Decentralized model-free continuous control for robot manipulators: tracking in finite time

Tracking of robot manipulators has been addressed with the aid of model-based regressor, and several techniques have been proposed, wherein asymptotic, and even exponential stability properties are obtained depending on how much knowledge is assumed over the regressor and the physical parameters of the robot. Well-posed finite time convergence using time base generators has been obtained, in contrast to the ill-posed terminal attractors with fractional powers. When the regressor is completely unknown, soft computing techniques have been proposed to reconstruct it and carry out adaptive compensation, while another input stabilize the system. However, they usually lack of formal stability results for tracking and they are computationally expensive to implement. In this paper, a new and very simple, chattering-free, decentralized nonlinear PID controller that does not use the regressor (and does not attempt to reconstruct it) is proposed, which guarantees local tracking in arbitrary finite time for robot manipulators. Simulation results show the performance of our controller compared versus regressor-based controllers and linear PID control.