MOTION CONTROL ALONG A PREDETERMINED CURVE AND THE INVERSE PROBLEM OF DYNAMICS

The problem of controlling the movement of a mechanical system refers to the inverse problems of dynamics, involving the definition of expressions of forces under the action of which the mechanical system makes movements with specified properties. Most fully, these properties are expressed in the form of a requirement for the implementation of the movement of a given law or a given curve in the coordinate space. Thus, in [1] the problem of determining the forces in the coordinate functions of their application points, under the action of which the planets describe conical sections, was set. In [2] and [3] the expressions of force corresponding to the motion of a material point along a plane curve are determined. In [4] the solution of a problem of construction of a potential force field on the set family of trajectories of the representing point in multidimensional space is offered. Some modern methods for solving inverse dynamics problems are proposed in [5]. In this paper, we consider the problem of controlling the movement of a mechanical system along a given curve in the state space. Methods of construction of control forces depending on the coordinates of the mechanical system are proposed.