Abstract
This paper proposes an optimization method for motion of non-holonomic mechanical systems. In such system, the number of degrees of freedom is less than the number of independent generalized coordinates, so the number of independent velocities (also the number of independent accelerations) is less than the number of independent coordinates. This makes it difficult to determine the boundary conditions for the system of motion equations. In this paper, the principle of compatibility and the method of transformation matrix are used to directly build the equations of motion of the constrained dynamics system in the form of ordinary differential equations (ODEs) avoiding the use of Lagrange multipliers and then the Pontryagin’s maximum principle is used to solve the optimization of dynamics problem. A selection of boundary condition for Hamiltonian costate variables is also proposed. For illustration, the optimal control for the steering motion of an automobile while satisfying the non-holonomic constraints is carried out.
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Khoa, D.D., Kien, T.S., Phong, P.D., Sanh, D. (2022). An Optimization Method for Dynamics of Non-holonomic Systems. In: Khang, N.V., Hoang, N.Q., Ceccarelli, M. (eds) Advances in Asian Mechanism and Machine Science. ASIAN MMS 2021. Mechanisms and Machine Science, vol 113. Springer, Cham. https://doi.org/10.1007/978-3-030-91892-7_12
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DOI: https://doi.org/10.1007/978-3-030-91892-7_12
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