Computational geometry: an introduction
Computational geometry: an introduction
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Retraction: A new approach to motion-planning
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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This paper addresses the methodology for constructing autonomous navigation schemes for which the path and free space corridor along the path are precomputed by means of Voronoi Diagram methods of computational geometry, and in which the position and the velocity of the vehicle are not exactly known during the navigation process. Such navigation schemes are useful in applications such as the routing of maneuvering missiles or robotic vehicles so that they, by traveling through the free space corridor, will avoid obstacles.An autonomous navigation scheme can be implemented by building it around an estimator which during the navigation process, can cyclically estimates not only the position and velocity of the craft but also the errors in the estimates of these two quantities. Kalman filter (KF) and, to a lesser extent, certain nonlinear extensions of KF, provide a formalism for estimating these errors through the estimates of estimation error covariances, also through the estimation of certain errors as a part of the system state vector. In practice, the use of this formalism requires a great deal of caution. During each navigation cycle, the estimates of position and velocity errors, computed in that cycle, can then be used to construct an uncertainty ellipsoid for position, which in turn is used to make a corrective adjustment in the course of the vehicle.