From Biology to Mechanism: Harnessing Compliance in Locomoting Systems

Inventors have long viewed the agility and grace of animals that crawl, swim, and fly in all environments with awe and envy. However, the ability to replicate the versatility, stability, and efficiency of biological locomotion in engineered systems has eluded scientists and engineers alike. This project will identify fundamental principles of locomotion, with an emphasis on the role of one of the most fundamental biological attributes, compliance. Compliance is ubiquitous in biological locomotion, appearing in diverse forms of life from the elastic ribbed tail of a fish, to the membrane wings of an insect, to the sinewy muscular body of a snake; when a human turns a door knob or picks up a spoon -- tasks that are nontrivial for robotic systems -- they can rely on compliance in the hand to passively adjust to small disturbances and uncertainties in the environment. This project seeks to bridge the gap between classical studies in rigid body mechanics that have long been the purview of the discipline of robotics, and compliant biological strategies for locomotion. The research will rationalize compliant strategies and structures that appear in nature. This knowledge can in turn be used to design new classes of versatile compliant machines, which may include robust strategies for locomotion and manipulation in robotic systems and new compliant mechanisms for harvesting energy.

This research, which lies at the intersection of controls and the mechanics of continuously deformable systems, will develop two new mathematical approaches to tame the complexity associated with optimization of compliant systems. The first takes its roots in geometric mechanics, which has already proven effective in the study of locomotion of simple systems. The second inverts the optimization problem by first solving for optimal kinematics (e.g. optimal stroke patterns for swimmers) with a dynamic cost function, and subsequently inverting the optimal kinematics to find the associated dynamic parameters (such as bending stiffness). In addition to the development of these two new mathematical tools, the project will investigate the role of compliance within the context of different biological locomotion modes. Through decades of cumulative research, the scientific community has established a reasonable understanding of the role of compliance in isolated applications, such as legged walking and running, but comparatively little is known in terms of how this concept extends to other modes such as crawling, swimming, and insect flight. This research will address the issue through investigations of the underlying physical principles that motivate the form and physiology of each of these systems. However, the greatest contribution will come through the amalgamation of these results. By developing new insights across multiple locomotion modes, this project aims to extend the findings into a generalized framework for compliance and locomotion. This framework will then serve as a jumping off point for engineers, who can situate their own systems within a greater map of compliant design methodologies.