PDE-Based Robust Robotic Navigation Computer Vision & Image Processing Laboratory (CVIP) University of Louisville, Kentucky. Aly A. Farag, M. Sabry Hassouna, Alaa E. Abdel-Hakim, and Mike Miller AI Robotics AI robot is the one that possesses unsupervised intelligent performance in dynamic or unknown environments. Sensor Suite Stereo cameras Stereo cameras Pan-tilt units GPS. Pan-tilt units GPS. Electronic Compass. Electronic Compass. Inclinometer. Inclinometer. Inertial Sensor. Inertial Sensor. Laser Scanners. Laser Scanners. Sonar Sonar. Robotic Path Planning In robotic navigation, path planning is aimed at getting the optimum collision-free path between a starting and target locations. The optimality criterion depends on the surrounding environment and running conditions. In most of indoor navigation, the optimum path is the safe one, while for outdoor navigation, the shortest path is more recommended. Global Vs. Local Planning Global planning takes into account all the information in the environment when finding the optimum path. However, it is time consuming in the pre-computation step. ( Cell decomposition-91, Voronoi-00, randomized sampling-02 ) Local Planning avoids dynamic obstacles within a close vicinity of the robot. Potential field methods. ( Latombe-86, Khatib-92 ) are the most popular ones, which are fast, but may converge to local minimum in dense environment. iRobot - CVIP Lab Indoor Outdoor Min. Cost Path Problem From geometrical optics, the solution satisfies the From geometrical optics, the solution satisfies the Eikonal equation Objective Developing novel path planning technique that overcome the voids in the current approaches. Integrating the current resources at University of Louisville and CVIP lab in mobile robots, simulation, and active vision, in order to develop a complete navigation platform that can be used in different missions for various environments. This project is envisioned to be the first step in a potentially long-term collaboration with NASA in smart robotics R&D for space exploration, especially unmanned missions to outer space. Medial Path Extraction Theorem The most stable method for solving this equation is the fast marching methods (FMM) (Sethian-95,-99). Numerical errors along diagonals. Non-optimal computational complexity. To overcome these limitations, we have developed a highly accurate numerical solution method, called the Multi-Stencils Fast Marching (MSFM), which combines multi-stencils with directional derivatives. Medialness Function λ(x) Euclidean Distance Field Absolute Divergence Field Optimum Path Extraction (OPE) In the isotropic fast marching, the fastest traveling is always along the direction perpendicular to the wave front (Bellman-65). Therefore, the OPE can be extracted by backtracking along the steepest Descent by solving the following ODE. Global Path Planning Extract the desired path between A and B. If dynamic objects are detected by robotic sensors, the map is updated and the path is re-planned. For terrain environment, we assume that we have its height map. For Shortest Path, For Hybrid Path, For Safe Path, If the robot is doing a regular job. Then, it is efficient to store the entire safe paths of the map such that given any two locations A and B, we can quickly compute the safest path between them. Local Path Planning Shortest PathSafe Path Hybrid Path Robot is represented by a white square. Experimental Results Method Local Planning Global Planning Safe Path Shortest Path Hybrid Path Local Min. Proposed Method x Virtual Forces xx Heurisitic Search A* xxxx Voronoi Planning xxxx 1. Entire Safe Paths for Global Planning 2. Global Path Planning 3. Safe Path Extraction from Different Source Points 4. Local Path Planning for Planar Environment Shortest PathSafest Path 5. Local Path Planning for Terrain Environment Terrain Environment Iso-Contours Shortest and Minimum Energy Paths Future Work References Fully autonomous navigation of robots for commercial and DoD applications. Perception-based navigation in unknown environments such as Mars to guide rovers like Spirit & Opportunity M. Sabry Hassouna, A.A. Farag, and Alaa Abdel-Hakim, "PDE-Based Robust Robotic Navigation," Journal of Image and Vision Computing (IMAVIS), Under Review. 2. M. Sabry Hassouna and Aly. A. Farag, "Accurate Tracking of Monotonically Advancing Fronts," Parametric and Geometric Deformable Models: An application in Biomaterials and Medical Imagery, Jasjit S. Suri and Aly Farag, Editors, Springer, M. Sabry Hassouna and Aly. A. Farag, "PDE-Based Three Dimensional Path Planning For Virtual Endoscopy," Parametric and Geometric Deformable Models: An application in Biomaterials and Medical Imagery, Jasjit S. Suri and Aly Farag, Editors, Volume 2, Springer, 2006 (in press). 4. M. Sabry Hassouna and A.A. Farag, "Accurate Tracking of Monotonically Advancing Fronts," Proc. of IEEE Conference on Computer Vision and Pattern Recognition (CVPR'06), New York, NY, USA June 17-22, M. Sabry Hassouna and A.A. Farag, "Robust Centerline Extraction Framework Using Level Sets," Proc. of IEEE Conference on Computer Vision and Pattern Recognition (CVPR'05), San Diego, CA, USA June 20-26, 2005, pp M. Sabry Hassouna, A.A. Farag, and Alaa E. Abdel-Hakim, "PDE-Based Robust Robotic Navigation," Proc. of Second Canadian Conference on Computer and Robot Vision (CRV'05), British Columbia, Canada, May 9-11, 2005, pp Has been nominated to appear in a special issue of "Journal of Image and Vision Computing".