Proceedings of 2015 Global Conference on Communication Technologies(GCCT 2015)
PSO based system architecture for Path Planning of Mobile Robot in Dynamic Environment Mihir Kanta Rath
B.B.V.L. Deepak
Automation Lab, Department of Industrial Design NIT ROURKELA ROURKELA, INDIA Email:
[email protected]
Automation Lab, Department of Industrial Design NIT ROURKELA ROURKELA, INDIA Email:
[email protected]
Abstract— The proposed research article illustrates the path planning of an intelligent mobile robot in unknown dynamic environment using Particle Swarm Optimization (PSO) technique. The main objective of the problem is to make the robot move from starting position to goal position while avoiding all obstacles and follow the possible shortest path. For solving the path planning problem, a new objective function is developed. By optimizing the developed objective function the global best particle is determined among the swarm. Thereby, the robot moves further towards the global best position. The robot will continuously move to these intermediate positions until it reaches the final destination. Simulation showing navigation of robots towards goal position is done with MATLAB 2013b. Keywords— Mobile robot, PSO,objective function,MATLAB
I.
INTRODUCTION
Robot path planning in unknown dynamic environment has been a challenge for the researchers from last decades. Solution of this kind of problem plays a crucial role in the field of robotics. The main task of path planning of robot is to move the robot from its source to goal position while avoiding obstacles and follow the optimum path. It’s an optimization problem because it involves generation of optimal collision free trajectories by the mobile robot. There are two types of path planning problem such as global path planning and local path planning. In global path planning problem the environment will be familiar with the robot while in local path planning the robot is ignorant of the surrounding. For solving the optimization problem a socially inspired popular metaheuristic optimization algorithm is used; which is known as Particle Swarm Optimization (PSO) technique. PSO was inspired by the social behavior of birds and fish. Particle Swarm Optimization (PSO) was developed by Eberhart and Kennedy [1], inspired by social behavior of bird flocking or fish schooling. Many previous researchers have been used this algorithm to solve path planning for a mobile robot. In [2, 3], authors have considered a set of mobile robots as swarm and they implemented the multi-robot-multi-target search with same fitness function in the work space. This
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optimization technique is suitable for noisy environments. If the environment is having arbitrary number of polygon obstacles, then the path followed by mobile robot can be considered as the vertex of obstacles and the particle swarm optimization is used to get a global optimized path [4]. Same approach with some modification [5] has been proposed by integrating mutation operator with PSO to solve mobile robot motion planning problem. Lu & Gong [6] have been developed another fitness function for solving mobile robot navigation problem using PSO. They achieved motion planning for a mobile robot both in static as well as dynamic environments. PSO-based motion planner has been modeled in [7,8] for an autonomous mobile robot which can avoid obstacles and generating feasible trajectories within its unknown environments. The particle with minimum fitness value in the swarm is considered as the global best position or the next position of the robot in presence of obstacles. This article deals with generation of optimal collision free trajectories of multiple mobile robots from their starting to destination position with both static and dynamic obstacles. To accomplish this desired task a new fitness function is proposed in this paper which takes into account parameters like distance between obstacle –robot, robot-goal and robot-robot. Simulation results are provided to verify the efficiency of the developed algorithm. II.
MATHEMATICAL REPRESENTATION OF PSO
As mentioned earlier, Particle Swarm Optimization technique is inspired by the social behavior of birds and fishes. In the case of bird flocking, when birds move in group then each bird in the flock is having its own position and velocity. This is nothing but the personal best position of each bird. The best position in the flock is gauged based on an input parameter known as objective function or fitness function. In case of bird flocking, the fitness function parameter is searching for food in less distance from the shelter of birds. So each bird is having some personal best position based on this fitness
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Proceedings of 2015 Global Conference on Communication Technologies(GCCT 2015)
function. The position of the bird which has optimal fitness value is considered as the global best position. As the birds share information among them, all birds will tend to move towards the global best position. As PSO is inspired by the social nature of bird flocking, each bird can be considered as one particle. So each particle has its own position and velocity. The position of particle which satisfy optimum fitness value criterion is chosen as the global best position. Fig.1 below shows the structure of PSO.
First of all, the mobile robot move towards the destination point until it senses any obstacle in front of it. If there is no obstacle in front of it then it reaches to the destination. But when the robot senses any obstacle, it generates some random particles within its sensing range. Later the robot calculates the fitness of each particle to find out the global best position. Thus further movement of the robot is decided towards the global best position. If suppose the global best position is the destination then it stops otherwise the process continues iteratively. For accomplishment of whole task fitness function plays the crucial role because based on this the positions of personal and global best position is determined. IV.
Fig.1: Structure of Particle Swarm Optimization
The mathematical equation which describes PSO is given below: Vi(k+1) = w* Vi(k)+c1*r1(YPbest-yi)+ c2*r2(YGbest-yi) (1) yi(k+1)= yi(k)+ Vi(k+1) (2) Where i = Particle Number. k= Iteration counter. w= Inertial weight (decreasing function). c1 and c2 = Acceleration coefficients known as cognitive and social parameters . r1 and r2 = Random values in [0,1]. YPbest = Best position of particle. YGbest = Global best position of particle. III.
MOBILE ROBOT ARCHITECTURE
Since the robot path planning is an optimization problem, So PSO can be implemented for solving robot path planning problem. There are certain assumptions considered in the architecture such as: 1. The robots are represented as some points in the search space. Let the search space is represented by Z and ‘N’ represents the number of particles. 2. The starting and ending points are also mentioned by different points. 3. The initial position of points is the personal best positions of robots and after that all the points tend to move towards a single point which is nothing but the global best position. 4. The whole process continues until robots reach the destination.
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FITNESS FUNCTION CONSIDERATION
Fitness function is nothing but the set of boundary conditions or constraints to fulfill the control objective. In this paper a new fitness function is generated to get the desired result. The validity of the fitness function is verified by simulation discussed later in this paper. The fitness function can be chosen like this 1. The distance between robot (particle) and destination should be as small as possible. Hence the fitness function should be directly proportional to distance between robot and destination. F Į ȽR-GOAL (3) Where F = fitness function. ȽR-GOAL = distance between robot and goal position. 2. The distance between the robot and obstacle should as large as desired. So the fitness function is inversely proportional to distance between robot and obstacle. F Į 1/ȽR-OBSTACLE (4) Where ȽR-OBSTACLE = distance between robot and obstacle. 3. Similarly the distance between robots within its sensing range is large. Hence F Į 1/ȽR-R (5) Where ȽR-R = distance between robot and robot which is time varying function. Now combining all the conditions the complete fitness function can be written like this FĮ ȽR-GOAL (6) ȽR-OBSTACLE *ȽR-R Now ȽR-GOAL =
( Rxi − goalx ) 2 + ( Ryi − goal y )2
(7)
Where Rxi , R yi are the robots (particles) positions and
goalx ,
goal y is goal position. ȽR-OBSTACLE =
( Rxi − Oxi )2 + ( Ryi − Oyi ) 2
(8)
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Proceedings of 2015 Global Conference on Communication Technologies(GCCT 2015)
Where Oxi , O yi are the obstacles in the search space? ȽR-R = μ1*t*VR-R+μ2* ș (9) Where t = time in seconds. VR-R = relative velocity between two robots. For simplicity velocity of all the robots is taken same that is uniform but it can be taken different for different robot. ș = angle of heading of robots. From equation (6) we can write F = ȥ * ȽR-GOAL (6) ȽR-OBSTACLE *ȽR-R By tuning the value of ȥ, different possible optimal paths for the mobile robot can be formed. The whole process can be summarized like 1. Define robot and goal position. Define maximum number of iterations. 2. Move the robot from its source to destination by incrementing the value of horizontal and vertical component of the position vector. 3. If there is no obstacle the robot will move to destination in the direction of slope between source and destination because slope is the shortest path between any two points. 4. If the robot senses any obstacle in front of it generates random particles and based on minimum fitness value criteria the global best position is found. 5. The robot will move to these global best positions until it reaches the destination. When it will reach the destination the iteration stops. The creation of random particles using MATLAB is shown below in the figure.
The termination criteria for the algorithm are that it should stop when the robots reach to the destination or maximum iteration is reached. The flow chart for the whole process can be done like this Start
1. Define robot position and destination position. 2. Define maximum number of iterations. Move the robot in the direction of destination.
Presence of Obstacle
No
Yes
Yes Stop
Run PSO
Generation of random particles and computation of global best position Robot moves to global best position
No
Goal Reached
Yes Stop Fig 3: Flowchart of the Algorithm Fig.2: Random particles with one global best position
The above figure with points in magenta color represents positions of different particles and the point in green color represents the global best position of all the particles.
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No
Goal Reached
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Proceedings of 2015 Global Conference on Communication Technologies(GCCT 2015)
Fig.4: 3D view of search space generated by particles
V.
SIMULATION RESULTS
The simulation of robot path trajectory is plotted using MATLAB 2013b. For generating different collision free trajectories the tuning parameter ȥ is tuned properly. The simulation is performed by choosing c1=1 and c2=1.However different values for c1 and c2 can be chosen. The value of r1 and r2 are chosen as one for simplicity. After tuning the parameter, it is found that the parameter at ȥ =0.36 gives better results. The simulation result validating the above statements shown below:
Fig.7: Robots reached goal in the absence of obstacles
Fig.8: Robots moving towards goal in presence of obstacles.
Fig.5: Robots in the absence of obstacles
Fig.9: Robots approaching goal in presence of obstacles.
Fig.6: Robots approaching goal in the absence of obstacles
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Proceedings of 2015 Global Conference on Communication Technologies(GCCT 2015)
REFERENCES [1]
[2]
[3]
[4]
Fig.10: Robots reached destination in presence of obstacle.
VI.
[5]
CONCLUSION
In this paper path planning of mobile robots have been addressed. The developed motion planner works for the robotic environment with static and moving obstacles. In order to avoid the sensed obstacles (static and dynamic) and generate shortest path, a new fitness function has been introduced. To validate the efficiency of the proposed methodology, simulation results have been presented in the various robotic environments.
[6]
[7]
[8]
James Kennedy and Russell Eberhart, Particle Swarm Optimization, Proc. IEEE International Conference on Neural Networks, IV, Piscataway, NJ, 1995, pp. 1942- 1948. Derr K and Manic M, Multi-robot, multitargetParticleSwarmOptimizationsearchinnoisywirelessenvironments, 2nd Int. Conference on Human System Interactions, 2009,Page(s): 81 – 86. Doctor S, Venayagamoorthy G K, Gudise V G, Optimal PSO for collective robotic search applications, Evolutionary Computations, 2004, Page(s) 1390 - 139 . Qiaorong Zhang ShuhongLI, A Global Path Planning Approach Based on Particle Swarm Optimization for a Mobile Robot, Proceedings of the 7th WSEAS International Conference on Robotics, Control & Manufacturing Technology, Hangzhou, China, 2007, 263-267. Yuan-Qing Qin, De-Bao Sun, Ning Li and Yi-Gang Cen,Pathplanningformobilerobotusingtheparticleswarmoptimizationwith mutation operator, Proceedings of 2004 International Conference on Machine Learning and Cybernetics,Vol. 4 Page(s): 2473 – 2478. Li Lu and Dunwei Gong, Robot Path Planning in Unknown Environments Using Particle SwarmOptimization,FourthInternational Conference on Natural Computation, 2008,Vol. 4, Page(s): 422 - 426 B. B. V. L. Deepak· Dayal R. Parhi· and B. M. V. A. Raju, Advance Particle Swarm Optimization-Based Navigational Controller For Mobile Robot, Arabian Journal for Science and Engineering (2014) 39:6477– 6487, DOI 10.1007/s13369-014-1154-z. BBVL Deepak and Dayal R. Parhi, PSO based path planner of an autonomous mobile robot, Central European Journal of Computer Science, 2012, 2(2): 152-168
In future the developed algorithm is to be implemented in robotic platform.
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