Escaping Local Minima in Path Planning Using a Robust Bacterial Foraging Algorithm
Abstract
:1. Introduction
- A unique idea of virtual obstacles is introduced that effectively helps the robots to recover from the local minima;
- The information about the virtual obstacles is shared among the whole swarm and can be utilized to pre-plan the route without conflicting with the same local minima;
- The proposed strategy is not computationally intensive; therefore, it can be easily utilized in real-time applications.
2. Preliminaries
2.1. Artificial Potential Field (APF)
2.1.1. Attractive Potential
2.1.2. Repulsive Potential
2.1.3. Total Potential
2.2. Bacteria and Bacterial Foraging Optimization
3. Implementation Details
3.1. The Robot’s Trajectory Process
3.2. Different Shapes of Obstacles
3.3. Robust Bacterial Foraging (RBF) Algorithm
Algorithm 1 Pseudocode of the robust bacterial foraging (RBF) algorithm. |
Input: ${q}_{s},{q}_{g},{d}_{min},{N}_{s},dis$ Procedure: Initialize robot position, $q\leftarrow \phantom{\rule{4pt}{0ex}}{q}_{s};$ ${l}_{o}\leftarrow 1;\phantom{\rule{3.33333pt}{0ex}}{l}_{p}\leftarrow 0;\phantom{\rule{3.33333pt}{0ex}}i\leftarrow 0;\phantom{\rule{3.33333pt}{0ex}}j\leftarrow 0;$ $d\leftarrow \u2225q-{q}_{g}\u2225;$ while $\left(d\ge {d}_{min}\right)$ ${l}_{p}\leftarrow {l}_{p}+1;$ while$i\le {N}_{s}$ generate random bacterium ${N}_{s}$ around q in radius $R;$ use Equation (9) to calculate the next point; use Equations (10)–(12) to calculate ${J}_{o}$, ${J}_{g}$, and $J;$ compute error using Equations (13) and (14); $i\leftarrow i+1;$ endwhile $i\leftarrow 0;$ sort cost function error in Equation (14); select best bacterium; $q\leftarrow bestpoint;$ save the trajectory, $T\left({l}_{p}\right)\leftarrow q;$ if robot falls in local minima then ${p}_{vo}\leftarrow q;$ $j\leftarrow {l}_{p};$ while $\u2225q-T\left(j\right)\u2225\le dis$ $j\leftarrow j-1;$ endwhile $virobstale\left({l}_{o}\right)\leftarrow {p}_{vo};$ ${l}_{o}\leftarrow {l}_{o}+1;$ use additional cost function in Equation (15) to reach a specific trajectory point, $q\leftarrow T\left(j\right);$ endif update $d;$ endwhile Output: Location of the virtual obstacles and trajectory of the robot. |
3.4. Local Minima Criterion
4. Results and Discussion
4.1. Scenario 1: Cases without Local Minima Problem
4.1.1. Case 1: Static and Moving Obstacle
4.1.2. Case 2: Three Obstacles Intercepting the Path
4.1.3. Case 3: An Obstacle on a Direct Path
4.2. Scenario 2: Cases with Local Minima Problem
4.2.1. Case 1: Two Circular-Shaped Obstacles Lying Close to Each Other
4.2.2. Case 2: L-Shaped Obstacle
4.2.3. Case 3: U-Shaped Obstacle
4.2.4. Case 4: Virtual Obstacles’ Information Exchange among the Robots
5. Conclusions and Future Work
- When the starting point is near a local minimum or over a local minimum, the robot becomes unable to return to a specific distance placed in its memory; hence, it stops moving;
- When the robot encounters a closed-form obstacle, it keeps on generating virtual obstacles in order to avoid the actual obstacle. Doing so fills the space with virtual obstacles, disrupting the forward motion.
Author Contributions
Funding
Conflicts of Interest
References
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Abdi, M.I.I.; Khan, M.U.; Güneş, A.; Mishra, D. Escaping Local Minima in Path Planning Using a Robust Bacterial Foraging Algorithm. Appl. Sci. 2020, 10, 7905. https://doi.org/10.3390/app10217905
Abdi MII, Khan MU, Güneş A, Mishra D. Escaping Local Minima in Path Planning Using a Robust Bacterial Foraging Algorithm. Applied Sciences. 2020; 10(21):7905. https://doi.org/10.3390/app10217905
Chicago/Turabian StyleAbdi, Mohammed Isam Ismael, Muhammad Umer Khan, Ahmet Güneş, and Deepti Mishra. 2020. "Escaping Local Minima in Path Planning Using a Robust Bacterial Foraging Algorithm" Applied Sciences 10, no. 21: 7905. https://doi.org/10.3390/app10217905