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 1 kHz 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.

中文翻译：

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通过质心模型预测步态合成快速在线规划双足运动

双足运动的全身运动和步进时间的规划被构建为模型预测控制（MPC）问题，其中需要在线解决一系列优化问题。虽然直接解决这些问题非常耗时，但我们提出了一种预测步态合成器来提供即时解决方案。基于全维模型，首先离线构建不同速度和周期的步态库。然后，所提出的步态合成器通过基于质心动力学的在线预测合成步态库来生成 1 kHz 的实时步态。我们证明构建的 MPC 问题可以确保 CoM 状态的统一最终有界 (UUB)，并表明我们提出的步态合成器可以为 MPC 优化问题提供可行的解决方案。