First order controllability and the time optimal control problem for rigid articulated arm robots with friction

Abstract

For non-linear systems, linear in the control, a relationship between the singularity of the time optimal control problem and the differential controllability of the linearized dynamics along a time optimal solution that satisfies the minimum principle is established. Known results concerning the solution of the time optimal control problem for a two link planar articulated arm robot without friction are extended to a general rigid articulated arm robot with friction. Finally, these results are used to prove differential controllability of the linearized dynamics (called first order controllability) along any trajectory of rigid articulated arm robots with friction.