An Adaptive Controller with Guarantee of Better Conditioning of the Robot Manipulator Joint-Space Inertia Matrix

The ill-conditioning of the joint-space inertia matrix plays an important role in the dynamic behavior of robot manipulators, as well as in the controllers' performance. Indeed, due to the ill-conditioning, small perturbations in the system can produce large changes in the numerical solutions, which can lead to instability. Moreover, this characteristic is intrinsic to a phenomenon of ill-conditioning in the mechanism itself, which suggests that it may be more difficult to control the mechanism. In this context, this paper proposes an adaptive controller to be used together with an algorithm that ensures better conditioning of the inertia matrix. To evaluate the proposed technique, we compared it with two widely used controllers via statistical analysis. The results showed that the proposed adaptive controller presents a better performance than the one based on the inverse dynamics with feedback linearization, and similar results when compared to a PID controller with gravity compensation.