Personnal implementation of a variational integrator for the simulation of dynamical systems in comparison with a Runge-Kutta 45 integrator. A simple pendulum with one DoF is used as a test case using biorbd.
Ressources:
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E. R. Johnson and T. D. Murphey, "Scalable Variational Integrators for Constrained Mechanical Systems in Generalized Coordinates," in IEEE Transactions on Robotics, vol. 25, no. 6, pp. 1249-1261, Dec. 2009, doi: 10.1109/TRO.2009.2032955.
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Wilson Jallet, Nicolas Mansard, Justin Carpentier. Implicit Differential Dynamic Programming. International Conference on Robotics and Automation (ICRA 2022), IEEE Robotics and Automation Society, May 2022, Philadelphia, United States. ff10.1109/ICRA46639.2022.9811647ff. ffhal-03351641v2f
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M. West, “Variational integrators,” Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2004. p 13 https://thesis.library.caltech.edu/2492/1/west_thesis.pdf
This project was used as a first stage to implement discrete mechanics and optimal control in bioptim.