Euler Elasticas for Optimal Control of the Motion of Mobile Wheeled Robots: the Problem of Experimental Realization
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This paper is concerned with the problem of optimal path planning for a mobile wheeled robot. Euler elasticas, which ensure minimization of control actions, are considered as optimal trajectories. An algorithm for constructing controls that realizes the motion along the trajectory in the form of an Euler elastica is presented. Problems and special features of the application of this algorithm in practice are discussed. In particular, analysis is made of speedup and deceleration along the elastica, and of the influence of the errors made in manufacturing the mobile robot on the precision with which the prescribed trajectory is followed. Special attention is also given to the problem of forming optimal trajectories of motion along Euler elasticas to a preset point at different angles of orientation. Results of experimental investigations are presented.
Keywordsmobile wheeled robot Euler’s elastica optimal control experimental investigations
MSC2010 numbers49K30 58E25 70Q05
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The authors extend their gratitude to A. A. Kilin, Yu. L. Sachkov and A. V. Klekovkin for fruitful discussions and useful remarks.
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