# Modular Robotic Design and Reconfiguring Path Planning
## 4 Simulation and Analysis of Path Planning for Module's Reconfiguration  
### Reconfiguration Path Simulation Experiment  
MATLAB models the reconfiguration platform environment and path planning simulation to verify the algorithm's effectiveness. Using the raster method for environment modeling, the algorithm parameters are set as shown in Table 3. The cooperative path planning of the clamping module and the interstitial module is an example in the simulation. The initial position of the clamping module is \"\(T_{1}\)\" (2,1) and the target point is \"\(E_{1}\)\" (13,20); the initial position of the interstitial module is \"\(T_{2}\)\" (1,3) and the target point is \"\(E_{2}\)\" (14,20). The raster method is used for environment modeling, and the basic ACO path planning method and the improved ACO path planning method proposed in this paper are compared in two experimental environments, respectively. The simulation results are shown in Figures 11-14. The solid red line in Figures represents the moving path \"\(L_{1}^{*}\)\" for the clamping function module, and the dashed blue line represents the moving path \"\(L_{2}^{*}\)\" for the interstitial function module.  
Figure 10: Flow chart of the optimization algorithm.  
Figure 11: Schematic diagram of the ant colony algorithm robot movement path (Environment 1). (a) Ant colony algorithm (b) Improved ant colony algorithm.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & \
\begin{tabular}{c} **Traditional Ant** \\ **Colony Optimization** \\ \end{tabular} &
\begin{tabular}{c} **Optimized Ant Colony** \\ **Optimization** \\ \end{tabular} \\ \hline Ant population & 50 & 50 \\ Iteration number & 100 & 100 \\ Pheromone inspired factor & 1 & 1 \\ Expectation heuristic factor & 3 & 3 \\ Pheromone evaporation factor & \(\rho_{0}\) & \(\rho_{0}+(1-p_{0})\frac{N}{N_{\text{max}}}\) \\ Distance heuristic factor & \(\frac{1}{d_{ij}}\) & \(\frac{1}{d_{ij}}\) \\ Nodal perspective heuristic factor & / & \(\frac{1}{d_{ij}+1}\) \\ Initial pheromone & Uniform distribution & Non-uniform distribution \\ Deadlock handling & / & Fallback strategy \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of algorithm parameter settings.  
Figure 12: Schematic diagram of the convergence curve change of the ant colony algorithm (Environment 1). (a) Ant colony algorithm (**b**) Improved ant colony algorithm.  
In the simulation results under the 20 \(\times\) 20 raster environment, the path planning graphs and iterative convergence curves of the basic ant colony algorithm and the improved ant colony algorithm proposed in this paper are shown respectively. From Figure 12, it can be concluded that in the set range of 100 steps, the traditional ant colony algorithm is difficult to converge the algorithm and there are still small fluctuations. The simulation results of the optimized algorithm show that the two types of functional modules converge at about 42 steps and 35 steps, respectively. The convergence efficiency has been increased and improved substantially. Moreover, the minimum path length is reduced by about 6.7%. The simulation results in experiment 2 are shown in Figures 13 and 14. The optimized simulation structure shows that the convergence efficiency of the two modules is improved by 12.5% and 26.7% respectively. The path length is also reduced by about 8.3%. In addition, it can be seen from the simulation path diagrams that the optimized path inflection point has been significantly reduced. In summary, the path planning method proposed in this paper has an obvious improvement effect and better search performance.  
Figure 14: Schematic diagram of the convergence curve change of the ant colony algorithm (Environment 2). (**a**) Ant colony algorithm (**b**) Improved ant colony algorithm.  
Figure 13: Schematic diagram of the ant colony algorithm robot movement path (Environment 2). (**a**) Ant colony algorithm (**b**) Improved ant colony algorithm.