Locomotion is everywhere. The capabilities that animals exhibit in converting internal joint motions into displacements inspires us to 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.
Project Outcomes: Optimal Gaits and Design for Locomoting System. The remarkable ability of animals to crawl, swim, fly, walk, and run in all sorts of conditions and terrains is readily evident in the natural world. The ease that animals exhibit in converting internal joint motions into displacements inspires us to to ask the question: "How can we imbue artificial systems with the same ease of motion?" In this project we design, control, and plan motions for a broad class of locomoting systems that maneuver in air, on land, and in the water. The true goal of this program is not to build a specific system, but rather to address the scientific underpinnings of locomotion. Outcomes 1 and 2 satisfy the Intellectual Merit criterion and Outcomes 2 and 3 satisfy the Broader Impact criterion. (Here we have included Outcome 2 in Broader Impact owing to the potential impact in biological fields.) Outcome 1: Efficient graphical methods for finding optimal gaits. Imagine you are given a machine such as the three-link device shown in the figure. You are then asked to activate the motors on the hinges in sequence to make the device swim. This is a non-trivial exercise that increases in complexity as the geometric complexity of the device increases. The task becomes even more difficult if you are asked to find, not just a sequence that works, but the best sequence for efficient swimming. One of the primary contributions of our work is the development of a graphical representation that makes it easy to identify, for a given device geometry, the optimal sequence of activation for swimming systems. Outcome 2: Different strokes for different folks: Comparing motion across and within swimming species. A second challenge in finding optimal strategies for locomotion lies in simply comparing two activation sequences. Suppose you are given videos of two different fish swimming. It is easy to determine which is "better" (e.g. by measuring speed or energy consumption), but how does one quantify how "close" the swimming strategies are to one another? Imaging you are then given a third video; how can one quantify whether it is "closer" to the first or the second? We have developed a systematic mathematical method to that quantifies the relative differences between complex locomoting behaviors. This metric can be used to build "kinematic trees," similar to genetic trees, to determine which organisms are behavioral neighbors. (This work was presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 2013). Outcome 3: Educating STEM students. One of our most valuable contributions is in educating students who go on to careers that employ their technical expertise across a broad range of disciplines. This project directly impacted two graduate students and three undergraduates who have gone on to pursue careers or higher education in STEM fields.
