Planning Motions for Robotic Systems Subject to Differential Constraints

Abstract

Abstract. We consider the problem of planning point-to-point motion for general robotic systems subject to non-integrable differential constraints. The constraints may be of first order (on velocities) or of second order (on accelerations). Various nonlinear control techniques, including nilpotent approximations, iterative steering, and dynamic feedback linearization, are illustrated with the aid of four case studies: the plate-ball manipulation system, the general two-trailer mobile robot, a two-link robot with flexible forearm, and a planar robot with two passive joints. The first two case studies are non-flat nonholonomic kinematic systems, while the last two are flat underactuated dynamic systems.

Reaching movements in dynamic environments: how do we move flexible objects?

“…The general formula (50) can be proved by the principle of mathematical induction. It holds true for .…”

“…Higher derivatives are used when the motion smoothness is important. For example, the solutions for and were used in, respectively, [50] and [31], to generate reference signals for robots with flexible links.…”