Animal locomotion is difficult to model accurately from first principles, and idealized mathematical approximations often neglect potentially significant physical effects. Yet these mathematical descriptions are the most powerful tools available to understand natural movement, and to replicate its effectiveness in engineered robotic systems. This project combines a powerful mathematical analysis and design framework with a data-driven method for developing predictive relations that reflect observed behavior. The geometric control approach allows the construction of motions that optimize certain beneficial attributes, such as the efficiency of travel, but requires comprehensive mathematical models of the dynamics. On the other hand, Data-Driven Floquet Analysis (DDFA) allows modeling of the dynamics of repetitive motions based on observations, but provides only a narrow portrait of the system behavior. This project will apply DDFA to construct geometric models, which will then enable use of the methods of geometric control to find desirable gaits. By building locomotion models from the observed outputs of the system's physical processes, this project will allow the complexities of real motions to be accommodated into powerful geometric design frameworks, with an efficient use of measurements. The results will advance the nation's prosperity and welfare by enabling robots that walk, swim, or crawl robustly and efficiently, for missions such as search-and-rescue or environmental monitoring. The project will also give insight on the locomotion strategy of animals. The project includes a student outreach component, with modules that provide hands-on learning about gaits.
This project combines two paradigms which consider whole-body interaction between a system and its environment from a rigorous mathematical perspective. One approach, based on gauge theory and geometric mechanics, looks at how the system dynamics vary across the configuration space. This global perspective allows for optimal gaits to be defined and their characteristics studied, but relies on detailed system models. The second approach, rooted in Floquet theory, views the gait cycle as fixed and analyzes perturbations away from its cyclic motions. In this perspective, a gait is a set of coupled oscillations in body shape and velocity. This body of work seeks to understand the nature of the coupling through empirical observation, but provides only local views of the system dynamics near fixed gaits, and does not provide clear vectors along which to optimize those gaits. This project unifies the geometric and data-driven Floquet paradigms in a way that combines their strengths while mitigating their weaknesses. It brings geometric notions of optimality into Floquet analysis and data-driven modeling techniques from the Floquet paradigm into the geometric modeling approach. Experiments on a range of systems with different body topologies and environmental interactions will play a key role in both the development and evaluation of this new framework.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
