The path-finding algorithm (modified A*) that guaranties the shortest length of trajectory and gives a result with minimum iterations has been developed and realized. The software that implements this routine has been developed. The check of the system has been performed on different samples

Mishkin, D.

Zbrutsky, A.

Electronic Archive of Kyiv Polytechnic Institute

UDK 681.518D. Mishkin. A. ZbrutskyPATH-FINDING ALGORITHM FOR THE MOBILE ROBOTINTRODUCTIONThe man-to-robot change in the dangerous tasks becomes more and more pressing need. The air heading monitoring, archeological and rescue operations etc need robots and other autonomous or remote controlled devices for performing different actions.PATH-FINDING ALGORITHM The robot that can execute tasks successfully must have intelligent control system that contains path-finding algorithm with allowance for obstacles. The path-finding tasks we can divide into two groups: with full information about obstacles a priori and without such information.The first type usually can guarantee that route will be the shortest one or will have the lowest ���cost��� (for example, when there are territories with roads heaviness ��� swamp, sand etc). But we can`t always use them. The second oneworks under any conditions but route that we get can be far from optimal one. The best solution is to combine both types of routines. At the first, theshortest route which avoids all known obstacles has been guided. If robot strikes a snag, the second type algorithm will be activated.One of the best routines for the path-finding with known obstacles is A*.The heuristic search evaluates each map node inverse proportion to the efficiency of the trajectory that contains  this node. It means better node has less ���cost���. The typical formula of the ���cost��� is given byf (n) = g(n) + h(n) (1)f(n) ��� resulting node n cost;g(n) ��� cost of the most efficient way from start to current node;h(n) ��� heuristic evaluation of the cost from current node to the finish.The length of route from start point to current has been chosed asthe g(n). The distance from current point to finish ignoring the obstacles has been choised as heuristic h(n).This algorithm is very flexible because we can add different penalties forgoing through ���bad��� regions, for example with roads heaviness or dangerous ones and A* routine will generate route taking into account all this conditions.A* has next properties:��� it guarantees the shortest (optimal) way if heuristics h(n) is not greaterthan correct distance to the finish;��� number of the calculations of the f(n) is minimal. The board tracing method has been chosen for the pass-around the unforeseen obstacles. It consits of going near obstacle border while the directionto finish is blocked by obstacle.Thus we have chosen the combination of A* and board tracingalgorithms.ROUTE SMOOTHINGRoute that we have got from A* method has some disadvantages. The main disadvantage is discreteness and aliasing. Because of square configuration of the node and crossover ia allowed to the nearest-neighbor nodes only, the route has a great number of turns. (look fig. 1)For example, the stage on the angle of 30 degrees will be substituted with some lines on the angle of 0, 45 and 90 degrees. That is why the route smoothing algorithm had been developed. Here it is.Step 0. Let us take two checkpoints (that are given by operator, not by path-finding routine)Step 1. Try to connect them with the right line. If there aren`t obstacles between them then go to the step 2. If there is an obstacle then go to the step 3. If the second point is finish point, then logout.Step 2. Replace the first point with the second point and the second ���with the next checkpoint that is given by operator. Go to the step 1.Step 3. Replace the second point with the temporary that lies in the middle of path-finding routine generated route between two current checkpoints. Go to the step 1.Software interface and route example is shown on fig. 1, 2ROBOT CONTROLThe Delphi program for the robot control and above mentioned algorithms implementation has been developed. Performance capabilities:Fig. 1. Interface of the ���Robot mobile control��� software and route generated by A* algorithm configurationFig. 2. Route after smoothing��� to create the map of the territory where the robot is operating and add checkpoints and obstacles by operator;��� to generate the shortest way taking into account all the obstacles and robot size;��� to trace the robot position on the map and to get full data from therobot sensors in real-time mode;��� to perform remote control of the robot if it is necessary.ConclusionThe robot control software and hardware for the automatic andautonomous path-finding and going has been developed.References1. Hubert Roth, Anatoly Sachenko, Vasyl Koval, Joochim Chanin,Oleh Adamiv. The 3D Mapping Preparation using 2D/3D Cameras for Mobile Robot Control./ ��Artifical intellegence�� 4���2008, p. 512-528.2. Apostolyuk V. A. Apostolyuk A. S. Intelligent control systems: lecture notes / ��� Kiev: NTUU ���KPI���, 2008. ��� 88 p.3. Patrick Lester. A* Pathfinding. http://www.policyalmanac.org.

Path-finding algorithm for the mobile robot

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