Computations and Analysis of Efficient Snake Locomotion

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Snake locomotion has been studied for several decades by biologists and engineers, but a general quantitative understanding of how snakes bend their bodies to move efficiently is lacking. A small number of typical snake motions (for example, lateral undulation and sidewinding) have been described and studied, but a much wider range of motions can occur biologically and mechanically. This project will use mathematical analysis and simulations to study a wide range of snake motions, identify those that move the snake body most efficiently, and understand how they depend on physical parameters and constraints. Snakes lack limbs but can nonetheless move efficiently on land. The research will develop accurate simulations of snake dynamics in the presence of friction and contact forces. Measuring the forces on real snakes performing a wide range of movements is difficult in experiments, so mathematical models and simulations are essential. The research will have broader impacts in the ongoing development of robust snake robots to explore, perform inspections and search-and-rescue operations, and assist internal medical procedures, often in confined and/or hazardous environments. The underlying physical principles will apply to efficient locomotion by a range of terrestrial organisms and robots. The project will involve interdisciplinary research training of undergraduates and a graduate student. Improvements in computations and analysis of two-dimensional snake locomotion will aim to accurately characterize optimally efficient motions in the regimes of moderate and small transverse friction, which are important biologically and for robotics. Little is known about such optima at present, and why transverse undulation is ineffective in this regime. Optimal motions will be identified under constraints including zero time-averaged body rotation and fixed energy consumption. Optimal motions in the presence of walls and obstacles will be computed using penalty forces preventing penetration of the solid barriers and giving additional frictional interactions. Such sharply varying forces will be computed accurately using adaptive quadrature of frictional and barrier forces in the vicinity of contact. The benefits of passive elasticity, well known for aquatic organisms, will be studied in snakes. Accurate computations of contact forces with the ground will allow for the study of optimal snake motions in three dimensions, accounting for the work done against gravity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.