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Mathematical Sciences

Robotics and Geometry

Date: 3:30pm - 4:30pm PDT April 1, 2015 Location: John Howard Hall, Room 254

John Howard Hall, Room 254

Dr. Ross Hatton, director of the Laboratory for Robotics and Applied Mechanics at Oregon State University, speaks on Robotics. 

Robotics research is built on a foundation of applied mathematics. Many recent advances in the field have been enabled by the rigorous application of statistics (for interpreting uncertain or inconsistent sensor readings) and differential geometry (for understanding the complex physical interactions that govern robots’ motions.

For example, understanding the locomotion of animals and robots can be a challenging problem, involving nonlinear dynamics and the coordination of many degrees of freedom. Differential geometry offers a vocabulary for discussing these dynamics in terms of lengths, areas, and curvatures. In particular, a tool called the *Lie bracket* combines these geometric concepts to describe the effects of cyclic changes in the locomotor’s shape, such as the gaits used by walking or crawling systems.

In this talk, I will review some basic principles of differential geometry and Lie group theory, and show how they provide insight into the locomotion of undulating systems (such as snakes and micro-organisms). I will then discuss my work on how coordinate representations affect the information provided by the geometric structures, and show that the choice of coordinates for a given system can be optimized in a simple, fundamental manner. Building on these results, I will demonstrate that the geometric techniques are useful beyond the “clean” ideal systems on which they have traditionally been developed, and can provide insight into the motion of systems with considerably more complex dynamics, such as locomotors in granular media.

 

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