Abstract—

Relevant problems on modeling mechanisms with elastic links imply the improvement of existing formalisms and algorithms for dynamic analysis, synthesis, and optimal control of the considered class of systems. At the same time, modern research in this area is mainly focused on increasing the speed of computational algorithms without decreasing in the accuracy. If elastic multi-link dynamical systems that do not include closed kinematic chains can be comprehensively investigated using the approach without inversion of the mass matrix (generalized Newton-Euler method), then elastic mechanisms with closed kinematic chains should be studied using the methods with inversion of the mass matrix. The latter class includes the problem on finding the conditional minimum of the action functional in the sense of Ostrogradsky in the presence of holonomic (geometric) additional constraints. In this article, we analyze the problem on optimizing the motion of an elastic three-link tracking manipulator that consists in minimizing the function of deviation of the actuator from a predetermined circumferential trajectory. This problem is also reduced to finding the conditional minimum of the Ostrogradsky action functional in the presence of a holonomic additional constraint.

中文翻译：

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优化弹性跟踪操纵器的问题

摘要-

有关具有弹性链接的建模机制的相关问题意味着改进了现有形式主义和算法，以对所考虑的系统类别进行动态分析，综合和最佳控制。同时，该领域的现代研究主要集中在提高计算算法的速度而又不降低精度的情况下。如果可以使用不对质量矩阵求逆的方法（广义牛顿-欧拉方法）对不包含运动链闭合的弹性多连杆动力学系统进行全面研究，则应使用求逆方法研究运动链闭合的弹性机理。质量矩阵 后一类包括在存在完整的（几何）附加约束的情况下在Ostrogradsky的意义上找到作用函数的条件最小值的问题。在本文中，我们分析了优化弹性三连杆跟踪操纵器运动的问题，该问题在于最大程度地减小执行器与预定圆周轨迹的偏离功能。这个问题也减少到在存在完整的附加约束的情况下找到Ostrogradsky作用函数的条件最小值。