Energy-Efficient Quadruped Locomotion with Compliant Feet

Summary

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion.

Abstract Summary

Quadruped robots are often designed with rigid feet to simplify control and maintain stable contact during locomotion. While this approach is straightforward, it limits the ability of the legs to absorb impact forces and reuse stored elastic energy, leading to higher energy expenditure during locomotion. To explore whether compliant feet can provide an advantage, we integrate foot compliance into a reinforcement learning (RL) locomotion controller and study its effect on walking efficiency. In simulation, we train eight policies corresponding to eight different spring stiffness values and then cross-evaluate their performance by measuring mechanical energy consumed per meter traveled. In experiments done on a developed quadruped, the energy consumption for the intermediate stiffness spring is lower by ~ 17% when compared to a very stiff or a very flexible spring incorporated in the feet, with similar trends appearing in the simulation results. These results indicate that selecting an appropriate foot compliance can improve locomotion efficiency without destabilizing the robot during motion.

Key Points

Uses reinforcement learning for policy optimization
Targets physical robot platforms

Robot Platform and Compliant Foot Design

The quadruped platform used here consist of four articulated legs, driven by electrically actuated joints, onboard sensing modules for state estimation, and an embedded computing system to execute the control policy. The overall structure follows the typical layout of four-articulated legs, in which every leg provides enough range of motion to stand, walk, and balance.

The legs follow a classic articulated configuration with rotary joints at the abduction, hip, and knee.

Robot Platform and Compliant Foot Design — Energy-Efficient Quadruped Locomotion with Compliant Feet — Figure 1: CAD model of a single leg module of the quadruped robot showing the actuator arrangement, link lengths, and the prismatic spring-loaded foot.

Control Architecture and Reinforcement Learning Setup

The control framework for our quadruped combines a learned high-level locomotion policy with a low-level actuator controller to ensure stable and efficient execution on hardware The following sections describe the policy inputs, action space, and training setup used to generate locomotion across different stiffness conditions.

Simulation Experiments and Hardware Deployment

The simulation experiments were conducted in NVIDIA Isaac Gym [ 26 ] using a quadruped model equipped with the compliant foot mechanism described earlier. The goal of these experiments was to train a set of locomotion policies under different foot stiffness settings and evaluate how each policy behaves when exposed to stiffness values outside its training condition.

During training, the agent receives task rewards that encourage accurate velocity tracking and auxiliary rewards that promote stable, transferable gaits.

Simulation Experiments and Hardware Deployment — Energy-Efficient Quadruped Locomotion with Compliant Feet — Figure 3: ROS2-based hardware deployment pipeline.

Sources and Demonstrations

Figures are reproduced from Pal et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.