Using Continuation Methods to Synthesize Families of Optimal Gaits for Legged Systems

• Applicant: Professor Dr. C. David Remy
• Subject Area: Mechanics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 533240481

In terms of legged locomotion, humans and animals are remarkably agile, versatile, and efficient. By using a broad repertoire of different gaits, they can readily adapt to travel at various speeds, prey, escape danger, or avoid obstacles. In each of their gaits, humans and animals cleverly exploit the mechanical dynamics of their bodies to minimize energy waste and maximize energetic economy. Looking at this repertoire, it is striking that the gaits of different animals tend to be so similar. Despite vast differences in their morphology, habitats, and lifestyles, many animals share the same basic motion patterns. Humans and birds, for example, walk at low speeds and run at higher speeds, and many quadrupedal mammals walk, trot, and gallop. These similarities must hence be the consequence of a fundamental physical process which renders certain ways of locomotion superior. The goal of this project, is to shed light onto this process and exploit it for robotic systems. In particular, we postulate that the different gaits that a legged system can exhibit are a manifestation of the unforced or natural dynamics of its mechanical structure. In energetically conservative and passive models of legged robotic systems, these dynamics enable a broad range of periodic motions or gaits that the models can perform without any actuator inputs. For a simple biped, for example, we were able to systematically find walking, running, hopping, skipping, and galloping among these passive gaits. In this project, we propose to exploit these unforced dynamical motions as the foundation for a novel approach to robotic gait synthesis. Because passive motions do not require any actuator inputs, we can interpret them as globally optimal and use them as templates to find energetically efficient gaits for real robots. To make this transition, we will establish so-called homotopies that can systematically grow the passive motions of simplified conservative models into optimal motions for actual robotic systems and that can be used to create families of gaits at different operating points, such as different speeds or moving on different slopes. These methods are based on numerical continuation techniques, which allow us to explore the solution space in an automated and systematic fashion. In the world of robotics, the clever use of different gaits that we see in nature, and the level of performance it enables, is currently still evading us. Our proposed approach and the theoretical work it is based on, will help realize this untapped potential and will substantially improve the performance of legged robotic systems. For example, our work will enable us to extend the battery life of inspection robots, to increase the locomotion speed of robots for search and rescue, and to build better robotic prostheses and exoskeletons.

• DFG Programme: Research Grants