Closed-form inverse kinematics solver for reconfigurable robots

A closed-form inverse kinematics solver for non-redundant reconfigurable robots is developed based on the product-of-exponentials (POE) formula. Its novelty lies in the use of POE reduction techniques and subproblems to obtain inverse kinematics solutions of a large number of possible configurations in a systematic and convenient way. Three reduction techniques are introduced to simplify the POE equations. Eleven types of subproblems containing geometric solutions of those simplified equations are identified and solved. Based on the sequence and types of robot joints, the solved sub-problems can be re-used for inverse kinematics of different robot configurations. This solver can cope with closed-form inverse kinematics of all robots with DOFs of 4 or less, 90 percent of the 5-DOF robots and 50 percent of the 6-DOF robots, as well as frequently used industrial robots with both prismatic and revolute joints. The solver is implemented as a C++ software package and is demonstrated through an example.