This project seeks to extend understanding of locomotion in robots with articulated bodies and limbs. A gait is a sequence of body shape changes that ends with the same shape as it starts, and that results in a net repositioning of the body within its environment. Arbitrarily large repositioning may be achieved by repeating the sequence over and over. Examples of gaits in four-legged animals include walking, trotting, cantering, and galloping in horses, and pronking in gazelles. A robot or animal may use a particular gait depending on need -- for example, the desired speed of travel will affect the relative energy efficiency of different gaits. Robots with body configurations similar to animals may use gaits adapted from nature, however not all robot configurations have obvious biological counterparts. Furthermore a strictly biomimetic approach may miss possible gaits that improve upon natural systems. This project will derive a systematic mathematical framework to search for desirable gaits in cases that cannot generally be handled using the current state of the art, including where some movements of the robot body cannot be actively controlled, or where the movement of the robot causes changes to the surrounding environment, or where properties of the surrounding environment are controlled to indirectly influence the movement of the robot. The results of this work will be applied to robots that can maneuver through challenging media, such as water, sand or mud. These results will have potential uses in search and rescue, environmental monitoring, and exploration of hostile environments. The results will also give insight into the locomotion strategies of biological organisms. The Principal Investigator has a track record of outreach and educational activities, including a graduate-level textbook on robotic locomotion.
Gait motions take advantage of asymmetries in the reaction forces generated from a system's interactions with its surroundings to gain net displacement in a cyclic way. Recent research in robotic gait locomotion has established a geometric framework for modeling a system's configuration space in the form of a principal fiber bundle; in such a formulation, a system -- either robot or animal -- has a configuration space that can be divided into a shape space and a position space. Gaits are cyclic paths in the shape space, which when followed, cause displacement in the position space. This fiber bundle structure has been used with nonlinear control techniques to analyze and engineer gaits for robotic motion planning, but prior work has been restricted to systems whose degrees of freedom can be neatly decomposed into those that are actuated directly and those that parameterize a symmetry group. Such systems represent only a fraction of the landscape of realistic locomotion problems, in particular, excluding systems in which energy efficiency can be derived from nonlinear dynamics involving additional unactuated degrees of freedom. This project will extend the applicability of symmetry-based methods for modeling and control to a broader class of problems in solitary and cooperative locomotion that emphasize efficiency, agility, and design principles at the boundary of natural and engineered systems.