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Optimización de trayectorias para sistemas sujetos a restricciones no holónomas

Keywords: nonholonomic systems, optimal control, numerical optimization, mobile robotics.

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Abstract:

this paper presents a numerical strategy to compute feasible trajectories for driftless systems under nonintegrable differential constraints that minimize the norm of the control. we made use of optimal control tools and nonlinear programming to formulate and solve the optimization problem. first, we analyze the necessary conditions to be satisfied by the optimal control. then, we transform the infinite-dimensional problem into a finite-dimensional nonlinear optimization problem. this formulation allows us to generate the desired trajectories by using a simple and efficient strategy based on the sequential quadratic programming (sqp). we compare the proposed strategy with the algorithm developed by [fernandes, et al., 1994], in terms of convergence and computational time, by using various kinematic models of mobile robots with wheels, chained systems and a dynamic model of space robot.

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