In order to solve the problem of poor local optimization of the Slime Mold Algorithm (SMA) in the Travelling Salesman Problem (TSP), a Two-way Parallel Slime Mold Algorithm by Flow and Distance (TPSMA) is proposed in this paper. Firstly, the flow between each path point is calculated by the “critical pipeline and critical culture” model of SMA; then, according to the two indexes of flow and distance, the set of path points to be selected is obtained; finally, the optimization principle with a flow index is improved with two indexes of flow and distance and added random strategy. Hence, a two-way parallel optimization method is realized and the local optimal problem is solved effectively. Through the simulation of Traveling Salesman Problem Library (TSPLIB) on ulysses16, city31, eil51, gr96, and bier127, the results of TPSMA were improved by 24.56, 36.10, 41.88, 49.83, and 52.93%, respectively, compared to SMA. Furthermore, the number of path points is more and the optimization ability of TPSMA is better. At the same time, TPSMA is closer to the current optimal result than other algorithms by multiple sets of tests, and its time complexity is obviously better than others. Therefore, the superiority of TPSMA is adequately proven.

In order to solve the tracking accuracy problem of the redundant manipulator, a PI control method with Henry gas solubility optimization parameter regulator (PI-HGSO) is proposed in this paper. This method consists of the controller and the parameter regulator. The characteristic is that the position deviation of a manipulator is equivalent to a specific function; namely, the proportional-integral (PI) controller is used to adjust the deviation input. The error can be better corrected by the processing of the PI controller so that the inverse kinematics solution of the minimum error can be realized. At the same time, the parameter selection of PI controllers has always been a difficulty in controller design. To address the problem, Henry gas solubility optimization (HGSO) is selected as a parameter regulator to optimize the parameters and obtain the optimal controller, thereby achieving high-precision trajectory tracking. Experiments on 9-DOF redundant manipulator show that our method achieves competitive tracking accuracy in contrast with others. Meanwhile, the efficiency and accuracy of the PI controller are greatly guaranteed by using HGSO to automatically optimize controller parameters instead of making approximate adjustments through infinite manual trial and error. Therefore, the feasibility and competitive superiority of PI-HGSO is fully proved in trajectory planning of redundant manipulators.