Resolving kinematic redundancy with constraints using the FSP (Full Space Parameterization) approach

A solution method is presented for the motion planning and control of kinematically redundant serial-link manipulators in the presence of motion constraints such as joint limits or obstacles. Given a trajectory for the end-effector, the approach utilizes the recently proposed Full Space Parameterization (FSP) method to generate a parameterized expression for the entire space of solutions of the unconstrained system. At each time step, a constrained optimization technique is then used to analytically find the specific joint motion solution that satisfies the desired task objective and all the constraints active during the time step. The method is applicable to systems operating in a priori known environments or in unknown environments with sensor-based obstacle detection. The derivation of the analytical solution is first presented for a general type of kinematic constraint and is then applied to the problem of motion planning for redundant manipulators with joint limits and obstacle avoidance. Sample results using planar and 3-D manipulators with various degrees of redundancy are presented to illustrate the efficiency and wide applicability of constrained motion planning using the FSP approach