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.

中文翻译：

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Euler Elasticas用于轮式机器人运动的最佳控制：实验实现的问题

本文关注的是移动轮式机器人的最佳路径规划问题。确保控制动作最小化的欧拉弹性体被认为是最佳轨迹。提出了一种构造控件的算法，该算法实现了以Euler elastica形式沿轨迹运动。讨论了该算法在实际应用中存在的问题和特点。特别地，分析沿着弹性体的加速和减速，以及在制造移动机器人时所产生的误差对遵循规定轨迹的精度的影响。还应特别注意以下问题，即沿着欧拉弹性带以最佳取向角度在预设点上形成最佳运动轨迹。