From Motion Explanation to Control Guidance: A Review of the Inverted Pendulum, Compass Gait, and SLIP in Bio-Inspired Legged Robotics

Abstract

Minimal models have played a central role in legged locomotion research by reducing complex biological and robotic systems to interpretable dynamical templates. This review examines three representative models—the inverted pendulum, compass gait, and sprin g-loaded inverted pendulum (SLIP) —to clarify their theoretical significance and continuing relevance to bio-inspired legged robotics. Through a comparative review of representative studies, the paper analyses how these models explain locomotion mechanics, support gait analysis, and inform robot control and design. The analysis shows that the inverted pendulum captures the global mechanics of walking and centre-of-mass motion, the compass gait highlights passive dynamics, hybrid transitions, and gait stability, and the SLIP model emphasises compliance, elastic energy storage, and dynamic efficiency. Taken together, the three models form a progressive theor etical chain from motion explanation to control-oriented abstraction. Although their simplifying assumptions limit direct application to modern robotic platforms, they remain valuable as interpretable and transferable templates for analysing locomotion, structuring controller design, and guiding future model extension. This review therefore argues that classical minimal models continue to provide an important conceptual bridge between biomechanics, dynamical analysis, and robotic implementation.