Abstract
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 Vallée.
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Dubois, F., Fortuné, D., Rojas Quintero, J.A., Vallée, C. (2015). Pontryagin Calculus in Riemannian Geometry. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_58
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DOI: https://doi.org/10.1007/978-3-319-25040-3_58
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