The control problem of the working tool movement along a predefined trajectory is considered. The integral of kinetic energy and weighted inertia forces for the whole period of motion is considered as a cost functional. The trajectory is assumed to be planar and defined in advance. The problem is reduced to a system of ordinary differential equations of the fourth order. Numerical examples of solving the problem for movement along straight, circular and elliptical trajectories are given.

中文翻译：

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物质点沿平坦轨迹运动的正则化：在机器人问题中的应用

考虑了工作工具沿预定轨迹运动的控制问题。整个运动周期的动能和加权惯性力的积分被认为是成本函数。轨迹被假定为平面并预先定义。问题简化为四阶常微分方程组。给出了求解沿直线、圆形和椭圆轨迹运动问题的数值例子。