Null space motion control of a redundant robot arm using matrix augmentation and saturation method

Implementation of a task using a redundant robot arm requires a solution of the inverse differential kinematic problem. Previous algorithms for this problem used various optimized objective functions to limit null space motion. The problem with using an objective function is that the weight needs to be adjusted according to the type of operation. Since the order of the objective function is lower than that of the kinematic constraints using a pseudo inverse, it is hard to predict null space motion for a repetitive task. This type of problem is said to be manually controlled by the objective function. In this study, we introduce a matrix augmentation method so that active control of the null space motion can be implemented. We use the normal vector of the plane defined by the wrist, elbow and shoulder points and the reference vector P_w-P_s as the control criterion, and we define the output angle between these two vectors. In addition, the saturation method is used to prevent violation of the joint angle limit constraints. A simulation and an experiment using a 7-DOF robot arm were carried out to verify the performance of the proposed algorithm. For the simulation, we used Matlab to generate the null space motion, and we used a 7-DOF robot arm developed in our lab to verify the proposed method experimentally. The proposed algorithm allows redundancy resolution, since intuitive and predictable null space motion can be generated according to a desired output angle.