Triangular Geometrized Sampling Heuristics for Fast Optimal Motion Planning

Rapidly-exploring Random Tree (RRT)-based algorithms have become increasingly popular due to their lower computational complexity as compared with other path planning algorithms. The recently presented RRT* motion planning algorithm improves upon the original RRT algorithm by providing optimal path solutions. While RRT determines an initial collision-free path fairly quickly, RRT* guarantees almost certain convergence to an optimal, obstacle-free path from the start to the goal points for any given geometrical environment. However, the main limitations of RRT* include its slow processing rate and high memory consumption, due to the large number of iterations required for calculating the optimal path. In order to overcome these limitations, we present another improvement, i.e, the Triangular Geometerized-RRT* (TG-RRT*) algorithm, which utilizes triangular geometrical methods to improve the performance of the RRT* algorithm in terms of the processing time and a decreased number of iterations required for an optimal path solution. Simulations comparing the performance results of the improved TG-RRT* with RRT* are presented to demonstrate the overall improvement in performance and optimal path detection.

[1]  Shimon Y. Nof,et al.  Handbook of Industrial Robotics , 2013 .

[2]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..

[3]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[4]  Stan C. A. M. Gielen,et al.  Neural Network Dynamics for Path Planning and Obstacle Avoidance , 1995, Neural Networks.

[5]  Emilio Frazzoli,et al.  Anytime Motion Planning using the RRT* , 2011, 2011 IEEE International Conference on Robotics and Automation.

[6]  Yoram Koren,et al.  Potential field methods and their inherent limitations for mobile robot navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[7]  O. Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[8]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[9]  Thierry Siméon,et al.  Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[10]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[11]  Yasar Ayaz,et al.  Triangular geometry based optimal motion planning using RRT*-motion planner , 2014, 2014 IEEE 13th International Workshop on Advanced Motion Control (AMC).

[12]  Russell H. Taylor,et al.  Medical robotics in computer-integrated surgery , 2003, IEEE Trans. Robotics Autom..

[13]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[14]  Rodney A. Brooks,et al.  A subdivision algorithm in configuration space for findpath with rotation , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Emilio Frazzoli,et al.  Asymptotically-optimal path planning for manipulation using incremental sampling-based algorithms , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[16]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[17]  Steven M. LaValle,et al.  RRT-connect: An efficient approach to single-query path planning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[18]  Lydia E. Kavraki,et al.  Probabilistic Roadmaps for Robot Path Planning , 1998 .

[19]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[20]  Oliver Brock,et al.  Balancing exploration and exploitation in motion planning , 2008, 2008 IEEE International Conference on Robotics and Automation.