Regularization of the movement of a material point along a flat trajectory: application to robotics problems

TL;DR

This paper addresses the control of a material point moving along a predefined flat trajectory, formulating it as an optimal control problem with energy-based cost functional and providing numerical solutions for various trajectories.

Contribution

It introduces a novel approach to trajectory control by reducing the problem to a fourth-order differential system and demonstrates its effectiveness through numerical examples.

Findings

Effective control solutions for straight, circular, and elliptical trajectories.

Reduction of the control problem to a fourth-order differential system.

Numerical validation of the proposed method.

Abstract

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.