Torque distribution using a weighted pseudoinverse in a redundantly actuated mechanism

Abstract

When mobility, the number of independent variables to describe system motion exactly, is greater than the degree-of-freedom of task space, the system is called a kinematically redundant system. On the other hand, redundant actuation indicates a situation when there are more actuators than a system's mobility. Redundant actuation yields many advantages. First, actuation redundancy can increase the force, velocity and acceleration of an end-effector. Second, if some actuators are out of order, the system can still work well. This fault-tolerant capability is useful for remote control robots in space or nuclear plants. Impulsive force can decrease when modulating arbitrary stiffness without feedback control. The performance of a system can be improved by optimizing redundancy. However, there are some issues of economic efficiency and minimization of a system, because redundant actuation may involve more actuators than non-redundant actuation. In addition, there are infinite torque sets of motors for the same task. We used a weighted pseudoinverse matrix for torque distribution. To reduce the maximum torque, we suggested the use of the minimum norm torque as the weighting values. This method allows for smaller motor capacity, and can contribute to economic efficiency and minimization of a system.