METHOD FOR PLANNING THE OPTIMAL TRAJECTORY OF A THREE-LINK MANIPULATOR IN TRIDIMENSIONAL SPACE WITH AN OBSTACLE

Abstract

Objectives. The method for planning the optimal trajectory of a three-link manipulator with 7 degrees of mobility in a tridimensional space containing an obstacle specified by an array of points of three-dimensional space and represented in the form of a sphere is considered in the article. A literature review on the research problem indicates that universal methods for planning the trajectory of the manipulator's movement are faced with problems of operational low accuracy or the algorithm's large computational complexity. The aim of the study is to develop methods for planning the optimal trajectory of a three-link manipulator in a tridimensional space with an obstacle. Methods. The study was carried out using the method of iterative piecewise linear approximation of the trajectory of an anthropomorphic manipulator and the choice of the optimal displacement trajectory according to the criterion of energy efficiency. Results. The method for planning the optimal trajectory of a three-link manipulator with 7 degrees of mobility in a tridimensional space containing an obstacle specified by an array of points of three-dimensional space and represented in the form of a sphere is considered in the article. The task is reduced to finding the Euler angles of the manipulator engines in order to pass to the final position either directly or using the developed method of searching for intermediate positions to achieve the result. The choice of the optimal trajectory for the obstacle bypass is made using the criterion of minimisation of the manipulator power consumption for the continuous operation of the mobile manipulative or anthropomorphic robot in offline mode. Conclusion. The method of planning the optimal trajectory of a three-link manipulator with 7 degrees of mobility in a three-dimensional space containing an obstacle specified by an array of points and represented in the form of a sphere possesses flexibility, which is achieved by varying the input parameter. Its increase makes the manipulator's movement more angular by reducing the number of intermediate states, which reduces computational costs while increasing energy costs and reducing the movement speed. Conversely, decreasing the parameter reduces energy consumption and increases the speed, but also increases computational costs, as the number of intermediate states increases and the movement becomes smoother. However, in order to reduce the estimated time, it is assumed that parallel calculations are used in calculating the Euler angles for the engines during the movement between the intermediate points, which greatly speeds up the calculation process. With the value of h=0, the trajectory degenerates into a curve and the application of the proposed method is not justified.