Space-carving Kernels for Accurate Rough Terrain Estimation

Accurate terrain estimation is critical for autonomous offroad navigation. Reconstruction of a three-dimensional (3D) surface allows rough and hilly ground to be represented, yielding faster driving and better planning and control. However, data from a 3D sensor samples the terrain unevenly, quickly becoming sparse at longer ranges and containing large voids because of occlusions and inclines. The proposed approach uses online kernel-based learning to estimate a continuous surface over the area of interest while providing upper and lower bounds on that surface. Unlike other approaches, visibility information is exploited to constrain the terrain surface and increase precision, and an efficient gradient-based optimization allows for realtime implementation. To model sensor noise over varying ranges, a non-stationary covariance function is adopted. Experimental results are presented for several datasets, including groundtruthed terrain and a large 3D stereo dataset.

[1]  M. Aizerman,et al.  Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[2]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[3]  Takeo Kanade,et al.  Ambler: an autonomous rover for planetary exploration , 1989, Computer.

[4]  Takeo Kanade,et al.  Terrain mapping for a roving planetary explorer , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[5]  Takeo Kanade,et al.  High-Resolution Terrain Map from Multiple Sensor Data , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[6]  R. Schaback.  Creating Surfaces from Scattered Data Using Radial Basis Functions , 1995 .

[7]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[8]  David Higdon,et al.  Non-Stationary Spatial Modeling , 2022, 2212.08043.

[9]  Ronald W. Schafer,et al.  Multi-resolution space carving using level set methods , 2002, Proceedings. International Conference on Image Processing.

[10]  Mark J. Schervish,et al.  Nonstationary Covariance Functions for Gaussian Process Regression , 2003, NIPS.

[11]  Martin Zinkevich,et al.  Online Convex Programming and Generalized Infinitesimal Gradient Ascent , 2003, ICML.

[12]  Alexander J. Smola,et al.  Online learning with kernels , 2001, IEEE Transactions on Signal Processing.

[13]  Bernhard Schölkopf,et al.  Kernel Methods for Implicit Surface Modeling , 2004, NIPS.

[14]  Kiriakos N. Kutulakos,et al.  A Theory of Shape by Space Carving , 2000, International Journal of Computer Vision.

[15]  Bernhard Schölkopf,et al.  Implicit Surface Modelling with a Globally Regularised Basis of Compact Support , 2006, Comput. Graph. Forum.

[16]  Alonzo Kelly,et al.  Toward Reliable Off Road Autonomous Vehicles Operating in Challenging Environments , 2006, Int. J. Robotics Res..

[17]  Larry D. Jackel,et al.  The DARPA LAGR program: Goals, challenges, methodology, and phase I results , 2006, J. Field Robotics.

[18]  Christian Laugier,et al.  Dense Mapping for Range Sensors: Efficient Algorithms and Sparse Representations , 2007, Robotics: Science and Systems.

[19]  Wolfram Burgard,et al.  Adaptive Non-Stationary Kernel Regression for Terrain Modeling , 2007, Robotics: Science and Systems.

[20]  Wolfram Burgard,et al.  An Efficient Extension to Elevation Maps for Outdoor Terrain Mapping and Loop Closing , 2007, Int. J. Robotics Res..

[21]  Nathan Ratliff,et al.  Online) Subgradient Methods for Structured Prediction , 2007 .

[22]  Michael R. Lyu,et al.  A Multi-Scale Tikhonov Regularization Scheme for Implicit Surface Modelling , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[23]  Denis Laurendeau,et al.  Mapping and Exploration of Complex Environments Using Persistent 3D Model , 2007, Fourth Canadian Conference on Computer and Robot Vision (CRV '07).

[24]  Wolfram Burgard,et al.  Learning predictive terrain models for legged robot locomotion , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[25]  Wolfram Burgard,et al.  Nonstationary Gaussian Process Regression Using Point Estimates of Local Smoothness , 2008, ECML/PKDD.

[26]  William Whittaker,et al.  Autonomous driving in urban environments: Boss and the Urban Challenge , 2008, J. Field Robotics.