Retraction maps in optimal control of nonholonomic systems
By: Alexandre Anahory Simoes , María Barbero Liñán , Anthony Bloch and more
Potential Business Impact:
Makes robots move more smoothly and precisely.
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct geometric integrators for the corresponding Hamilton equations. First, we obtain an intrinsic formulation of a discretization map on a distribution $\mathcal{D}$. Then, we illustrate this construction on a particular example for which the performance of different symplectic integrators is examined and compared with that of non-symplectic integrators.
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