Curve Architecture Optimization Based on Multiple Search Algorithms

The purpose of this paper is to construct and analyze a model for collision detection and velocity regulation in curved architectures based on multiple search algorithms using curve function and differential equation models. The study first calculates the arc length by curve equations and first-class curve integrals to determine the position and velocity of the curve architecture per second. Based on this, the differential equations of the polar angles of each part of the curved architecture are modeled with respect to time, and the approximate solutions are obtained using the Runge-Kutta method. Then, algebraic and geometric knowledge is applied to construct the position equations. In addition, this paper defines the collision conditions and constructs a collision detection model by an iterative method to finally derive the termination time. Finally, the relationship between the inverse curvature distance and the Euclidean distance between the parts of the curve architecture is demonstrated for the speed control aspect, and the multiple search algorithm is used to perform an accurate search and derive the minimum curvature distance corresponding to the maximum Euclidean distance. The results of this paper provide an effective optimization scheme for curved architectures, which is especially important in areas such as machine motion planning.