论文标题
riemannian几何形状中的蓬蒂古宁微积分
Pontryagin calculus in Riemannian geometry
论文作者
论文摘要
在这项贡献中，我们像机器人技术一样研究具有有限自由度的系统。一个关键的想法是将与动能相关的大量张量视为Riemannian配置空间中的度量。我们应用蓬松金的框架来得出对机械系统应用的控制力和扭矩的最佳演变。协变形式下的该方程式使用Riemann曲率张量。此贡献是为了记忆Claude vall {é} E（1945-2014）。
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 Pontryagin'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. This contribution is dedicated to the memory of Claude Vall{é}e (1945-2014).
