Algorithm 1 PI control method with HGSO parameter regulator

Import: trajectory points Output: PI parameters and tracking trajectory Initialization: Initialize HGSO parameters, $N$, $M$, $X_i$ (about PI controller parameters $4K$), $H_j$, $P_{i,j}$, $C_j$, etc. using Equation (17) and Equation (18) ($i=1,\cdots ,N;j=1,\cdots M$) while t < the maximum number of iterations do  Set the $X_i$ obtained by HGSO to PI parameters $K$ for solving joint angles according to the part of PI controller.  Complete the evaluation of the current $X_i$ by Equation (24).  for each search gas particles do  Update the position information $X_i$ using Equation (21).  for end  Update Henry’s coefficient of each gas type clusters using Equation (19).  Update solubility of each gas using Equation (20)  Select the poor particles according to Equation (22) by $F_{fitness}$.  Reset the position of these worst particles by Equation (19) to Equation (21).  t = t + 1 while end return $X_{best}$ (The final optimized parameters $K$)