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Steering nonholonomic integrator using orthogonal polynomials

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Document pages: 10 pages

Abstract: We consider minimum energy optimal control problem with time dependentLagrangian on the nonholonomic integrator and and find the analytical solutionusing Sturm-Liouville theory. Furthermore, we also consider the minimum energyproblem on the Lie group $ mathbb{SO}(3)$ with time dependent Lagrangian.We show that the steering of nonholonomic integrator and generalizednonholonomic integrator can be achieved by using various families of orthogonalpolynomials such as Chebyshev, Legendre and Jacobi polynomials apart fromtrigonometric polynomials considered in the literature. Finally, we show how tofind sub-optimal inputs using elements from a family of orthogonal functionswhen the cost function is given by the $ mathcal{L} 1$ norm of the input.

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