Predictive Control Based on Orbital Energy for Zero-Step Recovery on Bipedal Robots

Achieving stable landings and rapid recovery after dynamic motions like jumping and fast walking remains a challenge for bipedal robots. During rapid deceleration, substantial momentum must be dissipated efficiently to prevent instability. However, conventional controllers struggle with impact-induced uncertainties and trajectory tracking errors. To address these issues, we propose a novel control framework based on a three-dimensional variable-height inverted pendulum model (VHIP). First, an energy-based stabilization strategy, combined with a nonlinear model predictive controller (NMPC), determines the optimal states for emergency stop transitions. The constrained NMPC enables real-time trajectory adaptation for rapid velocity convergence and balance recovery, while explicitly handling kinematic constraints, unilateral contacts, and inherent model nonlinearities to dissipate large, multi-directional momentum. Second, to handle variations in the center of pressure (CoP), a divergent component of motion (DCM) feedback strategy is applied. An optimization-based method is also introduced to compute contact vertex forces for tracking the desired CoP. The proposed approach effectively addresses the challenges of maintaining dynamic stability in legged zero-step recovery (i.e. recovery without additional stepping), making it suitable for both walking-to-standing transitions and high-impact landing scenarios.