This paper presents a dynamic model based on the Archimedean spiral, focusing on the determination of the positions of the faucet and dragon body, collision detection, and pitch optimization. First, in the polar coordinate system, the geometric characteristics of the spiral and the numerical difference method are used to calculate the dynamic position of the faucet through the relationship between arc length and angle. Taking the faucet as the reference, the positions of each segment of the dragon body are derived, and the numerical difference method is used for iterative solution considering the interaction of velocity variables. Second, benches are regarded as line segments, and the convex hull method is used for collision detection. The Runge-Kutta method is employed to solve the faucet trajectory, and the collision threshold is determined by judging the distance between line segments and the intersection of convex hulls. Finally, a genetic algorithm optimization model is constructed with the goal of minimizing the pitch. By setting constraints such as collision detection and radial distance, and through encoding, fitness calculation, and genetic operations, the optimal pitch is obtained. This model achieves accurate calculation of motion trajectories and collision detection through the combination of multiple algorithms, providing an effective framework for dynamic trajectory planning.

Tianqi Xu. Research on Dynamic Trajectory Planning and Collision Detection Model Based on Numerical Difference Method and Genetic Algorithm. Academic Journal of Computing & Information Science (2025), Vol. 8, Issue 8: 35-42. https://doi.org/10.25236/AJCIS.2025.080806.

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