Abstract

A problem of the synthesis of programmed motions of mechanical systems based on the use of time polynomials is considered. The programmed trajectory is selected in the class of monotonic third-order polynomials on the given time interval based on the initial and final states of the system, as well as constraints on the state and control variables. The problem of taking into account the restrictions is solved analytically by choosing the time of the movement. In particular, a programmed motion with zero initial and final values of the generalized velocities and accelerations is constructed, which satisfies the required constraints on the values of generalized coordinates, velocities and accelerations. The proposed approach to plan motion trajectories taking into account the constraints is illustrated by the example of solving the motion control problem for a parallel delta robot.

中文翻译：

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使用三阶多项式构造受约束机械系统的程序运动

摘要

考虑了基于时间多项式的机械系统的编程运动的综合问题。根据系统的初始状态和最终状态以及状态和控制变量的约束，在给定的时间间隔内，在单调三阶多项式类别中选择编程轨迹。考虑到限制的问题可以通过选择运动时间来解析地解决。特别地，构造了具有零的广义速度和加速度的初始值和最终值的程序运动，其满足了对广义坐标，速度和加速度的值的要求约束。