Locomotion is everywhere. The capabilities that animals exhibit in converting internal joint motions into displacements inspire us to ask the question: ?How can we imbue artificial systems with the same ease of motion?? We propose to design, control, and plan motions for a broad class of locomoting systems. These systems maneuver both on land and in the water, and experience dynamics and nonholonomic constraints which may change dynamically. Specifically, the proposed work seeks to: (1) develop tools to design and optimize gaits, cyclic internal motions that result in a desired net motion and (2) use these tools to design optimal morphologies for locomoting mechanical systems. To achieve these goals, the proposed work will draw upon fundamentals of differential geometry to develop techniques to efficiently design gaits. Specifically, we will develop tools to analyze and manipulate the reconstruction equation so that it can be used for gait design. With these new efficient tools, we can design optimal gaits for locomoting systems, starting with kinematic systems and moving on to dynamic systems, both with nonholonomic constraints. The proposed work will then use these gait development tools to design optimal robot morphologies.
An improved understanding of locomotion is vital for mechanisms that can navigate in challenging terrains, e.g., for applications like urban search and rescue or searching for IEDs in hard to reach locations, such as the nooks and crannies prevalent in the ports of major cities. The proposed work will not provide a system for these tasks, but rather the theory developed in this work will advance robotic mobility and how to quantify it, so that these applications can be achieved and the scientific understanding of locomotion is advanced.
Animals locomote everywhere. Snakes crawl, fish swim, birds fly, and all manner of creatures walk. The facility with which animals use internal joint motions to move through their environments far exceeds that which has been achieved in artificial systems; consequently there is much interest in raising the locomotion capabilities of such systems to match or even surpass those of their biological counterparts. A fundamental aspect of animal locomotion is that it is primarily composed of gaits – cyclic shape changes which efficiently transport the animal. Examples of such gaits include a horse’s walking, trotting, and galloping, a fish’s translation and turning strokes, and a snake’s slithering and sidewinding. The efficacy of these motions, along with the abstraction that they allow from shape to position changes, suggests that gaits will form an equally important part of artificial locomotion. The goal of this work is to decode some of the fundamentals of biology in a mathematically rigorous manner and then use them to guide the design and control of robotic locomoters. The major outcomes of this work is that we provide a rigorous basis by which people can analyze, and hence design gaits for locomoting systems that use their full body to locomote. Essentially, three key pieces of insight came out of this work. The first was establishing a linear relationship between the inputs and outputs of the locomoting system. A linear relationship is important because it allows for calculations to be made very quickly on conventional computers. Previous work provided a linear relationship but were limited to small motions; our work allow for larger, and hence realistic, motions. The second insight has to do with choice of coordinate system. In high school physics, we learn that many phenomena like conservation of momentum are independent of the frame of reference. This is true for many systems and all phenomena. However, we observed and then proved that calculating displacement of a locomiting system actually depends on choice of coordinate system. This is counter-intuitive. This understanding allowed us to create the linear relationship, described above. The final insight in his work was the development of a means to visualize, and hence calculate, effort for a locomoting sytem. Simply designing a gait is not enough; we need to know the cost of transport for that gait. Our work took recourse to ideas in cartography to produce our results.
