Research on Motion Path Optimisation Based on Geometric Model and Optimisation Algorithm

In this paper, a series of solutions based on geometric models and optimisation algorithms are proposed for the problem of motion optimisation of complex motion systems in space. Firstly, a mathematical model based on the helix equation is constructed, the position of each motion node is calculated using the polar coordinate system and recurrence relation, and the velocity of the node is calculated by the differential method [1]–[2]. In order to determine the time for the system to move along the helix to the termination point, a collision detection model is introduced in this paper, which combines the space division technique with an iterative algorithm to accurately locate the collision moment [3]–[4]. Subsequently, a pitch optimisation model is established with collision avoidance and boundary conditions as constraints, and the optimal pitch is solved by an iterative method [5]. In addition, a geometric relationship-based optimisation model for the turnaround curve was designed, and the curve length was optimised using the Powell optimisation algorithm [6]. Finally, this paper constructs a speed relation model under the maximum speed constraint to optimise the maximum travel speed of the system using the dichotomy method [7]–[8]. The accuracy of the model is verified by numerical differentiation, and the proposed method effectively solves the path optimisation and speed control problems of the motion system.