Obstacle evasion using fuzzy logic in a sliding blades problem environment

Obstacle evasion using fuzzy logic in a sliding blades problem environment Shadrack Kimutai Information Communication Technology Department Rift Valley Technical Training Institute 244 Eldoret Kenya Tel: +254724226334 Shadrackkimutai@gmail.com Submitted on 1/5/2016 Abstract This paper discusses obstacle avoidance using fuzzy logic and shortest path algorithm. This paper also introduces the sliding blades problem and illustrates how a drone can navigate itself through the swinging blade obstacles while tracing a semi-optimal path and also maintaining constant velocity. General terms Theory, Algorithms, Management, Design Keywords Fuzzy Logic, Swinging Blades problem, Shortest Path Selection, Drones, Optimum Path to Goal, Obstacle Avoidance

Introduction The Current technological know-how in the field of computing, robotics and navigation is sufficient for development of self-navigated drones (robotic vehicles). In the recent years drones have become popular due to its ability to operate in environments that are hazardous to a human operator. Sadly though, nearly all drones be they space probes, submersibles or aircraft drones still rely on a human controller in areas such as navigating in environments consisting of chaotically moving Obstacles such as in the asteroid belt or in deep sea diving. Currently there are a handful of algorithms that offer good results example being the Virtual force field algorithm which has been in use for quite some time. This algorithm is based on the illusion that the robot repels the obstacle and tries any angle within 1800 to evade colliding with the object. While this method is extremely simple and practical in situations where the obstacle is static, it fails drastically with mobile obstacles as a result many other algorithms such as Kyongs Modified virtual force field (MVFF) (Kwon & Cho, 2006)which is a more robust algorithm capable of mapping an environment with mobile obstacles. The shortcoming of this algorithm is that it doesn’t factor in the shortest path approach to reaching the destination even when the ideal path is obstructed. Most of the methods identified (let alone a few like the General approach theory(Jaafar & McKenzie, 2007)) do not factor in the consideration of the optimal path redefinition hence resulting to the trajectory being followed being selected without considerations of its cost.(Yadav & Biswas, 2010) We will use a combination of fuzzy logic and shortest path first to establish the optimal path around obstacles between the source and the destination of the drone. To achieve this we are going to model the above scenario into the swinging blade problem which is a common test for navigation skills in gaming environments.

Approach to the Problem As identified above, we will use the swinging blade problem to establish our algorithm. Simply put swinging blade problem seeks to test the agent’s skill in navigating the swinging obstacles without colliding with either of them. It’s also important to state that the drone must have a 1800 “view” of the trajectory this may be possible through sensors such as sonar, edge mapping or any other technique that may deliver the same A typical environment in the swinging blade problem looks as shown below Whereby the dashed line shows the actual path followed and the bold straight line being the ideal path which also happens to be the shortest ideal path. This can be presented as follows

As per the diagram above the vectors Vd̃ represents the drone path while Võ represents the blade path Assume we draw the resultant vector diagram now that we have a clear picture of the problem is. We end up with this

From the abstracted diagram we can deduce the size of the object based on which we draw C Ṽo+Ṽd Ṽd-Ṽo A B E F D D Ṽo Ṽd D ṼṼ ṼṼ̃ o several scenarios we will later see, furthermore, at point D the drone must immediately calculate the following

1. The velocity vector Vo of the Obstruction and the rate it is approaching drone’s path.
2. Alternate paths to escape collision
3. Evaluate the cost of alternate paths Alternate paths include the following We also have to assume that velocity vectors Ṽo and Ṽd are equal a) if Sin BAC=Sin BDE favor path identified by vector Ṽ o+Ṽd =v᷉ b) if Sin BAC<Sin BDE Maintain path along Vector Ṽd c) if Sin BA᷉C > Sin BD᷉E favor vector Ṽ d-Ṽo=-ṽ if and only if the size of the blade which spans the angle <EDF should be smaller than <EDB else a new vector β̃ which is directly proportional to the size of the blade has to be added to –ṽ above so as to end up with –ṽ+β̃ We then map the above paths into our fuzzy relation as follows { 𝑣᷉ 0 −𝑣

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