2. Path Planning in Two Dimensions

  1. Antonios Tsourdos,
  2. Brian White and
  3. Madhavan Shanmugavel

Published Online: 8 NOV 2010

DOI: 10.1002/9780470974636.ch2

Cooperative Path Planning of Unmanned Aerial Vehicles

Cooperative Path Planning of Unmanned Aerial Vehicles

How to Cite

Tsourdos, A., White, B. and Shanmugavel, M. (2010) Path Planning in Two Dimensions, in Cooperative Path Planning of Unmanned Aerial Vehicles, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470974636.ch2

Author Information

  1. Cranfield Defence and Security, Cranfield University, UK

Publication History

  1. Published Online: 8 NOV 2010
  2. Published Print: 19 NOV 2010

ISBN Information

Print ISBN: 9780470741290

Online ISBN: 9780470974636



  • path planning in two dimensions - limited curvature or turn radius constraints;
  • algorithms for design of shortest routes - computational geometry, operations research and logistics;
  • shortest route in graph - the travelling salesman problem (TSP) and the Chinese postman problem (CPP);
  • Dubins paths with constant-curvature arcs - clothoid paths and Pythagorean hodograph (PH) paths;
  • flyable path design - polynomial curves, lines and arcs computing paths;
  • block diagram of path planner - generating shortest flyable paths;
  • Dubins path design - and principles of differential geometry;
  • Dubins and clothoid, two path formats - from arc and straight-line segments;
  • Pythagorean condition, sum of squares of sides of right-angled triangle - equal to square of its hypotenuse;
  • flyable path design - using 2D PH curve


This chapter contains sections titled:

  • Dubins Paths

  • Designing Dubins Paths using Analytical Geometry

  • Existence of Dubins Paths

  • Length of Dubins Path

  • Design of Dubins Paths using Principles of Differential Geometry

  • Paths of Continuous Curvature

  • Producing Flyable Clothoid Paths

  • Producing Flyable Pythagorean Hodograph Paths (2D)

  • References