MOTION PLANNING FOR MOBILE MANIPULATORS WITH A NONHOLONOMIC CONSTRAINT USING THE FSP (FULL SPACE PARAMETERIZATION) METHOD

The efficient utilization of the motion capabilities of mobile manipul ators, i.e., manipulators mounted on mobile platforms, requires the re solution of the kinematically redundant system formed by the addition of the degrees of freedom (DOF) of the platform to those of the manipu lator. At the velocity level, the linearized Jacobian equation for suc h a redundant system represents an underspecified system of algebraic equations, which can be subject to a varying set of contraints such as a non-holonomic constraint on the platform motion, obstacles in the w orkspace, and various limits on the joint motions. A method, which we named the Full Space Parameterization (FSP), has recently been develop ed to resolve such underspecified systems with constraints that may va ry in time and in number during a single trajectory. In this article, we first review the principles of the FSP and give analytical solution s for constrained motion cases with a general optimization criterion f or resolving the redundancy. We then focus on the solutions to (1) the problem introduced by the combined use of prismatic and revolute join ts (a common occurrence in practical mobile manipulators), which makes the dimensions of the joint displacement vector components non-homoge neous, and (2) the treatment of a non-holonomic constraint on the plat form motion. Sample implementations on several large-payload mobile ma nipulators with up to 11 DOF are discussed. Comparative trajectories i nvolving combined motions of the platform and manipulator for problems with obstacle and joint limit constraints, and with nonholonomic cont raints on the platform motions, are presented to illustrate the use an d efficiency of the FSP approach in complex motion planning problems. (C) 1996 John Wiley & Sons, Inc.