2024/02/20 by Bousclet, Anis, Boyer, Frederic, Chitour, Yacine +1
#93C20 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2402.13367
In this paper, we present an intrinsic derivation of the equations ruling the dynamics motion of a snake robot dynamics. Based on a Cosserat beam model, we first show that the extended configuration space is a Lie group. Endowing it with an appropriate left invariant metric, the corresponding Euler-Poincaré equations can be reduced to a system of hyperbolic PDEs in the Lie algebra \mathfrakse(3). We also provide the constitutive law describing the actuation in this system of PDEs.