Development of Optimization Algorithms for the Search of Optimal Passive Running Gaits of Elastic Legged Systems

Abstract

Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One way to improve their efficiency is by adding elastic elements, which allow the system to exploit natural dynamics for energy-efficient movement. This thesis investigates this concept by designing optimal control inputs that take advantage of the elasticity in legged systems. The approach is structured in several stages. It starts with a novel energy injection technique to identify passive motion patterns using direct collocation. This step enables the discovery of passive solutions even in systems with energy dissipation due to factors like friction and impact. We employ a continuation approach from these passive solutions to derive optimal, non-parameterized control inputs, ensuring flexibility and robustness. The method is tested on various models to demonstrate its applicability across different legged robotic systems. Additionally, we compare several cost functions to assess the effectiveness of the proposed control strategies. This comprehensive analysis provides valuable insights into the design and operation of elastic legged robots, offering pathways to improve their efficiency and adaptability.