Guiding Energy-Efficient Locomotion through Impact Mitigation Rewards

TL;DR

The paper addresses the gap between imitation-based gaits and the passive, energy-dissipative dynamics underlying efficient locomotion. It introduces the Impact Mitigation Factor (IMF) as a physics-informed reward that quantifies passive impact absorption and combines it with Adversarial Motion Priors (AMP) or handcrafted rewards to guide learning. Through simulation on Husky-v2, IMF-augmented policies achieve up to $32\%$ reductions in Cost of Transport ($CoT$) while also lowering peak mechanical power and joint torques across flat and rough terrains. This hybrid framework demonstrates that leveraging IMF enables policies to learn both explicit motion styles and the implicit dynamic principles of natural locomotion, with strong implications for energy-efficient, robust legged robots and future hardware validation.

Abstract

Animals achieve energy-efficient locomotion by their implicit passive dynamics, a marvel that has captivated roboticists for decades.Recently, methods incorporated Adversarial Motion Prior (AMP) and Reinforcement learning (RL) shows promising progress to replicate Animals' naturalistic motion. However, such imitation learning approaches predominantly capture explicit kinematic patterns, so-called gaits, while overlooking the implicit passive dynamics. This work bridges this gap by incorporating a reward term guided by Impact Mitigation Factor (IMF), a physics-informed metric that quantifies a robot's ability to passively mitigate impacts. By integrating IMF with AMP, our approach enables RL policies to learn both explicit motion trajectories from animal reference motion and the implicit passive dynamic. We demonstrate energy efficiency improvements of up to 32%, as measured by the Cost of Transport (CoT), across both AMP and handcrafted reward structure.

Figures (4)

• Figure 1: Arrows from the swing leg illustrate the pre-impact velocity and resulting impulse, both governed by the configuration-dependent Operational-Space Inertia Matrix ($\Lambda$). This matrix captures how the robot’s joint configuration influences impact dynamics, enabling effective mitigation.
• Figure 2: Northeastern University's Husky version-v.2 -- a platform designed to explore multi-modal dynamic-legged-aerial locomotion through appendage repurposing -- is the motivation for this study.
• Figure 3: Snapshot of locomotion under policies trained with and without IMF. a): Rough terrain locomotion without IMF reward on Husky v.2. b): Rough terrain locomotion with IMF reward on Husky v.2. For the same trotting gait, the policy trained with IMF reward reduces average mechanical power consumption.
• Figure 4: Comparison of average mechanical power across 100 flat-ground environments using four policies, with velocities ranging from 1.5 m/s to 2 m/s.