By Topic

A Geometric Algorithm to Compute Time-Optimal Trajectories for a Bidirectional Steered Robot

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Huifang Wang ; Interdepartmental Res. Center Enrico Piaggio, Univ. of Pisa, Pisa ; Yangzhou Chen ; Philippe Soueres

This paper addresses the problem of determining time-optimal trajectories, between two specified configurations, for a nonholonomic bidirectional steered robot. It presents an original geometric reasoning that is grounded on Pontryagin's maximum principle, which provides analytical solutions of this problem in a visually clear way and allows for an effective algorithm to compute the exact optimal trajectories between two arbitrarily specified configurations. The proposed geometric reasoning is based on the analysis of the switching functions of the optimal controller and the definition of a switching vector from which it is able to determine a unit vector rotating along a unit circle of an appropriate coordinate system. It is shown that simple geometric rules are sufficient to determine all possible rotations of this unit vector, from which the time-optimal trajectories can be uniquely determined. The proposed algorithm, which is based on this geometric reasoning, is guaranteed to be complete and has a low computational cost. Moreover, the proposed geometric representation provides an interesting insight into the structure of this class of nonholonomic systems, thereby offering a model for further studies.

Published in:

IEEE Transactions on Robotics  (Volume:25 ,  Issue: 2 )