Optimizing coordinate choice for locomotion systems with toroidal shape spaces

摘要: In a geometric mechanics framework, the configuration space is decomposed into shape and position space. The internal motion of system prescribed by closed loop in space, which causes net If simply connected domain an Euclidean then with optimal choice body frame, displacement reasonably approximated surface integral height function, functional relationship between variables. Our recent work has extended scope methods from limbless undulatory to those legs; interestingly, for such systems torus structure. However, best our knowledge, frame on was not explored. this paper, we develop method optimally choose results good approximation function. We apply centipede locomotion observe quantitative agreement prediction experimental results.