Stable neural PD controller for redundantly actuated parallel manipulators with uncertain kinematics

This paper proposes a stable Proportional Derivative Controller applied to redundantly actuated parallel robots with uncertainty in the kinematic parameters. It is shown that all the closed loop signals are uniformly ultimately bounded. Gravitational terms are approximated using a Radial Basis Function Neural Network with joint information feeding their activation functions and with on-line real-time learning. A depart from current approaches is the fact that damping is added at the joint level using the robot active joints and the fact that it does not require the exact knowledge of the kinematic parameters. The learning rule for the neural network weights is obtained from a Lyapunov stability analysis. Simulation results are reported and demonstrate the effectiveness of the proposed controller.