Optimal Motion Plans for Cooperating Nonholonomic Mobile Manipulators in an Environment with Obstacles

We address the motion planning problem for multiple cooperating manipulators on nonholonomic carts. The mobile manipulators possess the ability to manipulate and transport objects while holding them in a stable grasp. We present a general approach that allows the generation of optimal trajectories and actuator inputs for any given maneuver in the presence of obstacles. We assume a meaningful integral cost function and formulate the planning problem as a problem in the calculus of variations. Geometric constraints such as joint limits and obstacles, kinematic constraints such as nonholonomic velocity constraints and constraints on the turning radii of the mobile carts can be easily incorporated into the planning scheme. Numerical simulations for several maneuvers in cluttered environments including abrupt turns, parallel parking and changes in formation from \march abreast" to \march in a single le" are computed. Experimental results with open-loop control are presented for several motion plans.