Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots

TL;DR

The paper investigates how energy minimization shapes legged locomotion, addressing the limitations of pre-programmed gait libraries. It presents an analysis-by-synthesis framework where a model-free RL policy optimizes forward motion while minimizing work, trained on fractal terrains to produce emergent gaits on flat ground (walk, trot, bounce) and unstructured gaits on rough terrain. A distillation-based, velocity-conditioned policy enables smooth gait transitions, and a Sim-to-Real transfer module demonstrates robustness on a Unitree A1 robot. The results show emergent gaits align with mammalian patterns at comparable Froude numbers, supporting energy efficiency as a unifying principle for diverse terrains and speeds, with practical implications for robust, adaptable legged locomotion in real-world robots.

Abstract

Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However, fixing a set of pre-programmed gaits limits the generality of locomotion. Recent animal motor studies show that these conventional gaits are only prevalent in ideal flat terrain conditions while real-world locomotion is unstructured and more like bouts of intermittent steps. What principles could lead to both structured and unstructured patterns across mammals and how to synthesize them in robots? In this work, we take an analysis-by-synthesis approach and learn to move by minimizing mechanical energy. We demonstrate that learning to minimize energy consumption plays a key role in the emergence of natural locomotion gaits at different speeds in real quadruped robots. The emergent gaits are structured in ideal terrains and look similar to that of horses and sheep. The same approach leads to unstructured gaits in rough terrains which is consistent with the findings in animal motor control. We validate our hypothesis in both simulation and real hardware across natural terrains. Videos at https://energy-locomotion.github.io

Figures (11)

• Figure 1: We demonstrate via analysis-by-synthesis approach that learning to move forward by minimizing energy consumption plays a key role in the emergence of natural locomotion patterns in quadruped robots. We do not pre-program any primitives for leg motions and the policy directly output desired joint angles. Top: Bio-energetics driven learning on flat terrain leads to different gaits namely walk, trot and bounce (similar to gallop) as the speed increases. Our high-speed bounce gait displays an emergent flight phase despite low energy usage. This corresponds to the nearest animals (sheep/horse) with similar Froude numbers. Bottom: The same pipeline on diverse uneven terrains leads to unstructured gait as is true in general animal locomotion. Please see videos on the \pagelink.
• Figure 2: Energy consumed in moving 1m distance using our method and MPC shows why certain gaits are stable at certain speeds. Videos on the \pagelink.
• Figure 3: Complex real-world behaviors at the low speed in 2 settings. Top: key frames on rocky terrain. Bottom: Foot contact plots and key frames on unstable moving planks. Videos on the \pagelink.
• Figure 4: Foot contact plots for walking, trotting and bouncing gait of A1 robot in the real world. Bold color means the corresponding foot is in contact with the ground and the light color means the foot is in the air. (RF: Right-Front foot, LF: Left-Front foot, RR: Right-Rear foot, LR: Left-Rear foot)
• Figure 5: Trotting with 1 kg payload (two bottles of 500 ml water are strapped onto the robot). The 1 kg payload is out of the normal perturbation of environment parameters used in simulation training shown in Table \ref{['tab:ood-range']}. We show qualitative and gait patterns for other two gaits in the appendix. We find that the gait patters are robust and remain the same even in the presence of disturbances.