Download or read book Numerical Computation of Optimal Navigation Functions for Nonholonomic Planning written by Prashanth Kumar Konkimalla and published by . This book was released on 2000 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many robotic tasks require a motion strategy that commands a robot to move in a cluttered environment, satisfy differential (nonholonomic) motion constraints, and overcome uncertainties. We present a fast, numerical approach to computing optimal feed-back motion strategies for a nonholonomic robot in a cluttered environment. Although many techniques exist to compute navigation functions that can incorporate feedback, none of these methods is directly able to determine optimal strategies for general non-holonomic systems. Our approach builds on previous techniques in numerical optimal control, and on other previous efforts in developing algorithms that compute feedback strategies for problems that involve nondeterministic and stochastic uncertainties in prediction. The proposed approach efficiently computes an optimal navigation function for nonholonomic systems by exploiting two ideas: 1) the principle of Dijkstra's algorithm can be generalized to continuous configuration spaces and nonholonomic systems, and 2) a simplicial mesh representation can be used to reduce the complexity of numerical interpolation. The approach has been implemented, and we have used it to efficiently generate results for five different problems: 1) planning for an ideal car-like robot, 2) planning for a box-pushing robot, 3) planning for a car-like robot with prediction uncertainties, 4) planning for a car-like robot with sensing errors, and 5) a kinodynamic planning problem for a car-like robot.