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

Zipeng Fu1         ‪Ashish Kumar2         Jitendra Malik2         Deepak Pathak1
1Carnegie Mellon University          2UC Berkeley CoRL 2021

Walking, trotting and bouncing (galloping) gaits in real world emerge from learning fully in simulation by minimizing the energy consumption without any human priors about gaits.


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 is sufficient for 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.

Project Video

Gait Transition via a Velocity-Conditioned Policy

Similar Energy Consumption Trend
between Our Robot and Horses


In Biomechanics, Froude number is a metric characterizing gaits of quadrupeds and bipeds. Animals with a similar morphology but with different sizes tend to use the same gait when moving with equal Froude numbers. Our robot has similar Froude numbers as horses and sheep. The plot on the left (Hoyt et al. 1981) analyzes the energy consumption of different horse gaits across different speeds. Shown on the right, the energy consumption plot of our robot has a similar trend, which also validates certain gaits will emerge at certain speeds if we minimize the energy consumption.

Foot Contact Plots of Walking, Trotting, Bouncing (Galloping)

More Examples of Emergent Structured Gaits
(Walk, Trot & Bounce)

Walking Gait (0.375 m/s):


Trotting Gait (0.9 m/s):


Bouncing (Galloping) Gait (1.5 m/s):



Emergent Unstructured Gaits



Related Work

This work is part of our series of research on learning based control of legged robots. Please check out other works below.

RMA: Rapid Motor Adaptation for Legged Robots
Ashish Kumar, Zipeng Fu, Deepak Pathak, Jitendra Malik
RSS 2021

PDF | Video | Project Page
Coupling Vision and Proprioception for Navigation of Legged Robots
Zipeng Fu*, Ashish Kumar*, Ananye Agarwal, Haozhi Qi, Jitendra Malik, Deepak Pathak
CVPR 2022

PDF | Video | Project Page


  author    = {Fu, Zipeng and Kumar, Ashish and Malik, Jitendra and Pathak, Deepak},
  title     = {Minimizing Energy Consumption Leads to the Emergence of Gaits in Legged Robots},
  booktitle   = {Conference on Robot Learning ({CoRL})},
  year      = {2021},