Abstract: Foot structure is a core factor affecting the stair-climbing safety of humanoid robots, directly influencing support stability margins, swing-foot obstacle avoidance capability, and touchdown smoothness. Existing studies often use the geometric center of the sole as the foothold reference, without considering the risks of forward toe collision and rear heel overhang caused by ankle-configuration asymmetry, which may lead to motion instability near stair edges. To address this issue, this paper proposes a posterior-anchor-based motion control method for humanoid robots under asymmetric foot constraints. First, based on discrete-terrain contact dynamics, a parametric constraint model between the foot geometric envelope and stair edges is established to construct a safe foothold domain that satisfies the dual constraints of toe collision avoidance and heel overhang prevention. Second, to resolve the ambiguity of foothold references near stair edges, a posterior-anchor extraction mechanism with asymmetric-configuration compensation is introduced to transform terrain prior information into physical guidance features for policy learning. Finally, a nonlinear reward potential field and a dimensionally decoupled continuous trajectory control strategy are designed to drive the swing foot to converge to the optimal safe foothold interval. Experimental results show that, under variable locomotion speeds and variable step heights, the proposed method improves the safe foothold rate for step climbing by 54.2\% and 32.3\%, respectively, compared with existing methods, verifying its effectiveness and superiority.

Key words: motion control, robust control, posterior anchor, asymmetric foot, humanoid robot