Mathematical modeling of an active exoskeleton in the form of an electromechanical model containing three movable, controlled links interconnected by hinges has been carried out. For the considered mathematical model of the active exoskeleton, differential equations of motion are proposed. Numerical methods are used to solve the inverse and direct problems of dynamics in the created software package in the environment of the universal system of computer mathematics. A comprehensive study has been carried out, considering the problems of exoskeleton control, in the form of solving inverse and direct problems of dynamics, in relation to the created mathematical model of three moving parts of the exoskeleton, taking into account electric drives, using modern methods of mathematical modeling. Analytically determined are the angles between the links that define the anthropoid movement. Solving the inverse problem of dynamics, the moments controlling the movement of the links are calculated for each electric drive. The found moments are approximated by stepwise piecewise-constant functions simulating the impulse control of the exoskeleton motion. Dependences of the angular coordinates describing the positions of the links of the active exoskeleton over time are found. A comparative analysis of the numerical solution of the Cauchy problem for the mathematical model of the exoskeleton in the form of differential equations with the initial, given movement of the links is carried out. A good agreement between the results of simulation with impulse control and the original motion is established. The total energy costs have been calculated. Modeling is carried out taking into account the presence of electric drives: dynamic equations for this model are compiled. The Cauchy problem for the system is numerically solved taking into account the presence of electric drives. As a result of applying qualitative, analytical and numerical methods for studying the created mathematical model of three moving parts of the exoskeleton, taking into account the presence of electric drives, the significance of the influence of electric drives on the dynamics of the mechanism was established. The implementation of the electromechanical model of the three links of the exoskeleton was carried out in the environment of the universal system of computer mathematics “Wolfram Mathematica 11.3”.
Key words
exoskeleton, mathematical model, moving coordinate systems, Lagrange equations of the second kind, control moments, electric drives, angular coordinates, angular velocities, angular accelerations, energy consumption, numerical methods, software package, computer mathematics system
