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arXiv · 2304.10959

Riemannian formulation of Pontrygin's principle for robotic manipulators

François Dubois·Hedy César Ramírez-De-{Á}vila·Juan Antonio Rojas-Quintero
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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.

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François Dubois, Hedy César Ramírez-De-{Á}vila, Juan Antonio Rojas-Quintero. 2023-04-21. Riemannian formulation of Pontrygin's principle for robotic manipulators. https://arxiv.org/abs/2304.10959

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