Utilizing Kinematic Redundancy in Robotic Systems: Practical Implementations and Fundamental Limitations

The motion of kinematically redundant systems is typically represented by a linear relationship between end effector velocities or acceleration and joint velocities or accelerations. This allows one to formulate the inverse kinematic transformation in a conceptually appealing mathematical form. Unfortunately, such a formulation is usually a poor basis for the implementation of a numerical algorithm and also tends to abstract some of the limitations of a fundamentally nonlinear relationship. This work discusses some of the issues in implementing an efficient and numerically stable algorithm for utilizing redundancy. In addition, some of the limitations in the use of redundancy will be addressed including algorithmic singularities and repeatability.