2020/01/25 by Colombo, Leonardo J., de Diego, David Martín, Nayak, Aradhana +1
#22E70 #37J15 #37K05 #37M15 #37N35 #49J15 #91B69 #93C10 #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2001.10346
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the distribution which defines the nonholonomic constraints. The problem is studied from a geometric framework. Optimality conditions are determined by the Pontryagin Maximum Principle and also from a variational point of view, which allows the construction of geometric integrators. Examples and numerical simulations are shown to validate the results.