Maze solving algorithm

Abstract: This paper describes three examples of hardware implementations of path finding schemes based on the Lee-Moore maze solving algorithm. one is purely a demonstration circuit to show the technique. The other two are complete LSI implementations which should be usable in building large and useful path finding machines. One of these two LSI circuits, known as the MAZER, is designed to find shortest paths from one point to another on a plane, where there is only one layer of allowable routes to take. As its name suggests, this chip solves ordinary mazes, or on a more practical level, it can route wires on a one sided printed circuit board. The other LSI circuit, known as the PATHFINDER, is designed to handle the two sided printed circuit board case. It finds a least costly path from one point to another where there are two parallel planes on which routes are allowed. Crossing of the path from one plane to another can be either unrestrcited, as in free via printed circuit boards, or permitted only in certain places, as in fixed via boards. The phrase "least costly" above can, for now, be read as "shortest", although in a later section a more general definition will be revealed. The remainder of this document is divided into three parts. The first section outlines the original Lee-Moore algorithm for path finding on which the circuits described later are based. The second section details the one layer hardware, including both the demonstration circuit and the MAZER chip. Finally, the third section describes the PATHFINDER chip and the techniques used to conquer the problems encountered in two layer path finding. Documentation on the integrated circuits includes those results of testing and characterization which were available at the time of this writing.

Abstract: In this paper we have discussed a unique general algorithm for exploring and solving any kind of line maze with another simple one for simple mazes without loops or loops having highest two branches none of which are inward. For the general algorithm, we need a method to map the whole maze, which is required if the maze is complex. The proposed maze mapping system is based on coordinate system and after mapping the whole maze as a graph in standard 'Adjacency-list representation' method, shortest path and shortest time path was extracted using Dijkstra's algorithm. In order to find the coordinates of the turning points and junctions, linear distance between the points are needed, for which wheel encoder was used. However, due to non-linear movement of robot, the directly measured distance from the encoder has some error and to remove this error an idea is built up which ended by deriving equations that gives us almost exact linear distance between two points from the reading of wheel encoder of the robot moving in a non-linear path.

Abstract: In this paper we have discussed a unique general algorithm for exploring and solving any kind of line maze with another simple one for simple mazes without loops or with loops having highest two branches none of which are inward. For the general algorithm, we need a method to map the whole maze, which is required if the maze is complex. The proposed maze mapping system is based on coordinate system and after mapping the whole maze as a graph in standard `Adjacency-list representation' method, shortest path and shortest time path was extracted using Dijkstra's algorithm. In order to find the coordinates of the turning points and junctions, linear distances between the points are needed, for which wheel encoder was used. However, due to non-linear movement of robot, the directly measured distance from the encoder has some error and to remove this error an idea is built up which ended by deriving equations that give us almost exact linear distance between two points from the reading of wheel encoder of the robot moving in a non-linear path.

Abstract: This article gives hardware design concept of a maze robot taking SCM as a core based on research on design of a maze robot' hardware and maze solving algorithm directing at the problem that there are less sensor-based maze algorithm and it is very difficult to find the shortest path. It proposes a deep first search (DFS) algorithm based on left — right hand wall follower rule and in detail analyzes the realizing processes of this algorithm and this algorithm is realized. Experiments show that this system can find a shorter path from the entrance and the exit of a maze which is not too complicated through two times of search and it features smaller spatial complexity.