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Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning

  • L. Gurvits
  • Z. X. Li
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 192)

Abstract

In this paper, we present an algorithm for computing time-periodic feedback solutions for nonholonomic motion planning with collision-avoidance. For a first-order Lie bracket system, we begin by computing a holonomic collision-free path using the potential field method. Then, we compute a nonholonomic path approximating the collision-free path within a predetermined bound. For this we first solve for extended inputs of an extended system using Lie bracket completion vectors. We then use averaging techniques to calculate the asymptotic trajectory of the nonholonomic system under application of a family of highly-oscillatory inputs. Comparing the limiting trajectories with the extended system we obtain a system of nonlinear equations from which the desired admissible control inputs can be solved. For higher-order Lie bracket systems we use multi-scale averaging and apply recursively the algorithm for first-order Lie bracket systems. Based on averaging techniques we also provide error bounds between a nonholonomic system and its averaged system.

Keywords

Control Input Nonholonomic System Completion Matrix Primitive Motion Holonomic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • L. Gurvits
    • 1
  • Z. X. Li
    • 1
  1. 1.Robotics Research Laboratory, Courant Institute of Mathematical SciencesNew York UniversityNY.USA

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