Development of a model for constructing the optimal trajectory of the gripping device of a collaborative robot-manipulator taking into account the influence of the cargo mass and energy consumption

Abstract

In the current conditions of the development of Industry 5.0, collaborative robotic systems play a key role in increasing the efficiency of production processes, ensuring flexibility and safety of interaction with humans. One of the most critical elements of such systems is the gripping device of a collaborative robot-manipulator, which performs precise and energy-dependent actions in a complex dynamic environment. Given the constant change in the mass of the transported cargo and the limited energy resources, there is an urgent need to develop an optimal trajectory of movement that takes into account not only geometric constraints, but also the energy feasibility of the manipulator's movement. The relevance of the study is due to the need to reduce energy consumption when performing tasks of gripping and transporting objects in the presence of spatial obstacles, which is important for increasing the autonomy and productivity of robotic systems.The object of the study is the process of spatial movement of the gripping device of a collaborative robot-manipulator. The subject of the study is the optimization of the trajectory of movement taking into account dynamic constraints, variable cargo mass and energy consumption. The methods of mathematical modeling, numerical integration, energy analysis and spatial visualization of trajectories were used in the study. The basis for the formalization of the trajectory construction process is a system of motion dynamics equations, on which optimality conditions are imposed, taking into account energy consumption and avoidance of collisions with obstacles. The purpose of the study is to build a mathematical model and implement an algorithm for forming the optimal trajectory of the gripping device in 3D space, which allows minimizing energy consumption when transporting objects, taking into account their mass and existing obstacles. The results of the study include the construction of the optimal trajectory under given spatial constraints, substantiation of its effectiveness based on comparison with variable trajectories, as well as numerical confirmation of the reduction of energy consumption during the movement. The resulting model demonstrates the potential for implementation in collaborative robot control systems in real-time conditions. Based on the developed mathematical model, further research using the Pontryagin maximum principle in continuous time is recommended to develop analytical solutions and improve the control system for more complex trajectory planning problems under variable loads and complex obstacles.