On Locally Optimal Redundancy Resolution using the Basis of the Null Space

This paper presents two methods for the computation of the null space velocity command in redundant robots. Both these methods resort to the solution of a constrained optimization problem. The first one is a formalization of the traditional Gradient Projection Method (GPM) which guarantees the respect of the joint bounds and a gradual activation/deactivation of the null space command. The second one, called Null Space Basis Optimal Linear Combination Method (NSBM), finds the optimal coefficients of a basis of the null space of the Jacobian, ensuring in turn that the joint bounds are respected and that the null space is activated and deactivated gradually. The two methods are applied to the case study of a welding application in which the null space command must avoid the collision between the robot and an obstacle. The comparison of the results of the case study shows that NSBM performs better than GPM. The proposed algorithms are also tested on a real robotic platform to demonstrate that their computational time is compatible with the real-time requirements of the robot.