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.
CITATION STYLE
Dubois, F., Fortuné, D., Quintero, J. A. R., & Vallée, C. (2015). Pontryagin calculus in riemannian geometry. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9389, pp. 541–549). Springer Verlag. https://doi.org/10.1007/978-3-319-25040-3_58
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