Motion planning for mobile manipulators using the FSP (full space parameterization) approach

The efficient utilization of the motion capabilities of mobile manipulators, i.e., manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (d.o.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. In addition, constraints such as obstacle avoidance or joint limits may appear at any time during the trajectory of the system. 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. In this paper, we review the principles of the FSP and give analytical solutions for the constrained motion case, with a general optimization criterion for resolving the redundancy. We then focus on a solution to the problem introduced by the combined use of prismatic and revolute joints (a common occurrence in practical mobile manipulators) which makes the dimensions of the joint displacement vector components non-homogeneous. Successful applications to the motion planning of several large-payload mobile manipulators with up to 11 d.o.f. are discussed. Sample trajectories involving combined motions of the platform and manipulator under the time-varying occurrence of obstacle and joint limit constraints are presented to illustrate the use and efficiency of the FSP approach in complex motion planning problems