This work considers the control of underactuated bipedal walking, and a novel capturability-based control framework is presented. Compared with traditional approaches, the presented control method does not rely on the use of the Poincaré map, which may take significant computational cost. Firstly, a new definition of stable walking is presented, and a novel foot-placement based control method is proposed. Then, a controller design method is presented based on this control method. For the controller design, the foot placement adjustment is achieved by updating the virtual constraints using a heuristic method, and an improved virtual constraint control method is proposed to enforce the virtual constraints. Finally, the effectiveness of the presented control framework is illustrated on a five-link underactuated planar biped by numerical simulations.

Significant research interest has recently been attracted to the study of bipedal robots due to the wide variety of their potential applications. In reality, bipedal robots are often required to perform gait transitions to achieve flexible walking. In this paper, we consider the gait transition of a five-link underactuated three-dimensional (3D) bipedal robot, and propose a two-layer control strategy. The strategy consists of a unique, event-based, feedback controller whose feedback gain in each step is updated by an adaptive control law, and a transition controller that guides the robot from the current gait to a neighboring point of the target gait so that the state trajectory can smoothly converge to the target gait. Compared with previous works, the transition controller is parameterized and its control parameters are obtained by solving an optimization problem to guarantee the physical constraints in the transition process. Finally, the effectiveness of the control strategy is illustrated on the underactuated 3D bipedal robot.