Including a non-holonomic constraint in the FSP (full space parameterization) method for mobile manipulators' motion planning

The efficient utilization of the motion capabilities of mobile manipulators, Le., manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (d.0.f.) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a set of constraints such as obstacles in the workspace and various limits on the joint motions. A method, which we named the FSP (Full Space Parameterization), has recently been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. The application of the method to motion planning problems with obstacle and joint limit avoidance was discussed in some of our previous work. In this paper, we present the treatment in the FSP of a non-holonomic constraint on the platform motion, and give corresponding analytical solutions for resolving the redundancy with a general optimization criterion. Comparative trajectories involving a 10 d.0.f. mobile manipulator testbed moving with and without a non-holonomic constraint for the platform motion, are presented to illustrate the use and efficiency of the FSP approach in motion planning problems for highly kinematically redundant and constrained systems.