Abstract— The path length and number of turns are the major factors in path planning of transportation and navigation systems. Shortest path planning has been widely studied in the literatures. Most researches only take the issue of shortest distance into account, and the impact of turns are rarely mentioned, that is, the shortest path may not be the fastest. Considering both two factors in a path-searching algorithm is NP-complete. This paper proposes two algorithms: the Least-Turn Path Algorithm and the Minimum-Cost Path Algorithm to balance both the path length and turns. The proposed algorithms adapt Lee’s rectilinear routing algorithm to find a least-turn path with turn penalty on a mesh-connected network. In addition, Kirby’s concept and a modified Dijkstra’s algorithm are also introduced for the proposed minimum-cost path algorithm, which considers the turn penalty and the length factor on a transportation network. The time complexities for both algorithms are O(N), where N is the number of nodes on a mesh-connected network or the intersections on a transportation network. Key Words: Shortest path, Dijkstra’s algorithm, Lee’s algorithm, NP-Complete, transportation networks, turn penalties. I. INTRODUCTION LANNING a connected path from a source node to a destination node on a mesh-connected network under certain criteria is an important research subject, and has been widely applied to Printing Circuit Board (PCB) wiring, Integrated Circuit (IC) layout and the route-searching for transportation vehicles and robots in the Geographical Information System (GIS). Researches for transportation vehicles assume that the vehicles are under a constant speed, and most of them try to find a shortest path with a least amount of time. However, due to inertia and safety, the vehicles need to slow down and brake hard before the corner and this will increase the total time. Thus, the number of turns is also an important factor and cannot be overlooked in the path planning. The background of this article starts from Lee’s research on finding a shortest path in a raster space, and the path connection algorithm for searching the shortest path is still being widely studied [1]. The concept of turn penalty in path planning was first introduced by Caldwell [2], which established a pseudo- network to show the relationship between the nodes on a transportation network. Martin [3] employed other method to detect the occurrence of a turn via the variants of a constant. Kirby [4] dealt with the "The Mixed Rural Postman Problem with Turn Penalties (MRPPTP)" and a polynomial transformation was proposed to translate the problem into the "Asymmetric Traveling Salesman Problem (ATSP)". Frank [5] proved that the time complexity of these algorithms presented by Caldwell, Kirby and Potts were too large. Very recently, many turn cost related researches were proposed [6][7]. In this article, two path planning algorithms are proposed. The first one is try to find a path with minimum turns from the source node to the destination node on a mesh-connected network. The idea of this algorithm is based on Lee’s rectilinear routing concept. The second algorithm applies Kirby’s concept and a modified Dijkstra’s algorithm. We employ the accumulative concept to define the cost of a path, reestablish a two-dimensional network, and construct the minimum-cost path under turn penalty and length factor. This algorithm can be used for the mesh-connected networks and transportation networks. The time complexity for both algorithms is O(N) where N is the number of nodes. The contents of this paper are as follows: Section II introduces the space structure and Lee’s algorithm. The least- turn path algorithm and the minimum-cost path algorithm are presented in Section III and Section IV, respectively. Section V concludes the paper. II. SPACE STRUCTURE AND LEE’S STRUCTURE A. Raster Graph A raster is a graph that can be represented by rectangular, triangular, and hexangular cells. Our approach adapts the first model whereas the rectangular cells can be further divided into smaller cells recursively. The cell map indicates which cells constitute obstacles at the very least. As the algorithm unfolds, the cell map can also be used to indicate the intermediate status of the cells. Lee’s algorithm considers four directions of each central cell, Transportation Network Navigation with Turn Penalties Ming Che Lee S. G. Hsieh Yung-Yuan Chen Gene Eu Jan Member, IEEE Institute of Electrical Engineering National Taipei University Sun Shia, Taipei, Taiwan gejan@mail.ntpu.edu.tw Department of Computer and Communication Engineering, Ming Chuan University Taoyuan, Taiwan leemc@mcu.edu.tw Department of Electrical Engineering National Taiwan Ocean University Keelung, Taiwan sghsieh@mail.ntou.edu.tw Department of Computer Science Chung Hwa University, Hsin-Chu, Taiwan chenyy@chu.edu.tw P 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics Suntec Convention and Exhibition Center Singapore, July 14-17, 2009 978-1-4244-2853-3/09/$25.00 ©2009 IEEE 1224