Biolocomotion refers to the methods that creatures use to move through fluids or across terrain. For life scientists, studying biolocomotion can clarify the relationship between the physiology of a creature and the physical laws that govern its movement. For engineers, studying biolocomotion can improve modeling and design tools that are used to create advanced vehicles and mobile robots. A perennial challenge for vehicle designers is the fundamental tradeoff among size, weight, and power, a tradeoff that the natural world has resolved in myriad, fascinating ways. Besides being extremely efficient in their use of stored energy, many creatures exhibit astonishing degrees of control authority and maneuverability. This award supports fundamental research to discover new methods for integrated optimal design of both the geometry and movement of biologically inspired aquatic and atmospheric vehicles. Civil and commercial applications of these engineered systems range from the mundane (such as unobtrusive traffic monitoring) to the futuristic (such as aquaculture, pollination, or pest control). Moreover, the modeling and design tools developed under this effort can be used to better understand natural swimmers and flyers, feeding a virtuous cycle of knowledge flow between the life and engineering sciences. The educational program will support interest in biolocomotion with formal courses and informal, publicly available tutorials that visually demonstrate biophysical applications of mathematics.
Geometric control and generalized averaging theory can enable integrated optimal design of the morphology and gaits of biologically inspired aquatic and atmospheric vehicles. The approach requires dynamical system models that are general enough to represent a large class of systems but have a structure that is amenable to analysis. The research team will investigate the use of underactuated mechanical system models for biological and biomimetic motion, validating these models through comparisons with diverse examples from biology. The team will then construct a taxonomy of design optimization problems for biomimetic locomotion and address a selection of compelling problems as illustrative examples for use in visualizations and tutorials. The research focus will be on the origin and nature of control authority in biological or biomimetic systems that move by periodically modulating their internal shape. For a large class of system models, one may simplify the nonlinear, time-periodic dynamics using first or higher order averaging theory. Control authority may then be inferred from the symmetric product vector fields that define the given system's time-averaged dynamics. Analysis of these vector fields reveals the role that morphology and input waveforms play in determining the system's overall motion. The analysis and design tools developed under this research program will therefore enable the optimization of geometric and control parameters for biomimetic or biological motion, where the moving agent is modeled as an underactuated mechanical system.
