PD based Robust Quadratic Programs for Robotic Systems In this paper, inspired by ProportionalDerivative (PD) control laws, we present a class of Control Lyapunov Function (CLF) based Quadratic Programs (QPs) for robotic systems. ProportionalDerivative (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 (PDQPs), 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 PDQPs: modelbased and modelfree. Furthermore, for tracking timevarying trajectories, we establish asymptotic stability for the modelbased PDQP, and ultimate boundedness for the modelfree PDQP. The performance of the PDQPs is evaluated on two robot models: a fully actuated cartpole and an underactuated 5DOF biped.

Local stability of PD controlled bipedal walking robots Abstract   We establish stability results for PD tracking control laws in bipedal walking robots. Stability of PD control laws for continuous robotic systems is an established result, and we extend this for hybrid robotic systems, an alternating sequence of continuous and discrete events. Bipedal robots have the legswing as the continuous event, and the footstrike as the discrete event. In addition, bipeds largely have underactuations due to the interactions between feet and ground. For each continuous event, we establish that the convergence rate of the tracking error can be regulated via appropriate tuning of the PD gains; and for each discrete event, we establish that this convergence rate sufficiently overcomes the nonlinear impacts by assumptions on the hybrid zero dynamics. The main contributions are (1) Extension of the stability results of PD control laws for underactuated robotic systems, and (2) Exponential ultimate boundedness of hybrid periodic orbits under the assumption of exponential stability of their projections to the hybrid zero dynamics. Towards the end, we will validate these results in a 2link bipedal walker in simulation.