Accession Number : ADA323814

Title :   Control Uncertainty in Fine Motion Planning.

Descriptive Note : Doctor thesis,

Corporate Author : STANFORD UNIV CA DEPT OF COMPUTER SCIENCE

Personal Author(s) : Shekhar, Shashank

PDF Url : ADA323814

Report Date : JUN 1993

Pagination or Media Count : 111

Abstract : The goal of Fine Motion Planning is to generate provable robot programs in the presence of control, sensing, and model uncertainty. In particular, fine motion planning includes part mating sequences that require force control. We first present a new result in the formalism of fine motion planning that, embedding the knowledge of the termination condition in the construction of preimage, augments the size of preimage. We, then, present new results on the characterization of control uncertainty. Define forward projection of a state to be the union of all possible states such that there exists a trajectory connecting the two states for controls that remain within a given model of control uncertainty. Computing forward projection is a problem in differential inclusion. Previous work in this area by Blagodat-skikh and Filippov (1986) allows one to compute the boundary of attainable set that are states reachable at a given instant. We consider computing the boundary of forward and backprojection on smooth sets of an arbitrary but autonomous control scheme. The control equations include state-dependent differential equations governing general rigid body motion, in contact with other rigid bodies or moving freely. We characterize the boundary as an integral manifold of a Hamilton-Jacobi equation (Butkovskii, 1982). This integral manifold is a solution of a system of 2n ordinary differential equations where n is the dimension of the state space. We give conditions for the existence and uniqueness of the local boundary of the forward and backprojection of a state described by a regular closed subset. The Global boundary may have several connected components. Some of these are subsets of the boundary of perturbations of the unstable and the stable manifold of saddle type singularity.

Descriptors :   *ROBOTICS, *CONTROL THEORY, UNCERTAINTY, ADAPTIVE CONTROL SYSTEMS, ROBOTS, THESES, NONLINEAR SYSTEMS, MOBILE, BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS, PERTURBATIONS, SYSTEMS ANALYSIS, AUTONOMOUS NAVIGATION, SET THEORY, HAMILTONIAN FUNCTIONS.

Subject Categories : Cybernetics

Distribution Statement : APPROVED FOR PUBLIC RELEASE