segments, we assumed that these structurally analogous segments might be derived from an identical structural template by programming the geometrical parameters ( Figure S1, Supporting Information). As the dimension of the segments declines from the base to the tip of the tails, these homologous segments have different inertia moments I y . Assuming the same elasticity modulus E for all the segments, the equivalent bending stiffness K B ¼ EI y of the basal segment is %130.96 times that of the distal one; therefore, the distal end of the tapered tail can curl more easily during grasping ( Figure 2B, Video S1, Supporting Information). [27] This result indicates that programming the dimensions of a defined building block, independent of the material properties, results in varying mechanical properties. This understanding can inspire a paradigm for the development of programmable building blocks for in situ reconfigurable continuum robots.

Bio-Inspired TBB
Inspired by the structural characteristics of the seahorse tail, we proposed a cuboid TBB as a programmable template, as shown in Figure 1. The template with the physical dimensions of length l, width w, and height h contains two square ring-like layers, which are alternately connected by two transverse and two stretchable struts. Four longitudinal struts are divided into two groups to link to the adjacent layers by rotary hinges. In the template, each stretchable strut is composed of an inner rod, an outer rod, and two modulation buttons. As the outer rod is equipped with five assembly positions, the length of the stretchable strut can be modulated as 40, 45, 50, 55, and 60 mm. Hence, the TBB exhibits five typical homologous types by programming the length of the www.advancedsciencenews.com www.advintellsyst.com  www.advancedsciencenews.com www.advintellsyst.com stretchable strut, namely, types 1-5 ( Figure S2, Supporting Information). [28] To distinguish these TBBs easily, we also employed five single-color blocks to describe the typical homologous types, as shown in Figure 1. Then, we fabricated these types by 3D printing and measured the corresponding physical dimensions l-w-h of each type, as shown in Figure 2C (Table S1, Supporting Information). Then, we quantified the equivalent bending stiffness K B of the types and found that the structural stiffness declined with the decrease in the length of the stretchable struts ( Figure 2D). Here, the diverse types of TBB exhibit different trends of stiffness variation with increasing weight, which may be caused by both the strong structural geometric nonlinearity and the difference in the friction force. By comparing the experimental results, the stiffness of the type 1 reaches 0.52 AE 0.09 N mm degree À1 , which is about 3.98 times that of type 5. This result indicates that the mechanical property of our bio-inspired TBB can be programmed by regulating the dimension. Therefore, when continuum robots were constructed by the template, we could regulate the local mechanical property on demand by switching the type of the TBB and accomplish in situ reconstruction for continuum robots.

Continuum Robot with In Situ Reconfigurable Characteristics
We first developed a continuum robotic prototype by assembling ten TBBs, in all of which the initial configurations were set to be type 1, and then used four tension cables (No. 1-4) that passed through the corresponding preexisting holes of each TBB to actuate the robot (Con. 1), as shown in Figure 3A. When the length variation of the cables satisfies the actuation criterion of Δl s ∶Δl r ¼ 5∶1, our continuum robot is able to bend about the Y-axis in the XOZ plane, transforming into a specific curved profile from the initially straight shape ( Figure 3B, Video S2, Supporting Information). Here, we extracted the robotic distal end trajectories from both experimental and predicted configurations. The fine agreement between the scattered points and the colored lines indicates that the predicted results match well with the experimental law; therefore, we concluded that the mechanical model could predict the motion of the robot accurately. Then, we compared the bending curvature of the TBBs and discovered that these TBBs exhibited an approximately equal curvature that matched the bending stiffness, as shown in Figure 3C. For example, when both cables 1 and 2 are pulled by 150 mm, the bending curvature measured from experiments is 7.74 AE 0.48 m À1 , which is only 2.17% larger than the 7.47 m À1 obtained from the simulation, respectively. This small difference may be ascribed to insufficient pretension in cables, and the friction between cables and/or struts is neglected in the modeling.
To elaborate on the in situ reconfigurable concept of the continuum robot, we switched the TBBs of type 1 to types 2, 3, 4, and 5, respectively, forming four other configurations with constant crosssections, marked as Cons. 2, 3, 4, and 5, as shown in Figure 4A. As the height of the types varies, the robotic length L can be programmed by regulating the types of the TBB, resulting in the configurations demonstrating diverse robotic profiles under the identical actuation criterion. The distal end trajectories of these configurations indicate that the prototype with programmable robotic length can interact with objects located within a range of distances ( Figure 4B). For example, the robotic length of the Con. 5 reaches 0.60 m, 1.50 times that of the Con. 1, enabling it to be prone to interact with remote objects. Moreover, this enables the Con. 5 to develop a large enveloped area of 0.03 m 2 during grasping, which can improve the grasping stability. Then, we calculated the bending angles θ of these configurations and found that the bending angles rise linearly with the robotic lengths, following θ ¼ 424.91L À 6.21 ( Figure 4C). According to the curvature formula ρ j ¼ θ j =L j ( j = 1, 2, …, 5), the bending curvatures of the configurations constructed by www.advancedsciencenews.com www.advintellsyst.com the identical type of TBBs are approximately consistent ( Figure 4D). This result means that the curvature of each TBB in the configurations is approximately uniform after deformation when the robot is constructed using the identical TBB types, which may impede the application potentials of the robot to conformally interact with objects with complicated varying curvatures.

Continuum Robot Composed of Diverse Homologous TBBs
To enhance the interaction capability of the continuum robot to environments with varying curvatures, the robot with a tapered profile may be an effective scheme. [29] Here, we programmed the type of the TBBs to develop a tapered robot. Specifically, we used the type 1 as the first TBB of the robot and then replaced the TBBs marked by the even numbers with types 1-5 in sequence, as shown in Figure 5A. Then, we introduced four transitional TBBs, which composed of stretchable struts with different lengths, to connect the aforementioned TBBs marked by the even numbers. These transitional TBBs have been marked as diverse gradient color blocks according to the type of adjacent typical homologous types. For example, the gradient color of TBB 3 is transited from blue to purple because it is used to connect types 1 and 2. Therefore, a new continuum robotic configuration can be reconstructed, namely, Con. 6, in which the heights of the transitional TBBs consecutively increase, as shown in Figure 5B. Then, we employed the identical actuation criterion to deform the Con. 6 and discovered that both the robotic length and bending angle of the Con. 6 are very similar to those of the Con. 3 ( Figure 5C). In contrast to the Con. 3, each TBB of the Con. 6 exhibits diverse bending curvatures because of regulating the types of the TBBs, which is expected to enable this configuration to interact with varying-curvature objects, as shown in Figure 5D. Specifically, the transitional TBBs exhibit greater curvatures, resulting in a zig-zag curvature distribution. To analyze the causes of this distribution, we measured the bending stiffness K B of the transitional TBBs ( Figure 5E). For example, the bending stiffness of TBB 3 is 0.31 AE 0.03 N·mm/deg, which is merely 59.62% and 72.09% that of the adjacent TBBs. As the bending stiffness of transitional TBBs is smaller than that of the adjacent TBBs, the local curvature of the Con. 6 varies and thus yields a zig-zag curvature distribution. Based on the theoretical analysis, we considered that the curvature of the robotic configuration could be regulated by combining the diverse TBBs. Hence, to further enhance the ability of the robot to interact with complicated objects, programming the distribution of the TBBs to regulate local curvature may be a feasible strategy.

Continuum Robot with Programmed Local Curvature
Taking a transitional TBB as an example, in which stretchable struts were 40 and 60 mm, we tested the strategy of regulating the local curvature of the continuum robot. First, we replaced the basal, middle, and distal locations of the Con. 1 with the two identical transitional TBBs connected through forward connection, by www.advancedsciencenews.com www.advintellsyst.com which we formed three additional configurations, namely, Cons. 7, 8, and 9 ( Figure 6A). By this, we could reach a local curvature of 17.95 AE 0.02 m À1 , 2.55 times the curvature of TBBs that have not been tuned. This indicates that the transitional TBBs can regulate the local curvature of the robot. Although the bending angles of these configurations are approximately equal, the robot is able to conformally grasp and interact with varying-curvature objects because of the difference in the replacement position, such as the water ladle, the taro, and the fist, exhibiting greater interaction capability. Similarly, we could also connect the transitional TBBs through reverse connection and employed it to replace the basal, middle, and distal locations of the Con. 5, forming Cons. 10, 11, and 12, as shown in Figure 6B. Here, we could program the robot to adapt to the objects with different orientations. For example, the continuum robot is able to achieve conformal grasping of an apple in the orientation 1 with the Con. 10. When the apple rotated to the orientations 2 or 3, we could reconfigure the robotic configuration into the Cons. 11 or 12 to effectively grasp the apple. Therefore, we considered that reconstructing the robotic configuration in situ is a promising strategy for enhancing the interaction capability.

Application Demonstration
To evaluate the performance of the concept of in situ reconstruction, we fabricated a ten-TBB continuum robot of the Con. 1 and mounted the first TBB on a rigid robotic arm (SJ 602-A, Anno, China), as shown in Figure 7A. The continuum robot is actuated by four cables pulled by two motors (DS3135, DS-Servo, China), all of which are coordinated by a microcontroller (Uno R3, Arduino, Italy), as shown in Figure 7B. To quantify the grasping performance of the continuum robot, we first prepared five foam balls with diverse diameters, ranging from 10 to 20 cm, to represent the objects with varying physical dimensions. Then, the continuum robot is reconstructed to the corresponding configurations to conformally interact with these foam balls ( Figure 7C). As shown in Figure S5, Supporting Information, the close fitting between the robotic profile and the balls indicates that the environmental adaptability of our continuum robot can be improved by reconstructing the robotic configuration (Video S3, Supporting Information). Then, we assumed that a potential application for our robotic system could be intelligent agriculture scenarios, owing to its high adaptability in interacting with objects in various shapes and dimensions. Specifically, harvesting robots recently have been extensively employed to reduce the working intensity of farmers. Previous farmers usually use universal agricultural machinery to collect varying agricultural products, reducing the cost of purchasing devices, because often more than one agricultural product is required to be planted in the same farm over a year. [30] However, conventional machinery with fixed gripping apparatus cannot conformally interact with diverse agricultural products and therefore can damage them caused by excessive stress. It is estimated that the economic losses caused by mechanical damage account for 30-40% of the total agricultural output worldwide. [31] Therefore, a reconfigurable continuum robot that can interact with the agricultural products with diverse geometrical profiles without causing a damage is an urgent requirement. Here, we demonstrated our continuum robot to grasp fruit and vegetable products (FVPs), such as apples, www.advancedsciencenews.com www.advintellsyst.com pineapples, mangos, pitayas, and peppers, as shown in Figure 7D (Video S4, Supporting Information). To quantify the contact force F on the surface of the FVPs during grasping, we installed a force sensor on the continuum robot, and the real-time contact force is shown in Figure 7E. Then, we evaluated the corresponding maximum contact stress σ max when the FVPs were grasped, as shown in Figure 7F. The maximum contact stress between the continuum robot and the apple is measured as 0.37 AE 0.04 MPa. Because of the conformal interaction between the continuum robot and the FVPs, the maximum contact stress in general ranges from 0.35 to 0.60 MPa, which is about an order of magnitude below the yield stress (%5 MPa) of the ripe FVPs [32] . Therefore, this continuum robot with conformal interaction capability can assist the farmers in achieving non-destructive collection/transportation of the FVPs. Moreover, we summarized the existing cable-driven continuum robots by comparing the design scheme, actuation system layout, curvature programmability, and in situ reconfigurability, as provided in Table 1, to further demonstrate the advantages of our robotic paradigm.

Conclusion
In this article, inspired by the structural characteristics of seahorse tails, we created an original structural template based on a programmable TBB to construct a continuum robotic paradigm. This enables us to reconstruct robotic configurations in situ to interact with varying-curvature objects, without disassembling the robot. Taking a ten-TBB continuum robot as an example, both theoretical and experimental results suggest that our proposed programmable template offers a facile and rapid reconstruction scheme of the continuum robots, which greatly improves the robotic interaction capability and overcomes time-consuming and labor-intensive limitations for programming the module type and/or arrangement sequence. Future Figure 6. Programming the local curvature by introducing varying TBBs into the continuum robot. A) Regulating two adjacent TBBs at the basal, middle, or distal positions in Con. 1 with two forward connection TBBs for reconstructing the continuum robot. The reconfigurable configurations can be employed to interaction with varying objects, such as the water ladle, the taro, and the fist. B) Regulating two adjacent TBBs at the basal, middle, or distal positions in Con. 5 with two reverse connection TBBs for reconstructing the continuum robot. The reconfigurable configurations can be employed to interact with the object with varying orientations.
www.advancedsciencenews.com www.advintellsyst.com studies should develop strategies that can enhance the ability of continuum robots in interacting with varying-curvature objects in real time by adding an active modulation system, for instance, by using the advanced materials to regulate the length of the stretchable struts. [33][34][35]

Experimental Section
Mechanical Model: To predict the configuration of the continuum robot after deformation, we employed the multi-body dynamic framework to formulate a mechanical model. [36] Then, three assumptions were made for the components throughout the modeling to reduce the computational  complexity in the simulation. 1) The struts were considered as rigid bodies with uniform crosssections along their longitudinal axes. 2) The cables were merely subject to tension, each segment of which remained straight.
3) The friction force between the struts and cables was negligible.
Based on these assumptions, we used generalized coordinates q i ¼ ½R T i , Θ T i T to describe the ith strut, in which R i and Θ i denote the corresponding position vector and the orientation coordinate, respectively (Note S1, Supporting Information). To reduce the dimension of generalized coordinates, we adopted spring damping actuators to replace the function of the cables. According to the linear elastic constitutive relation, we calculated the elastic forces of the cables and formulated the internal forces in the system as Qðq, tÞ. By employing the constraint equations Φðq, tÞ, these components that contain n t transverse struts, n l longitudinal struts, n s stretchable struts, and n c tension cables can be assembled. Here, the constraint force Φ T q λ was introduced into the robotic system, in which Φ q and λ represent the Jacobian matrix and Lagrange multiples of the constraint equations, respectively. Then, we applied the actuation criterion f ðq, Δl, tÞ to actuate the robot, in which Δl represents the length variation of the cables being pulled. Therefore, the general governing equations can be written as Equation (1) (Note S1, Supporting Information) Calculation of the Bending Curvature: To measure the bending curvature ρ, we first chose several points in the TBB with the coordinates of P i ¼ ðx i , y i , z i Þ. [37] As these points were assumed to lie on the circumference of a fitting circle in XOZ plane with yet unknown radius r and the center point P c ¼ ðx c , y c , z c Þ, the circle equation can be written in the general form as Equation (2). Here, we introduced the variable p ¼ ½a, b, c T to formulate the equation in another form as Equation (3) ðx i À x c Þ 2 þ ðz i À z c Þ 2 ¼ r 2 (2) When the number of the points was greater than 3, Equation (3) transforms to an equation of an overdetermined system, expressed as Equation (4). We solved this equation with help of a pseudoinverse, so the variables of the circle equation, namely, a, b, and c, can be calculated as p ¼ A þ B, in which A þ ¼ ðA T AÞ À1 A T . Then, the curvature of the TBB can be expressed as ρ ¼ 1=r Measurement of the Equivalent Bending Stiffness: We built an experimental setup to measure the equivalent bending stiffness of the TBBs [13] . Then, we installed a TBB on a supporting structure and applied the weight with a mass of m (m = 10 g, 20 g, …, 40 g) to the TBB. Therefore, the bending angle θ was generated by the bending moment T ¼ mgw=2. According to the definition of the bending stiffness K B ¼ T=θ, we could measure the bending stiffness of the TBBs by K B ¼ mgw=2θ.
Measurement of the Contact Stress: To evaluate the extrusion stress of the FVPs during grasping, we employed a pressure sensor (RDF-6, RuiLide, China) with a diameter of d ¼ 2mm to measure the force F between the continuum robot and the corresponding FVPs. Here, we installed the pressure sensor on the transverse strut of the TBB 5 and calculated the contact stress σ according to the formula σ ¼ 4F πd 2 .

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.