Reinforcement learning (RL) has demonstrated substantial potential for humanoid bipedal locomotion and the control of complex motions. To cope with oscillations and impacts induced by environmental interactions, compliant control is widely regarded as an effective remedy. However, the model-free nature of RL makes it difficult to impose task-specified and quantitatively verifiable compliance objectives, and classical model-based stiffness designs are not directly applicable. Lipschitz-Constrained Policies (LCP), which regularize the local sensitivity of a policy via gradient penalties, have recently been used to smooth humanoid motions. Nevertheless, existing LCP-based methods typically employ a single scalar Lipschitz budget and lack an explicit connection to physically meaningful compliance specifications in real-world systems. In this study, we propose an anisotropic Lipschitz-constrained policy (ALCP) that maps a task-space stiffness upper bound to a state-dependent Lipschitz-style constraint on the policy Jacobian. The resulting constraint is enforced during RL training via a hinge-squared spectral-norm penalty, preserving physical interpretability while enabling direction-dependent compliance. Experiments on humanoid robots show that ALCP improves locomotion stability and impact robustness, while reducing oscillations and energy usage.

翻译：强化学习在双足人形机器人运动及复杂动作控制中展现出显著潜力。为应对环境交互引发的振荡与冲击，合规控制被广泛视为有效手段。然而，强化学习的无模型特性使其难以施加面向特定任务且可量化验证的合规性目标，而经典基于模型的刚度设计亦无法直接适用。近期，通过梯度惩罚正则化策略局部灵敏度的Lipschitz约束策略（LCP）被用于平滑人形机器人运动。但现有基于LCP的方法通常采用单一标量Lipschitz预算，且与真实系统中具有物理意义的合规性规范缺乏明确关联。本研究提出各向异性Lipschitz约束策略（ALCP），将任务空间刚度上限映射为策略雅可比矩阵的状态相关Lipschitz型约束。该约束通过铰链平方谱范数惩罚在强化学习训练中实施，在保持物理可解释性的同时实现方向依赖性合规。人形机器人实验表明，ALCP提升了运动稳定性与抗冲击鲁棒性，同时减少了振荡与能量消耗。