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.

Stability and Gait Switching of Underactuated Biped Walkers This paper introduces a new gait switching approach for underactuated biped walkers. The switching condition relies on a reduced region of attraction xe2x80x94 that of the unactuated dynamics xe2x80x94 which is shown to be sufficient to predict falls. A gait transition is accordingly stable (as in xe2x80x9cthe robot does not fall if the bipedxe2x80x99s state is within the reduced region of attraction of the switchedin gait when switching takes place. Two and fivelink biped models complete a sequence of random gait transitions using the switching logic. The condition is also used to enlarge the full region of stability of the fivelink model by embedding feedbackstabilized trajectories from a gait library in a mapping. The mapping stitches stable trajectories to the orbit of the desired gait based on each gaitxe2x80x99s reduced region of attraction. This improves the robustness of the fivelink model walking on uneven terrain without ground perception regardless of the size of the gait library.