# Escaping Local Minima in Path Planning Using a Robust Bacterial Foraging Algorithm
## 1 Introduction
Recently, [24] proposed an improved version of APF, where they employed the concept of reward and penalty as in reinforcement learning (RL). More precisely, an additional force is introduced that helps the robot to avoid the local minimum. From a wide class of PP algorithms, BFO, proposed by [25], is relatively new and has a lot of potential as it can find an optimal path quite effectively. Using this path, a robot can prevent obstacles in the workspace, hence ensuring maximum safety. BFO is a simple and effective bio-inspired method of optimization that has solved many issues of engineering and mobile robotics, including problems related to PP [26]; however, the solution is not always guaranteed. Ideally, BFO can encounter only single local minima, located at the desired configuration. In practice though, it can run into situations where the attractive and repulsive forces can produce local minima at unknown locations. The robot cannot estimate local minima in an unobserved environment. In other words, the simple control strategy based upon gradient may or may not converge to the goal. The local minima correspond to the local valleys, where the robot can get stuck. Avoidance of a local minimum in BFO has also been explored by some researchers; e.g., the authors in [27] claimed that the considered potential functions do not require gradient computation, and thereby do not suffer from local minima. An enhanced BFO proposed by [28] demonstrated that the mobile robot successfully avoids both static and dynamic obstacles. In a similar work [17], some authors explored the inherent characteristics of BFO in order to suggest an improved version of the basic BFO. However, most of these solutions only considered circular obstacles in order to support their claim. There is a strong chance that these approaches may not be able to avoid the local minima whenever non-circular obstacles are encountered. The main impetus of this work was to devise a PP strategy that has the ability to avoid being trapped in local minima whenever non-circular shaped obstacles are encountered in an unknown environment. For that purpose, a virtual obstacle is introduced to assist the robot in escaping a local minimum. The number of virtual obstacles is dependent upon the size of the obstacle. The proposed robust bacterial foraging (RBF) algorithm, can be thought of as an extension to the work of [17; 18]. Most existing works consider only the circular obstacles; therefore, the escape from local minima is not guaranteed against non-circular shaped obstacles. The proposed approach is quite reliable and is less complex; hence, it can be used for real-time PP. Additionally, the given approach can be extended to a swarm of robots, where the virtual obstacles' information is exchanged among them in order to reduce time and error. The major contributions of this paper are three-fold:  
1. A unique idea of virtual obstacles is introduced that effectively helps the robots to recover from the local minima;
2. 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;
3. The proposed strategy is not computationally intensive; therefore, it can be easily utilized in real-time applications. The remainder of the paper is organized as follows. Section 2 covers the basic knowledge about APF and BFO in order to better understand the proposed approach. The generation of an optimal path using the proposed algorithm is discussed in Section 3. Simulation results are displayed in Section 4 to validate the proposed approach, and brief concluding remarks and potential future topics are given in the last section.