On the Control of the Movement of Robots Due To Introducting Holonomic Quasi-Ideal Constraints

A method for studying the dynamics of motion of controlled mechanical systems is proposed. The method is based on the introduction of control actions as functions of the reactions of holonomic nonideal constraints. The physical meaning of the introduced functions is forces, the virtual work of which on virtual displacements of the original mechanical system is equal to zero. The introduction of such forces makes it possible to compose differential equations of motion in the traditional form of Lagrange equations with indefinite factors, and the determination of the optimal control by one criterion or another is reduced to determining the extremum of a function of many variables, in the simplest case, to establishing the coefficients of the linear transformation of the reactions of constraints. An example of a model problem is given.