High-Speed Motion Control of Mechanisms under Average Heat Generation Restriction. 3rd Report. Trajectory Planning Method of Three-Degrees-of-Freedom SCARA-Type Robotic Manipulator with Short Calculation Time.

Abstract

The objective of this paper is to solve the minimum-time trajectory planning problem of a robotic manipulator under both the average heat generation restriction and the intermediate state variable restriction. We have already proposed a new numerical method to solve this problem in which the trajectory is approximated by the fifth-order Hermite polynomial expression. In analyzing a many-degrees-of-freedom manipulator, however, this method cannot be carried out within a short calculation time because of its duplicated iterative calculation procedure. To reduce the calculation time, we investigated the properties of the method and found two useful characteristics. The first characteristic is that the duplicated iterative calculation is not necessary when the robotic manipulator is a conservative system in a mechanical sense. The second one is that the polynomial solution can be derived when the robotic manipulator is governed by the constant coefficient linear differential equations. Using these characteristics, we constructed the trajectory planning method, which can generate the trajectory of the three-degrees-of-freedom SCARA-type robotic manipulator within a short calculation time. Numerical examples were shown to prove that the proposed method was practical enough to be applied to industrial robotic manipulators.