Inertially Favorable Trajectories for Robot Motion in Space

Abstract

Robot manipulators generally display non-linear coupled dynamic forces which increase with speed. Efficiencies can be achieved by finding trajectories which take advantage of those inertial forces, and such trajectories are especially significant and appropriate for space applications. This research addresses the problem of planning globally optimal trajectories for manipulators for point-to-point motions in the absence of gravity; the applicable optimality criteria are those which can be measured as the time integral of actuation effort. The equations of motion for a typical robot manipulator show that motions governed purely by inertial effects can be formulated as paths in an inertia manifold. Geodesics in the manifold are discussed physically and mathematically; they have properties making them good first approximations to the optimal solutions. However, geodesics themselves are not easily calculated, so a heuristic method, termed the `CG straight-line path method,' is developed to approximate the geodesic. Trajectories so produced are then used as initial trial trajectories for iterative improvement, producing the optimal trajectories reliably and efficiently.