Modeling the dynamics of an exoskeleton link of variable length using the Lagrange – Maxwell system of differential equations of motion

Abstract

The objective of the study is the development of 3D variable-length link model with electric drives to be used in designing of next-generation comfortable exoskeletons. The developed link model has two inertial absolutely rigid sections on its ends and a variable- length section, considered weightless, in between. The mechanical part of the variable-length link model has been implemented in the universal computer math "Wolfram Mathematcia 11.3" environment by building the system of Lagrange – Maxwell differential equations. The electro-mechanical link model with electric drives has been implemented in the MatLab Simulink environment. The implemented model includes the following units: the trajectory synthesis unit per each degree of freedom, the unit for controlling torques calculation based on differential equations of motion, the unit for selecting electric motors with gears, the unit for calculating electric current per each motor and implementing the control system. The electric motors, reducers, rack and pinion gears implementing the specified and programmed link motion have been selected. The inertial and geometrical variable-length link parameters corresponding to the human tibia in the period of the single-support step phase have been selected. The drives implementing the link rotation are situated in the bottom link point in the combination of two orthogonal cylindrical hinges. One of these hinges is fixed to the supporting surface, the other one is fixed to the link end. This hinge combination simulates human ankle joint in the single-support step phase. The drive controlling the link length change is situated at the end of the bottom absolutely rigid weighty link section. The programmed trajectories for generalized coordinates are specified based on the simulation requirements of the anthropomorphic tibia motion. As a result, the electro-mechanical model of a variable- length link with parameters corresponding to the average man’s tibia has been developed. The drives and gears that allow implementing the motion close to anthropomorphic one have been selected. The implementation of this motion based on the developed software in the computer math "Wolfram Mathematica 11.3" environment and in the MatLab Simulink system has been demonstrated. The numerical calculations are presented.

Using neural-fuzzy inference to control the functioning of a human-machine system in the form of an exoskeleton with links of variable length, taking into account the effects of lag and synchronization of electric drives

“…The second problem is the significant expenditure of computer resources when composing equations of motion for multilink spatial models of exoskeletons, especially with links of variable length [1][2]. The use of relative angles between the links [3][4][5], rather than angles measured from a fixed directionvertical or horizontal, also increases time and labor intensity. If for a model with two links (Figure 1A), the time to compile a system of differential equations on a conventional office computer is a few seconds, for a model with three links about an hour (Figure 1 B), with four links (Figure 1 C) for about a day, then for a model with five links (Figure 1 D) it takes several days.…”

Comparative analysis of the dynamics of 3D electromechanical models of exoskeletons with 4 and 5 links of variable length and generalization to the case of an arbitrary finite number n of links

“…This form of notation can later be used in previously developed [11][12] high-speed matrix and recurrent algorithms for compiling systems of differential equations of motion, which significantly reduce the time for developing mathematical models of exoskeletons with control in hinges and in sections of variable length. Equations ( 2) are supplemented by the corresponding relations for the electrical control subsystem, which are written, for example, in the form of the Lagrange-Maxwell equations [13], which we will not dwell on in detail here.…”

Electromechanical model of exoskeleton with three mobile links

“…The exoskeleton models, previously developed by the authors, are presented in the papers. [1][2][3][4] The issues of simulating exoskeletons and anthropoid mechanisms with various actuators, including electric drives, are covered in the papers. [5][6][7][8][9][10] The studies are focused on some exoskeleton applications.…”