Legged robot research is presently focused on bipedal or quadrupedal robots, despite capabilities to build robots with many more legs to potentially improve locomotion performance. This imbalance is not necessarily due to hardware limitations, but rather to the absence of principled control frameworks that explain when and how additional legs improve locomotion performance. In multi-legged systems, coordinating many simultaneous contacts introduces a severe curse of dimensionality that challenges existing modeling and control approaches. As an alternative, multi-legged robots are typically controlled using low-dimensional gaits originally developed for bipeds or quadrupeds. These strategies fail to exploit the new symmetries and control opportunities that emerge in higher-dimensional systems. In this work, we develop a principled framework for discovering new control structures in multi-legged locomotion. We use geometric mechanics to reduce contact-rich locomotion planning to a graph optimization problem, and propose a spin model duality framework from statistical mechanics to exploit symmetry breaking and guide optimal gait reorganization. Using this approach, we identify an asymmetric locomotion strategy for a hexapod robot that achieves a forward speed of 0.61 body lengths per cycle (a 50% improvement over conventional gaits). The resulting asymmetry appears at both the control and hardware levels. At the control level, the body orientation oscillates asymmetrically between fast clockwise and slow counterclockwise turning phases for forward locomotion. At the hardware level, two legs on the same side remain unactuated and can be replaced with rigid parts without degrading performance. Numerical simulations and robophysical experiments validate the framework and reveal novel locomotion behaviors that emerge from symmetry reforming in high-dimensional embodied systems.

翻译：当前足式机器人研究主要集中于双足或四足机器人，尽管构建更多腿的机器人可能提升运动性能。这种不平衡并非必然源于硬件限制，而是缺乏能解释何时以及如何通过增加腿数提升运动性能的原理性控制框架。在多足系统中，协调大量同步接触会引发严重的维度灾难，这对现有建模与控制方法构成挑战。作为替代方案，多足机器人通常采用最初为双足或四足机器人开发的低维步态进行控制。这些策略未能充分利用高维系统中涌现的新对称性和控制机会。在本工作中，我们开发了一个用于发现多足运动中新控制结构的原理性框架。我们利用几何力学将密集接触的运动规划简化为图优化问题，并提出了源自统计力学的自旋模型对偶框架，以利用对称性破缺指导最优步态重组。通过该方法，我们为六足机器人识别出一种非对称运动策略，实现了每运动周期0.61体长的前进速度（较传统步态提升50%）。由此产生的非对称性体现在控制与硬件两个层面。在控制层面，身体朝向在快速顺时针转向阶段与慢速逆时针转向阶段之间非对称振荡以实现前进运动。在硬件层面，同侧的两条腿保持无驱动状态，可替换为刚性部件而不影响性能。数值仿真与机器人物理实验验证了该框架，并揭示了高维具身系统中通过对称性重构涌现的新型运动行为。