Riemannian formulation of Pontrygin's principle for robotic manipulators
Optimization and Control
2023-04-24 v1
Abstract
In this work, we consider a mechanical system whose mass tensor implements a scalar product in a Riemannian manifold. This system is controlled with the help of forces and torques. A cost functional is minimized to achieve an optimal trajectory. In this contribution, this cost function is supposed to be an arbitrary regular function invariant under a change of coordinates. Optimal control evolution based on Pontryagin's principle induces a covariant second-order ordinary differential equation for an adjoint variable featuring the Riemann curvature tensor. This second order time evolution is derived in this contribution.
Keywords
Cite
@article{arxiv.2304.10959,
title = {Riemannian formulation of Pontrygin's principle for robotic manipulators},
author = {François Dubois and Hedy César Ramírez-De-{Á}vila and Juan Antonio Rojas-Quintero},
journal= {arXiv preprint arXiv:2304.10959},
year = {2023}
}