Motion planning in velocity affine mechanical systems

Abstract

We address the motion planning problem in specific mechanical systems whose linear and angular velocities depend affinely on control. The configuration space of these systems encompasses the rotation group, and the motion planning involves the system orientation. Derivation of the motion planning algorithm for velocity affine systems has been inspired by the continuation method. Performance of this algorithm is illustrated with examples of the kinematics of a serial nonholonomic manipulator, the plate-ball kinematics and the attitude control of a rigid body.

Keywords:

• mechanical system
• position
• orientation
• motion planning
• continuation method

Acknowledgements

This research was supported by a statutory grant from Wrocław University of Technology. The authors want to thank anonymous reviewers for suggesting valuable improvements of presentation of this article. The authors owe the courtesy of Prof F. Thomas and Dr A. Mazur in Figures 1 and 2 presenting the parallel nonholonomic manipulator and the planar nonholonomic manipulator.