articles

The research is devoted to the development of an algorithm for applying the quaternion formalism to the modeling of the dynamics of exoskeletons and similar anthropomorphic mechanisms, such as robots, space suits, simulators, and related systems. The fundamental problem of developing exoskeletons, anthropomorphic mechanisms, and robotic systems is being investigated, which requires accelerating the process of analytical construction of mathematical models described by differential equations. To tackle this problem, the authors propose the use of hypercomplex number algebra, specifically quaternions. The application of quaternion algebra to the study of locomotion in anthropoid robotic devices such as exoskeletons with active propulsion systems that control the relative positions of the joints during movement should improve the construction of the mathematical model. These arguments determine the relevance of the research topic and the scientific novelty of the study. The development of high-speed methods for writing differential equations of motion based on quaternion algebra to describe the locomotion of spatial mechanical anthropoid systems determines the practical significance of the research results. The work presents a method for constructing an algorithm to model the dynamics of the shank of an exoskeleton, represented as a link connected by a spherical joint allowing rotation with respect to a fixed reference frame. The proposed mechanical model has been implemented as a program within the universal computer algebra system Wolfram Mathematica. The program is designed for simulating the dynamics of the exoskeleton link. Since the system does not provide built-in functions for working with analytically defined quaternions, the authors developed the required routines themselves. The program consists of several modules: a module for quaternion operations; a module for transformation matrices (used for validation and debugging of the quaternion module); a module for the automated formulation of the Lagrange equations of the second kind; a module for specifying the programmed motion of the model and computing the control torques in the joints; a module for numerically solving the Cauchy problem; and a module for animation and visualization of the model’s motion as well as for exporting the graphical results of the numerical simulations. The program’s results allow for the analysis of the dynamics of a mathematical model of a system based on the solution of the direct and inverse dynamics problem, and can be recommended for the design of exoskeletons, anthropomorphic robots, and manipulators with a programmable operating mode.