Pontryagin calculus in Riemannian geometry  Danielle Fortune, Francois Dubois, Juan Antonio Rojas Quintero

Author: Danielle Fortune, Francois Dubois, Juan Antonio Rojas Quintero
DOI URL: http://dx.doi.org/10.1007/9783319250403_58
Video: http://www.youtube.com/watch?v=uiOKLhoh3IA
Slides: Dubois Pontryagin calculus Riemannian.pdf
Presentation: https://www.see.asso.fr/node/14340
Creative Commons AttributionShareAlike 4.0 InternationalAbstract:
In this contribution, we study systems with a finite number of degrees of freedom as in robotics. A key idea is to consider the mass tensor associated to the kinetic energy as a metric in a Riemannian configuration space. We apply Pontryaginâ€™s framework to derive an optimal evolution of the control forces and torques applied to the mechanical system. This equation under covariant form uses explicitly the Riemann curvature tensor.