# Joints Trajectory Planning of Robot Based on Slime Mould Whale Optimization Algorithm
## 1 Introduction
### Contribution and Organization  
The global search in the early stage and local search in the late stage of the WOA cannot jump out of the local optimal operation. Although the performance is excellent on simple problems, the optimization effect is unstable on complex problems. The slime mould optimization algorithm (SMA) [34] was proposed based on the diffusion and foraging behaviour of slime mould, which has the characteristics of fast convergence and strong optimization ability. In this paper, the WOA and SMA are fused, and the respective advantages of WOA and SMA algorithm are preserved. A hybrid whale slime mould optimization algorithm (SMVOA) is proposed, and the proposed algorithm is applied to the commonly used 6-DOF serial manipulator for joint trajectory optimization. The main innovations are as follows:  
Change the value of a in WOA. The value of parameter a is replaced by that of the SMA, which can be dynamically adjusted with the advance of iteration times to adapt to the complex nonlinear search process.  
The fitness weight \(\omega\) is introduced. The fitness weight in SMA can adaptively adjust the distance between the current individual and the optimal individual. After its introduc  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Based Algorithm** & **Improved Algorithm** & **Interpolation Method** \\ \hline \multirow{3}{*}{Particle swarm optimization (PSO)} & PSO [10; 23] & Quintic non-uniform rational \\  & & B-spline curve (NURBS) \\ \cline{2-3}  & Cosine reduced-weight PSO [13] & Cubic polynomial \\ \cline{2-3}  & Multi-objective PSO (MOPSO) [22] & Quintic B-spline curve \\ \hline \multirow{3}{*}{Genetic algorithm (GA)} & GA [15; 25] & Cubic B-spline curve \\  & & Fourth-fifth order polynomial \\ \cline{2-3}  & Adaptive Genetic Algorithm [11] & Cubic spline interpolation \\ \cline{2-3}  & Ranking Adaptive Genetic & \\  & Algorithm (RAGA) [14] & Quintic B-spline curve \\ \cline{2-3}  & Combining genetic algorithm and & \\  & adaptive simulated annealing & Cubic polynomial \\ \cline{2-3}  & & SUMTNSUA-II [20] & Quintic B-spline curve \\ \cline{2-3}  & Non-dominated sorting genetic & \\  & algorithm with elitist strategy & \\  & (NSGA-II) [21] & Quintic B-spline curve \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Whale optimization \\ algorithm (WOA) \\ \end{tabular} } & Improved WOA [16] & Quintic polynomial \\ \cline{2-3}  & IWOA-PSO [26] & Quintic B-spline curve \\ \hline \hline \end{tabular}
\end{table}
Table 1: Commonly used trajectory optimization algorithms.  
tion into WOA, searching range and speed can be adaptively adjusted to strengthen the global search ability and accelerate the convergence speed.  
The hybrid whale slime mould optimization algorithm (SMWOA) is proposed. The time optimal trajectory optimization of the six-joint manipulator is carried out with the cubic uniform B-spline interpolation method.  
The rest of this article is organized as follows: Section 2 introduces the basic principles of WOA and SMA. The SMWOA is proposed and introduced in detail in Section 3. The process of joint trajectory optimization based on the SMWOA is introduced in Section 4 where the optimization results are analysed. Section 5 summarizes the content of this paper.