| Abstract: |
| Consider the problem of optimizing the forward locomotion of a snake robot. Being limbless, this robot achieves motion by changing the shape of its body. We can therefore separate the configuration space of the robot into variables that represent the shape and variables that represent the displacement of the robot. This is the starting point for geometric mechanics.
In this talk I will describe how a principal bundle describes the geometry present in the snake robot mechanical system. The physical constraints on the system are encoded in a connection on this principal bundle. Parallel transport over a trajectory in shape space gives the forward displacement effected by that trajectory. Finally, I will describe how a metric on shape space gives a measure of efficiency as a trajectory. On a robot model, this efficiency is given by forward displacement divided by the electrical energy consumed during the trajectory. This is a natural quantity to optimize, and I will discus robot experiments to verify optimal efficiency. |
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