PD based Robust Quadratic Programs for Robotic Systems

In this paper, inspired by Proportional-Derivative (PD) control laws, we present a class of Control Lyapunov Function (CLF) based Quadratic Programs (QPs) for robotic systems. Proportional-Derivative (PD) control laws are independent of the robot model, however, they fail to incorporate physical constraints, such as torque saturation. On the other hand, most optimization based control design approaches ensure satisfaction of the physical constraints, but they are sensitive to errors in the robot model. The PD based Quadratic Programs (PD-QPs), presented in this paper, are a first step towards bridging this gap between the PD and the optimization based controllers to bring the best of both together. We derive two versions of PD-QPs: model-based and model-free. Furthermore, for tracking time-varying trajectories, we establish asymptotic stability for the model-based PD-QP, and ultimate boundedness for the model-free PD-QP. The performance of the PD-QPs is evaluated on two robot models: a fully actuated cart-pole and an underactuated 5-DOF biped.