# Joints Trajectory Planning of Robot Based on Slime Mould Whale Optimization Algorithm
## 1 Introduction
### Literature Review
The Wolf optimization algorithm and particle swarm optimization (PSO) algorithm were compared. The improved algorithm is more accurate and is faster. In terms of energy optimization, [PERSON] et al. [17] used B-spline curves and variational method to optimize the trajectory of redundant robots. [PERSON] et al. [18] combined a genetic algorithm and an adaptive simulated annealing algorithm. The minimum moment was set as the optimization objective for trajectory optimization. [PERSON] et al. [19] established a distributed dynamic physical model of a variable stiffness flexible robotic arm based on [PERSON]'s theory. The minimum vibration displacement, minimum energy consumption, and minimum trajectory tracking deviation were taken as the performance objectives. The motion trajectory planning of the variable stiffness flexible robotic arm was carried out based on a cloud adaptive differential evolution (CADE) optimization algorithm. For multi-objective optimization, [PERSON] et al. [20] used the penalty function method to improve the objective function in the optimization process for the constraint problem. The improved objective function was solved by an improved genetic algorithm with elite strategy, and the diversity of the solution set was maintained. Different penalty costs for different levels of objective functions were significantly improved in terms of solution speed and efficiency. Based on the quintic non-uniform rational B-spline (NURBS) curve mathematician, taking the running time, energy consumption and trajectory pulsation as the objectives, [PERSON] et al. used the non-dominated sorting genetic algorithm with an elitist strategy [21] (NSGA-II) and multi-objective particle swarm optimization algorithm [22] (MOPSO) to optimize the trajectory of industrial robots, respectively. The Pareto optimal solution set was obtained, and the normalized weight objective function was constructed to obtain a high-order continuous optimal trajectory. [PERSON] et al. [23] fitted the trajectory of the robot joint space by the high-order polynomial interpolation method based on the particle swarm optimization algorithm to ensure the stability of the joint motion according to the kinematics characteristics of the robot. The algorithm structure is simple and easy to implement. [PERSON] et al. [24] achieved a fast convergence of error-free smooth continuous trajectories by the grey wolf optimization (GWO) method setting the tracking error, acceleration, etc. as the optimization objective. In the case of the consideration of multiple obstacles, taking time and energy consumption as optimization objectives, [PERSON] et al. [25] used fourth- and the fifth-order polynomials as interpolation curves to fit the joint trajectory and an optimal trajectory under relevant constraints, based on a genetic algorithm, was obtained. [PERSON] et al. [26] constructed the trajectory of the manipulator in the joint space with the quintic B-spline interpolation method. An optimal objective function based on the time and average acceleration was then built and a hybrid optimization method of improved whale algorithm and particle swarm optimization (IWOA-PSO) was proposed. An effective time pulsation path planning algorithm was established. Vibration of the serial robot was reduced and working efficiency was improved. Setting the minimizing trajectory error, flight time and space as optimal objects, [PERSON] et al. [27] optimized the point-to-point motion planning in robot arm trajectory planning using non-dominated sorting genetic algorithm (NSGA-II), genetic algorithm (GA), artificial bee colony algorithm (ABC) and particle swarm optimization (PSO). The results were compared about the distance and time. Through the above analysis, it can be seen that the trajectory planning of the manipulator is mainly in the form of a polynomial or spline curve. The commonly used trajectory optimization algorithms mainly include particle swarm optimization (PSO) algorithms, genetic algorithms (GA), whale optimization algorithms (WOA), etc.