Information-Seeking Control Under Visibility-Based Uncertainty

We address the problem of exploring an unknown environment using a range sensor. In the presence of opaque objects of arbitrary shape and topology, exploration is driven by minimization of residual uncertainty, that is primarily due to lack of visibility. The resulting optimal control is approximated with a computationally efficient heuristic, that is proven to complete exploration of a compact environment in a finite number of steps.

[1]  Stefano Soatto,et al.  Control recognition bounds for visual learning and exploration , 2012, 2013 Information Theory and Applications Workshop (ITA).

[2]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Micha Sharir,et al.  Ray Shooting amidst Convex Polyhedra and Polyhedral Terrains in Three Dimensions , 1996, SIAM J. Comput..

[4]  Leonidas J. Guibas,et al.  Intersecting Line Segments, Ray Shooting, and Other Applications of Geometric Partitioning Techniques , 1988, SWAT.

[5]  David J. Kriegman,et al.  Vision-based motion planning and exploration algorithms for mobile robots , 1995, IEEE Trans. Robotics Autom..

[6]  Francesco Bullo,et al.  Maximizing visibility in nonconvex polygons: nonsmooth analysis and gradient algorithm design , 2005, Proceedings of the 2005, American Control Conference, 2005..

[7]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[8]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[9]  Stefano Soatto,et al.  Steps Towards a Theory of Visual Information: Active Perception, Signal-to-Symbol Conversion and the Interplay Between Sensing and Control , 2011, ArXiv.

[10]  J. Sethian,et al.  Ordered upwind methods for static Hamilton–Jacobi equations , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[11]  E. Rouy,et al.  A viscosity solutions approach to shape-from-shading , 1992 .

[12]  Simeon C. Ntafos,et al.  Optimum Watchman Routes , 1988, Inf. Process. Lett..

[13]  Xiaotie Deng,et al.  How to learn an unknown environment , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[14]  Li-Tien Cheng,et al.  Visibility of Point Clouds and Mapping of Unknown Environments , 2006, ACIVS.

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

[16]  Richard Tsai,et al.  Properties of a Level Set Algorithm for the Visibility Problems , 2008, J. Sci. Comput..

[17]  Yanina Landa,et al.  Visibility of point clouds and exploratory path planning in unknown environments , 2008 .

[18]  S. Osher,et al.  Visibility and its dynamics in a PDE based implicit framework , 2004 .

[19]  Steven M. LaValle,et al.  Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances , 2007, IEEE Transactions on Robotics.

[20]  J. Sack,et al.  Handbook of computational geometry , 2000 .

[21]  Stefano Soatto,et al.  Detachable Object Detection: Segmentation and Depth Ordering from Short-Baseline Video , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Haomin Zhou,et al.  Approximate solutions to several visibility optimization problems , 2011 .

[23]  Stanley Osher,et al.  Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations , 2003, SIAM J. Numer. Anal..

[24]  Li-Tien Cheng,et al.  Redistancing by flow of time dependent eikonal equation , 2008, J. Comput. Phys..

[25]  Stefano Soatto,et al.  On the set of images modulo viewpoint and contrast changes , 2009, CVPR.

[26]  Micha Sharir,et al.  Ray Shooting Amidst Convex Polygons in 2D , 1996, J. Algorithms.

[27]  Micha Sharir,et al.  Ray Shooting Amidst Spheres in Three Dimensions and Related Problems , 1997, SIAM J. Comput..

[28]  James A. Sethian,et al.  Fast-marching level-set methods for three-dimensional photolithography development , 1996, Advanced Lithography.

[29]  Stefano Soatto,et al.  Learning and matching multiscale template descriptors for real-time detection, localization and tracking , 2011, CVPR 2011.

[30]  François X. Sillion,et al.  Conservative volumetric visibility with occluder fusion , 2000, SIGGRAPH.

[31]  Stefano Soatto,et al.  Detachable Object Detection with Efficient Model Selection , 2011, EMMCVPR.

[32]  Jorge Urrutia,et al.  Art Gallery and Illumination Problems , 2000, Handbook of Computational Geometry.

[33]  Andreas Krause,et al.  Optimal Nonmyopic Value of Information in Graphical Models - Efficient Algorithms and Theoretical Limits , 2005, IJCAI.

[34]  Howie Choset,et al.  Sensor-Based Exploration: The Hierarchical Generalized Voronoi Graph , 2000, Int. J. Robotics Res..

[35]  Li-Tien Cheng,et al.  Visibility Optimization Using Variational Approaches , 2005 .

[36]  Sylvain Petitjean,et al.  A Computational Geometric Approach to Visual Hulls , 1998, Int. J. Comput. Geom. Appl..

[37]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[38]  Stefano Soatto,et al.  Sparse Occlusion Detection with Optical Flow , 2012, International Journal of Computer Vision.

[39]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

[40]  Elbridge Gerry Puckett,et al.  Two new methods for simulating photolithography development in 3D , 1997 .

[41]  J. Tsitsiklis.  Efficient algorithms for globally optimal trajectories , 1995, IEEE Trans. Autom. Control..