Analysis of the Weighting Matrix for Load Distribution Using Weighted Pseudoinverse in a Redundantly Actuated System

Redundant actuation indicates a situation when there are more actuators than a system’s mobility. A redundant actuated system has many strengths, such as better performance than a non-redundant system, avoiding singularity, reducing impact force using active stiffness control and fault tolerance. However, there are some issues on economic efficiency and minimization of a system, because redundant actuation can use more actuators than non-redundant actuation. Also, in a redundant actuation system, the actuator torque does not have one solution, but rather there are infinite torque sets even though a robot works on the same task. Therefore, it is very important to select a torque distribution method that is suitable for the objectives of the robot. In this paper, we used the weighted pseudoinverse matrix for torque distribution. This method is applied to a five bar link system and the influence of the weighting variables is analyzed. By adjusting the weighting values, we can find the relation between the actuator input and the weighting value and obtain various torque sets in real time. In other words, we find how each actuator torque changes according to the variation of each weighting value and how much the maximum torque reduce for the suggested weighting matrices.