Path planning for simple wheeled robots: sub-Riemannian and elastic curves on SE(2)

Craig David Maclean, James Biggs

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper presents a motion planning method for a simple wheeled robot in two cases: (i) where translational and rotational speeds are arbitrary and (ii) where the robot is constrained to move forwards at unit speed. The motions are generated by formulating a constrained optimal control problem on the Special Euclidean group SE(2). An application of Pontryagin’s maximum principle for arbitrary speeds yields an optimal Hamiltonian which is completely integrable in terms of Jacobi elliptic functions. In the unit speed case, the rotational velocity is described in terms of elliptic integrals and the expression for the position reduced to quadratures. Reachable sets are defined in the arbitrary speed case and a numerical plot of the time-limited reachable sets presented for the unit speed case. The resulting analytical functions for the position and orientation of the robot can be parametrically optimised to match prescribed target states
within the reachable sets. The method is shown to be easily adapted to obstacle avoidance for static obstacles in a known environment.
LanguageEnglish
Pages1285-1297
Number of pages18
JournalRobotica
Volume31
Issue number08
Early online date7 Jun 2013
DOIs
Publication statusPublished - Dec 2013

Fingerprint

Path Planning
Motion planning
Robot
Robots
Reachable Set
Curve
Unit
Arbitrary
Jacobi Elliptic Function
Hamiltonians
Elliptic integral
Maximum principle
Constrained Control
Obstacle Avoidance
Motion Planning
Collision avoidance
Maximum Principle
Quadrature
Optimal Control Problem
Euclidean

Keywords

  • robot motion planning
  • sub-Riemannian curves
  • elastic curves
  • parametrical optimisation

Cite this

Maclean, Craig David ; Biggs, James. / Path planning for simple wheeled robots : sub-Riemannian and elastic curves on SE(2). In: Robotica. 2013 ; Vol. 31, No. 08. pp. 1285-1297.
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Path planning for simple wheeled robots : sub-Riemannian and elastic curves on SE(2). / Maclean, Craig David; Biggs, James.

In: Robotica, Vol. 31, No. 08, 12.2013, p. 1285-1297.

Research output: Contribution to journalArticle

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