Simple Passive Dynamic Models for Emerging Quadrupedal Gaits

Kurzfassung

Nowadays legged robots are being preferred to wheeled vehicles for applications like mapping and exploration of unstructured environments. Usually, these mechanical systems perform the required motions thanks to suitable controllers. However, recent works suggest that energy-efficient solutions can be obtained by designing elastic systems that naturally exhibit locomotion patters. Inspiration is taken from nature and biological legged locomotion. Animals use different gaits to move at certain speeds while minimizing energy consumption. To understand the underlying dynamics of biological locomotion, simplified models have been proposed. The most common one, the SLIP (Spring Loaded Inverted Pendulum) model, can explain the effect of the radial elasticity of linear legs and generate patterns for locomotion of different legged systems. Unfortunately, it is inappropriate for the study of stability of limit cycles in systems with articulated legs. The aim of this work is to revisit simplified dynamic models for quadrupedal elastic robots, and characterize their stability in order to facilitate the exploitation of their natural dynamics for locomotion purposes. Two simple passive quadrupedal models featuring segmented elastic legs are introduced. One model exploits only leg radial elasticity, while the other model exploits also the rotational one. The dynamic behavior of these models is analyzed using numerical simulation and a continuation approach. From the passive dynamics of such models, gaits emerge without imposing contact sequences a priori. Conducting a parametric analysis on the most important gaits found on this model, the effect of the main system design parameters on gait stability has been identified. The obtained results help in the design of elastic quadrupedal robots that naturally exploit inherent system elasticity.