Motion Representations for the Lafferriere-Sussmann Algorithm for Nilpotent Control Systems

Authors:
Ignacy Dulęba;Jacek Jagodziñski
Affiliations:
Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland;Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, ul. Janiszewskiego 11/17, 50-372 Wrocław, Poland
Venue:
International Journal of Applied Mathematics and Computer Science - Issues in Advanced Control and Diagnosis
Year:
2011

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Abstract

In this paper, an extension of the Lafferriere-Sussmann algorithm of motion planning for driftless nilpotent control systems is analyzed. It is aimed at making more numerous admissible representations of motion in the algorithm. The representations allow designing a shape of trajectories joining the initial and final configuration of the motion planning task. This feature is especially important in motion planning in a cluttered environment. Some natural functions are introduced to measure the shape of a trajectory in the configuration space and to evaluate trajectories corresponding to different representations of motion.