Concerning the problem of tooth movement path planning in virtual orthodontic treatment system, a method of tooth movement path planning based on simplified mean particle swarm with normal distribution was proposed. Firstly, the mathematical models of single tooth and whole teeth were established. According to the characteristics of tooth movement, the orthodontic path planning problem was transformed into a constrained optimization problem. Secondly, based on the simplified particle swarm optimization algorithm, a Simplified Mean Particle Swarm Optimization based on the Normal distribution (NSMPSO) algorithm was proposed by introducing the idea of normal distribution and mean particle swarm optimization. Finally, a fitness function with high security was constructed from five aspects:translation path length, rotation angle, collision detection, single-stage tooth moving amount and rotation amount, so as to realize the orthodontic movement path planning. NSMPSO was compared with basic Particle Swarm Optimization (PSO) algorithm, the mean Particle Swarm Optimization (MPSO) algorithm and the Simplified Mean Particle Swarm Optimization with Dynamic adjustment of inertia weight(DSMPSO) algorithm. Results show that on Sphere, Griewank and Ackley, these three benchmark test functions, this improved algorithm tends to be stable and convergent within 50 iteration times, and has the fastest convergence speed and the highest convergence precision. Through the simulation experiments in Matlab, the optimal path obtained by the mathematical models and the improved algorithm is verified to be safe and reliable, which can provide assisted diagnosis for doctors.

Aiming at the problem that the traditional artificial potential field method is easy to fall into trap area and local minimum in the path planning process, an improved artificial potential field method was proposed. Firstly, the concept of safe distance was proposed to avoid unnecessary paths, so as to solve the problems of long path length and long algorithm running time. Then, in order to avoid the robot being trapped in the local minimum and trap area, the predictive distance was introduced into the algorithm, so that the algorithm was able to react before the robot being trapped in the local minimum or trap area. Finally, the robot was guided to avoid the local minimum and trap area by setting the virtual target points reasonably. The experimental results show that, the improved algorithm can effectively solve the problem that the traditional algorithm is easy to fall into the local minimum and trap area. At the same time, compared with those of the traditional artificial potential field method, the path length planned by this proposed algorithm is reduced by 5.2% and its speed is increased by 405.56%.