A Simple Approach on Global Control of a Class of Underactuated Mechanical Robotic Systems This paper presents an approach to show global controllability of a class of underactuated mechanical systems. This class of systems include gymnastic robots and the classic cartpole system. For this class of systems, we can define a connection point, and design a damping controller u(t) with the Lyapunov method to drive all states to the connection point. Further by exploiting the time reversal symmetry of the system and spline interpolation, a controller u(t) can be obtained to drive the system from the connection point to any other state. The system is thus shown completely controllable, i.e., there exists an admissible trajectory from any given state to any given final state. Swingup control designs for a pendubot, cartpole system and triple pendulum are given as illustrative examples.

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.