Resolve redundancy with constraints for obstacle and singularity avoidance subgoals

In this work we analyse the general form solution of the Inverse Redundant Kinematics (IRK) problem from a geometric point of view. We propose two new methods, Velocity Projection Constraints Method (VPCM) and On-line Task Modification Method (OTMM), which formulate the obstacle and singularity avoidance as constraints, and will be incorporated in the standard Quadratic Programming (QP) method to resolve the IRK problem. This will avoid the compromise or conflict between weighted optimization criteria for the obstacle and singularity avoidance subgoals, as well as the complicated weight adjustment process. The OTMM is effective not only to redundant manipulators but also to nonredundant manipulators. Numerical simulation examples validate and prove the effectiveness of the proposed methods.