The planning of whole-body motion and step time for bipedal locomotion is constructed as a model predictive control (MPC) problem, in which a sequence of optimization problems needs to be solved online. While directly solving these problems is extremely time-consuming, we propose a predictive gait synthesizer to offer immediate solutions. Based on the full-dimensional model, a library of gaits with different speeds and periods is first constructed offline. Then the proposed gait synthesizer generates real-time gaits at 1kHz by synthesizing the gait library based on the online prediction of centroidal dynamics. We prove that the constructed MPC problem can ensure the uniform ultimate boundedness (UUB) of the CoM states and show that our proposed gait synthesizer can provide feasible solutions to the MPC optimization problems. Simulation and experimental results on a bipedal robot with 8 degrees of freedom (DoF) are provided to show the performance and robustness of this approach.
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