Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems
Optimization and Control
2020-01-29 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.2001.10346,
title = {Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems},
author = {Leonardo J. Colombo and David Martín de Diego and Aradhana Nayak and Rodrigo T. Sato Martín de Almagro},
journal= {arXiv preprint arXiv:2001.10346},
year = {2020}
}
Comments
21 pages, 22 figures. arXiv admin note: text overlap with arXiv:1901.10374