Animals, and their analogous biologically-inspired robots out-perform traditional robots (e.g., cars, planes, boats) in many environments and for many tasks. Unfortunately, control of biologically-inspired robots differs from that of traditional robots, preventing their adoption. Achieving control of biologically-inspired robots with the same ease as traditional robots would markedly transform the field of robotics. The main challenge is that locomotion requires time-varying periodic control inputs, known as gaits, to achieve movement. The discrete nature of the gaits and their time-varying structure means that standard control strategies do not apply. It is critical that this class of robots be as simple to control as traditional robots if widespread adoption is to occur. This award supports fundamental research into a mathematical framework that will lead to simpler formulations for control of these robots. The simpler formulation will be of value to society as biologically-inspired robots are envisioned to be of great practical use for a variety of robotic application domains, such as search and rescue, defense, surveillance, and plant integrity inspection. Furthermore, biologically-inspired robots are quite popular with youth and the public. We will capitalize on this appeal to increase and broaden participation in engineering and engineering research.
Biologically-inspired robotic systems are typically nonholonomic systems that require time-varying control inputs, making optimal control-based design of trajectories challenging. Further, these systems rely on families of parametrizable, time-varying control inputs, called gaits, to generate movement. Gaits are disjoint controls, in that applying one gait precludes the use of another. Thus, not only must the control input be time-varying, but the reachability properties are gait-dependent and may require switches of control modes for some navigation goals. On account of these challenges, the development of a framework for trajectory generation and planning of these systems is still an open problem. Drawing on concepts from differential geometry, geometric mechanics, and averaging theory to exploit the geometric and temporal symmetries of these robotic systems, a reduced optimal control formulation will be derived. The connection of these concepts to multi-mode, multi-dimensional control systems will be delineated to resolve the switched, optimal control problem associated to systems with multiple gait strategies. To generate initial trajectory estimates for the optimal control solver, we will specialize a kino-dynamic path planning algorithm to incorporate the geometric and multi-gait properties of biologically-inspired robotic systems.
