Periodic Trajectory Planning and Robust Output Zeroing Control for Underactuated Bipedal Robots with Predicted Disturbances For underactuated bipedal robots, it is important to compensate disturbances which affects the zero dynamics to realize a stable locomotion when we use output zeroing controllers. In order to deal with such disturbances, this paper presents a framework of a periodic trajectory planning and a robust output zeroing controller using a disturbance model learned by Gaussian process regression (GPR). In particular, we propose a control method considering the modeling uncertainty of the disturbance model by using a variance information of GPR model. We show the effectiveness of the proposed method through a numerical simulation of walking control of an underactuated robot model affected by an external force.

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.