The Effect of Physical Leg Compliance in Template-Based Quadrupedal Trotting

Abstract

Legged animals achieve efficient locomotion by exploiting intrinsic mechanical compliance, where elastic tissues store and release energy during stance. In contrast, most legged robots rely on rigid actuation and emulate compliance through control, leading to high actuator torque demands. Motivated by this gap, this paper investigates the role of physical leg compliance in template-based quadrupedal locomotion. We propose a leg-aligned hip-to-foot spring design that operates in parallel with the actuators during stance and integrate it into a Clock Torque Actuated Spring-Loaded Inverted Pendulum (CT-SLIP) framework with optimization-based force distribution. By explicitly separating spring-generated forces from actuator-generated ground reaction forces, the proposed formulation enables a systematic analysis of passive load compensation. Extensive MuJoCo simulations on the Unitree Go1 quadrupedal robot across a wide range of trotting speeds demonstrate substantial torque redistribution, achieving up to a 67% reduction in mean knee torque and a 59% reduction in peak knee torque compared to a baseline without compliance. These results highlight how appropriately designed physical compliance can effectively complement template-based control to alleviate actuator loads in quadrupedal robots.