# An Artificial Plant Community Algorithm for Collision-Free Multi-Robot Aggregation
## 6 Benchmark Data and Experiments
### Performance Comparison
\begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Method**} & \multicolumn{6}{c}{**Number of Robots**} \\  & & \(R_{max}\) = 1 & \(R_{max}\) = 3 & \(R_{max}\) = 5 & \(R_{max}\) = 7 & \(R_{max}\) = 9 & \(R_{max}\) = 11 & \(R_{max}\) = 13 & \(R_{max}\) = 15 \\ \hline APC & Makespan \(k_{T}^{make}\) & **0.887** & 0.685 & **0.576** & 0.515 & **0.478** & 0.463 & 0.452 & **0.443** & **0.562** \\  & Total collision time \(k_{T}^{total}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & 0.268 & 0.285 & **0.294** & **0.303** & 0.323 & 0.328 & **0.332** & **0.355** & **0.311** \\  & Total travel distance \(D_{T}^{travel}\) & 0.218 & 0.222 & 0.230 & **0.219** & 0.228 & 0.221 & 0.225 & **0.219** & **0.223** \\  & Solution time (s) & 509 & 521 & 524 & 533 & 537 & 544 & 556 & 565 & 536.1 \\ GWO & Makespan \(k_{T}^{make}\) & 0.938 & 0.693 & 0.587 & 0.529 & 0.501 & 0.478 & 0.467 & 0.448 & 0.580 \\  & Total collision time \(k_{T}^{total}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & 0.274 & 0.287 & 0.306 & 0.312 & 0.326 & 0.334 & 0.346 & 0.359 & 0.318 \\  & Total travel distance \(D_{T}^{travel}\) & 0.231 & 0.228 & 0.229 & 0.234 & 0.226 & 0.232 & 0.227 & **0.224** & 0.229 \\  & Solution time (s) & 504 & **506** & 519 & 520 & 541 & 538 & **543** & 564 & **529.4** \\ GA & Makespan \(k_{T}^{make}\) & 0.936 & 0.694 & 0.582 & **0.513** & 0.482 & 0.466 & **0.451** & 0.444 & 0.571 \\  & Total collision time \(k_{T}^{total}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & **0.267** & 0.295 & 0.308 & 0.319 & 0.324 & 0.339 & 0.350 & 0.367 & 0.321 \\  & Total travel distance \(D_{T}^{travel}\) & 0.218 & 0.226 & 0.228 & 0.231 & 0.229 & **0.220** & **0.219** & 0.225 & 0.225 \\  & Solution time (s) & 508 & 520 & 523 & 532 & **535** & 542 & 547 & **557** & 533.0 \\ PSO & Makespan \(k_{T}^{make}\) & 0.931 & **0.682** & 0.587 & 0.523 & 0.484 & 0.471 & 0.468 & 0.452 & 0.575 \\  & Total collision time \(k_{T}^{total}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & 0.283 & 0.301 & 0.302 & 0.308 & **0.319** & 0.332 & 0.343 & 0.361 & 0.319 \\  & Total travel distance \(D_{T}^{travel}\) & **0.217** & 0.227 & **0.218** & 0.228 & 0.223 & 0.225 & 0.231 & 0.228 & 0.225 \\  & Solution time (s) & 517 & 509 & 517 & 521 & 538 & 553 & 549 & 563 & 533.4 \\ ACO & Makespan \(k_{T}^{make}\) & 0.922 & 0.695 & 0.581 & 0.527 & 0.489 & **0.462** & 0.467 & 0.454 & 0.575 \\  & Total collision time \(k_{T}^{all}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & 0.287 & 0.294 & 0.312 & 0.313 & 0.325 & 0.329 & 0.335 & 0.372 & 0.321 \\  & Total travel distance \(D_{T}^{travel}\) & 0.222 & 0.229 & 0.231 & 0.225 & **0.221** & 0.226 & 0.228 & 0.229 & 0.226 \\  & Solution time (s) & **503** & 514 & **512** & 526 & 539 & 548 & 551 & 558 & 531.4 \\ DL & Makespan \(k_{T}^{make}\) & 0.892 & 0.689 & 0.582 & **0.513** & 0.481 & 0.464 & 0.453 & **0.443** & 0.565 \\  & Total collision time \(k_{T}^{coll}\) & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0** & **0.000** \\  & Total energy consumption \(e_{T}^{total}\) & 0.278 & **0.281** & 0.299 & 0.314 & 0.320 & **0.325** & 0.339 & 0.357 & 0.314 \\  & Total travel distance \(D_{T}^{travel}\) & 0.223 & **0.218** & **0.218** & 0.224 & 0.227 & 0.224 & 0.222 & 0.230 & **0.223** \\  & Solution time (s) & 1955 & 2083 & 2196 & 2221 & 2231 & 2238 & 2396 & 2476 & 2224.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of algorithms under varying numbers of robots. APC algorithm can search for the optimal solutions with fast convergence while effectively avoiding local optima.