Multiresolution Hierarchical Path-Planning for Small UAVs Using Wavelet Decompositions

We present an algorithm for solving the shortest (collision-free) path planning problem for an agent (e.g., a small UAV) with limited on-board computational resources. The agent has detailed knowledge of the environment and the obstacles only in the vicinity of its current position. Far away obstacles are only partially known and may even change dynamically. The algorithm makes use of the wavelet transform to construct an approximation of the environment at different levels of resolution. We associate with this multiresolution representation of the environment a graph, whose dimension can be made commensurate to the on-board computational resources of the agent. The adjacency list of the graph can be efficiently constructed directly from the approximation and detail wavelet coefficients, thus further speeding up the whole process. Simulations are presented to test the efficiency of the algorithm using non-trivial scenarios.

[1]  Dinesh K. Pai,et al.  Multiresolution rough terrain motion planning , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[2]  Panagiotis Tsiotras,et al.  Beamlet-like data processing for accelerated path-planning using multiscale information of the environment , 2010, 49th IEEE Conference on Decision and Control (CDC).

[3]  Efstathios Bakolas,et al.  A hierarchical on-line path planning scheme using wavelets , 2007, 2007 European Control Conference (ECC).

[4]  Ta-Hsin Li,et al.  Multiscale Representation and Analysis of Spherical Data by Spherical Wavelets , 1999, SIAM J. Sci. Comput..

[5]  Sven Behnke,et al.  Local Multiresolution Path Planning , 2003, RoboCup.

[6]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[7]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[8]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[9]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[10]  P. Tsiotras,et al.  Multiresolution on-line path planning for small unmanned aerial vehicles , 2008, 2008 American Control Conference.

[11]  David Furcy,et al.  Lifelong Planning A , 2004, Artif. Intell..

[12]  W. Freeden,et al.  Spherical wavelet transform and its discretization , 1996 .

[13]  Panagiotis Tsiotras,et al.  Multi-resolution path planning: Theoretical analysis, efficient implementation, and extensions to dynamic environments , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  Marina L. Gavrilova,et al.  Path planning in dynamic environment using an adaptive mesh , 2007, SCCG.

[15]  A. Kurdila,et al.  Multiresolution and Adaptive Path Planning for Maneuver of Micro-Air-Vehicles in Urban Environments , 2005 .

[16]  Dongwon Jung Jung,et al.  Hierarchical Path Planning and Control of a Small Fixed-wing UAV: Theory and Experimental Validation , 2007 .

[17]  Randal W. Beard,et al.  Vision-based local multi-resolution mapping and path planning for Miniature Air Vehicles , 2009, 2009 American Control Conference.

[18]  G. Ulivi,et al.  Indoor robot navigation using log-polar local maps , 2003 .

[19]  Sivasankar Ramarasu.  Vision based navigation for an unmanned aerial vehicle , 2007 .

[20]  Jean-Claude Latombe,et al.  New heuristic algorithms for efficient hierarchical path planning , 1991, IEEE Trans. Robotics Autom..

[21]  Efstathios Bakolas,et al.  Multiresolution Path Planning Via Sector Decompositions Compatible to On-Board Sensor Data , 2008 .

[22]  Kyu Ho Park,et al.  A fast path planning by path graph optimization , 2003, IEEE Trans. Syst. Man Cybern. Part A.

[23]  Larry S. Davis,et al.  Multiresolution path planning for mobile robots , 1986, IEEE J. Robotics Autom..

[24]  Yang Yimin,et al.  Hierarchical path planning approach for mobile robot navigation under the dynamic environment , 2008, 2008 6th IEEE International Conference on Industrial Informatics.

[25]  Panagiotis Tsiotras,et al.  Real-time Implementation and Validation of a New Hierarchical Path Planning Scheme of UAVs via Hardware-in-the-Loop Simulation , 2009, J. Intell. Robotic Syst..

[26]  I. Daubechies,et al.  Wavelet Transforms That Map Integers to Integers , 1998 .

[27]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[28]  Sven Koenig,et al.  Agent-Centered Search , 2001, AI Mag..

[29]  Ju-Jang Lee,et al.  Mobile robot navigation using multi-resolution electrostatic potential field , 2005, 31st Annual Conference of IEEE Industrial Electronics Society, 2005. IECON 2005..

[30]  Hiroshi Noborio,et al.  A quadtree-based path-planning algorithm for a mobile robot , 1990, J. Field Robotics.

[31]  Panagiotis Tsiotras,et al.  Beyond quadtrees: Cell decompositions for path planning using wavelet transforms , 2007, 2007 46th IEEE Conference on Decision and Control.

[32]  Panagiotis Tsiotras,et al.  Beyond Quadtrees: Cell Decomposition for Path Planning using the Wavelet Transform , 2007 .

[33]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[34]  Zijian Zhang,et al.  Q-Learning Based Method of Adaptive Path Planning for Mobile Robot , 2006, 2006 IEEE International Conference on Information Acquisition.

[35]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[36]  Yann LeCun,et al.  Mapping and planning under uncertainty in mobile robots with long-range perception , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[37]  P. Tsiotras,et al.  Multiresolution path planning with wavelets: A local replanning approach , 2008, 2008 American Control Conference.

[38]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .