Surface Optimal Path Planning Using an Extended Dijkstra Algorithm

Extensive studies have been conducted on the Dijkstra algorithm owing to its bright prospect. However, few of them have studied the surface path planning of mobile robots. Currently, some application fields (e.g., wild ground, planet ground, and game scene) need to solve the optimal surface path. This paper proposes an extended Dijkstra algorithm. We utilize the Delaunay triangulation to model the surface environment. Based on keeping the triangle side length unchanged, the triangle mesh on the surface is equivalently converted into a triangle on the two-dimensional plane. Through this transformation, we set up the two-dimensional developable passable channel of the surface and solve the optimal route on this channel. Traversing all the two-dimensional developable and passable paths of the surface, we can get the shortest route among all the optimal paths. Then the inverse transformation from the two-dimensional plane coordinates to the corresponding surface coordinates obtains the surface optimal path. The simulation results show that, compared with the traditional Dijkstra algorithm, this method improves the accuracy of the surface optimization path in single-robot single-target and multi-robot multi-target path planning tasks.

[1]  Mark A. Tarbell,et al.  Globally optimal rover traverse planning in 3D using Dijkstra’s algorithm for multi-objective deployment scenarios , 2019 .

[2]  Dong Guo,et al.  A vehicle path planning method based on a dynamic traffic network that considers fuel consumption and emissions. , 2019, The Science of the total environment.

[3]  Roberto Galery,et al.  Mine fleet cost evaluation - Dijkstra's optimized path , 2019, REM - International Engineering Journal.

[4]  Juan Chen,et al.  Collision-Free Route Planning for Multiple AGVs in an Automated Warehouse Based on Collision Classification , 2018, IEEE Access.

[5]  G. Jan,et al.  Near-Shortest Path Planning on a Quadratic Surface With $O(n\log n)$ Time , 2015, IEEE Sensors Journal.

[6]  Jeffery L. Kennington,et al.  The one-to-one shortest-path problem: An empirical analysis with the two-tree Dijkstra algorithm , 1993, Comput. Optim. Appl..

[7]  Micha Sharir,et al.  Some modified algorithms for Dijkstra's longest upsequence problem , 2004, Acta Informatica.

[8]  M. T. Lee,et al.  Route Planning for Light-sport Aircraft in Constrained Airspace , 2013 .

[9]  Lei Yan,et al.  A 2-D ESPO Algorithm and Its Application in Pedestrian Path Planning Considering Human Behavior , 2009, 2009 Third International Conference on Multimedia and Ubiquitous Engineering.

[10]  Cheolkeun Ha,et al.  Control of a Quadrotor Using a Smart Self-Tuning Fuzzy PID Controller , 2013 .

[11]  Pedro Arias,et al.  Point clouds for direct pedestrian pathfinding in urban environments , 2019, ISPRS Journal of Photogrammetry and Remote Sensing.

[12]  A. Wong.  Routing and time-slot assignment in optical TDM networks , 2004, IEEE Journal on Selected Areas in Communications.

[13]  Masato Noto,et al.  A method for the shortest path search by extended Dijkstra algorithm , 2000, Smc 2000 conference proceedings. 2000 ieee international conference on systems, man and cybernetics. 'cybernetics evolving to systems, humans, organizations, and their complex interactions' (cat. no.0.

[14]  Anderson Rodrigo de Queiroz,et al.  Optimizing routing and tower spotting of electricity transmission lines: An integration of geographical data and engineering aspects into decision-making , 2019, Electric Power Systems Research.

[15]  Tae-Hwan Kim,et al.  High-Throughput and Area-Efficient MIMO Symbol Detection Based on Modified Dijkstra's Search , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Justin P. Coon,et al.  Route Selection Based on Connectivity-Delay-Trust in Public Safety Networks , 2019, IEEE Systems Journal.

[17]  Ming Liu,et al.  Robotic Online Path Planning on Point Cloud , 2016, IEEE Transactions on Cybernetics.

[18]  Kanisius Karyono,et al.  Computational load analysis of Dijkstra, A*, and Floyd-Warshall algorithms in mesh network , 2013, 2013 International Conference on Robotics, Biomimetics, Intelligent Computational Systems.

[19]  Zvi Shiller,et al.  Optimal motion planning of autonomous vehicles in three dimensional terrains , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[20]  Mario Gerla,et al.  On routing with QoS constraints in ATM networks , 1997, HPN.

[21]  Georgios K. D. Saharidis,et al.  A hybrid approach to the problem of journey planning with the use of mathematical programming and modern techniques , 2017 .

[22]  Kurt Mehlhorn,et al.  A Heuristic for Dijkstra's Algorithm with Many Targets and Its Use in Weighted Matching Algorithms , 2001, Algorithmica.

[23]  Derya Birant,et al.  A Gradual Approach for Multimodel Journey Planning: A Case Study in Izmir, Turkey , 2017 .

[24]  Oskar von Stryk,et al.  Supervised footstep planning for humanoid robots in rough terrain tasks using a black box walking controller , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.

[25]  Lingli Yu,et al.  A Path Planning and Navigation Control System Design for Driverless Electric Bus , 2018, IEEE Access.

[26]  Jun Bi,et al.  Electric Vehicle Routing Problem with Charging Time and Variable Travel Time , 2017 .

[27]  Eyad I. Abbas,et al.  An Efficient Optimal Path Finding for Mobile Robot Based on Dijkstra Method , 2019, 2019 4th Scientific International Conference Najaf (SICN).

[28]  Hui Zhang,et al.  An Improved Ant Colony Routing Algorithm for WSNs , 2015, J. Sensors.

[29]  Yujin,et al.  Optimal Route Planning of Parking Lot Based on Dijkstra Algorithm , 2017, 2017 International Conference on Robots & Intelligent System (ICRIS).

[30]  Simon X. Yang,et al.  A Multi-Scale Map Method Based on Bioinspired Neural Network Algorithm for Robot Path Planning , 2019, IEEE Access.