Curved Surface Patches for Rough Terrain Perception

Attaining animal-like legged locomotion on rough outdoor terrain with sparse foothold affordances -a primary use-case for legs vs other forms of locomotion- is a largely open problem. New advancements in control and perception have enabled bipeds to walk on flat and uneven indoor environments. But tasks that require reliable contact with unstructured world surfaces, for example walking on natural rocky terrain, need new perception and control algorithms. This thesis introduces 3D perception algorithms for contact tasks such as foot placement in rough terrain environments. We introduce a new method to identify and model potential contact areas between the robot's foot and a surface using a set of bounded curved patches. We present a patch parameterization model and an algorithm to fit and perceptually validate patches to 3D point samples. Having defined the environment representation using the patch model, we introduce a way to assemble patches into a spatial map. This map represents a sparse set of local areas potentially appropriate for contact between the robot and the surface. The process of creating such a map includes sparse seed point sampling, neighborhood searching, as well as patch fitting and validation. Various ways of sampling are introduced including a real time bio-inspired system for finding patches statistically similar to those that humans select while traversing rocky trails. These sparse patch algorithms are integrated with a dense volumetric fusion of range data from a moving depth camera, maintaining a dynamic patch map of relevant contact surfaces around a robot in real time. We integrate and test the algorithms as part of a real-time foothold perception system on a mini-biped robot, performing foot placements on rocks.

[1]  Dov Katz Jacqueline Kenney Oliver Brock How Can Robots Succeed in Unstructured Environments ? , 2008 .

[2]  Ingemar J. Cox,et al.  Autonomous Robot Vehicles , 1990, Springer New York.

[3]  Ming Zeng,et al.  A memory-efficient kinectfusion using octree , 2012, CVM'12.

[4]  Tuan Q. Pham Non-maximum Suppression Using Fewer than Two Comparisons per Pixel , 2010, ACIVS.

[5]  Nassir Navab,et al.  Adaptive neighborhood selection for real-time surface normal estimation from organized point cloud data using integral images , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[6]  David Malah,et al.  Stable fitting of 2D curves and 3D surfaces by implicit polynomials , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Paul Filitchkin,et al.  Feature-based terrain classification for LittleDog , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[8]  Frédo Durand,et al.  A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach , 2006, International Journal of Computer Vision.

[9]  Olivier Stasse,et al.  Fast Humanoid Robot Collision-Free Footstep Planning Using Swept Volume Approximations , 2012, IEEE Transactions on Robotics.

[10]  Kourosh Khoshelham,et al.  Accuracy analysis of kinect depth data , 2012 .

[11]  Richard Szeliski,et al.  A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms , 2001, International Journal of Computer Vision.

[12]  Satoshi Kagami,et al.  A Probabilistic Walk Path Model Focused On Foot Landing Points And Human Step Measurement System , 2006, 2006 IEEE International Conference on Systems, Man and Cybernetics.

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

[14]  Derek D. Lichti,et al.  A Closed-Form Expression of the Positional Uncertainty for 3D Point Clouds , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Daisuke Kihara,et al.  Salient critical points for meshes , 2007, Symposium on Solid and Physical Modeling.

[16]  David B. Cooper,et al.  The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Olivier Stasse,et al.  Real-time (self)-collision avoidance task on a hrp-2 humanoid robot , 2008, 2008 IEEE International Conference on Robotics and Automation.

[18]  Mauro R. Ruggeri,et al.  Complex and photo-realistic scene representation based on range planar segmentation and model fusion , 2011, Int. J. Robotics Res..

[19]  Roland Siegwart,et al.  Introduction to Autonomous Mobile Robots , 2004 .

[20]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[21]  Lena Osterhagen,et al.  Data analysis for scientists and engineers , 1975 .

[22]  Olivier D. Faugeras,et al.  Building visual maps by combining noisy stereo measurements , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[23]  Peter-Pike J. Sloan,et al.  Interactive ray tracing for isosurface rendering , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[24]  Babak Taati,et al.  Difference of Normals as a Multi-scale Operator in Unorganized Point Clouds , 2012, 2012 Second International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission.

[25]  Daniel E. Whitney,et al.  Real robots don't need jigs , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[26]  Matthew T. Mason,et al.  Creation Myths: The Beginnings of Robotics Research , 2012, IEEE Robotics & Automation Magazine.

[27]  Horst Bunke,et al.  Fast segmentation of range images into planar regions by scan line grouping , 1994, Machine Vision and Applications.

[28]  Andrew W. Fitzgibbon,et al.  An Experimental Comparison of Range Image Segmentation Algorithms , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[29]  François Keith,et al.  Point-cloud multi-contact planning for humanoids: Preliminary results , 2013, RAM.

[30]  A. Patla,et al.  Visual information from the lower visual field is important for walking across multi-surface terrain , 2008, Experimental Brain Research.

[31]  Sylvain Petitjean,et al.  A survey of methods for recovering quadrics in triangle meshes , 2002, CSUR.

[32]  Dominik Belter,et al.  PRECISE SELF-LOCALIZATION OF A WALKING ROBOT ON ROUGH TERRAIN USING PTAM , 2012 .

[33]  Maria Isabel Ribeiro,et al.  Gaussian Probability Density Functions: Properties and Error Characterization , 2004 .

[34]  Paul Ozog,et al.  Real-time SLAM with piecewise-planar surface models and sparse 3D point clouds , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[35]  Roger W. Brockett,et al.  Robotic manipulators and the product of exponentials formula , 1984 .

[36]  Hyo-Kyung Lee,et al.  Foot Placement Selection Using Non-geometric Visual Properties , 2005, Int. J. Robotics Res..

[37]  Daniel Cremers,et al.  Dense visual SLAM for RGB-D cameras , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[38]  M. Hollands,et al.  Visually guided stepping under conditions of step cycle-related denial of visual information , 1996, Experimental Brain Research.

[39]  Alireza Bab-Hadiashar,et al.  Range image segmentation using surface selection criterion , 2006, IEEE Transactions on Image Processing.

[40]  R. Dillmann,et al.  Design and kinematics of a biologically-inspired leg for a six-legged walking machine , 2010, 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics.

[41]  Hobart R. Everett,et al.  Sensors for Mobile Robots: Theory and Application , 1995 .

[42]  Henk Nijmeijer,et al.  Foot placement for planar bipeds with point feet , 2012, 2012 IEEE International Conference on Robotics and Automation.

[43]  Daniel Maier,et al.  Integrated perception, mapping, and footstep planning for humanoid navigation among 3D obstacles , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[44]  F. Park Computational aspects of the product-of-exponentials formula for robot kinematics , 1994, IEEE Trans. Autom. Control..

[45]  Sander Oude Elberink,et al.  Accuracy and Resolution of Kinect Depth Data for Indoor Mapping Applications , 2012, Sensors.

[46]  Oussama Khatib,et al.  SupraPeds: Humanoid contact-supported locomotion for 3D unstructured environments , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[47]  Xin Li,et al.  An estimation-based approach for range image segmentation: on the reliability of primitive extraction , 2003, Pattern Recognit..

[48]  Zeyun Yu,et al.  A Morse-Theory Based Method for Segmentation of Triangulated Freeform Surfaces , 2009, ISVC.

[49]  Michael E. Mortenson,et al.  Geometric Modeling , 2008, Encyclopedia of GIS.

[50]  Markus H. Gross,et al.  Efficient simplification of point-sampled surfaces , 2002, IEEE Visualization, 2002. VIS 2002..

[51]  John Hallam Resolving Observer Motion by Object Tracking , 1983, IJCAI.

[52]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[53]  Takeo Kanade,et al.  Footstep Planning for the Honda ASIMO Humanoid , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[54]  Ieee Robotics,et al.  Proceedings : 2001 ICRA : IEEE International Conference on Robotics and Automation : May 21〜26, 2001, COEX, Seoul, Korea , 2001 .

[55]  Chee-Meng Chew,et al.  Blind walking of a planar bipedal robot on sloped terrain , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[56]  Dinesh Manocha,et al.  Probabilistic Collision Detection Between Noisy Point Clouds Using Robust Classification , 2011, ISRR.

[57]  Denis Laurendeau,et al.  Scene reconstruction and description: geometric primitive extraction from multiple viewed scattered data , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

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

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

[60]  David Wettergreen,et al.  Dante II: Technical Description, Results, and Lessons Learned , 1999, Int. J. Robotics Res..

[61]  Donald Bernard Gennery,et al.  Modelling the environment of an exploring vehicle by means of stereo vision , 1980 .

[62]  Marsette Vona,et al.  Sparse surface modeling with curved patches , 2013, 2013 IEEE International Conference on Robotics and Automation.

[63]  Andreas Birk,et al.  Efficient Representation in 3D Environment Modeling for Planetary Robotic Exploration , 2010 .

[64]  Don Ray Murray,et al.  Patchlets: Representing Stereo Vision Data with Surface Elements , 2005, 2005 Seventh IEEE Workshops on Applications of Computer Vision (WACV/MOTION'05) - Volume 1.

[65]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[66]  John J. Leonard,et al.  Kintinuous: Spatially Extended KinectFusion , 2012, AAAI 2012.

[67]  Andrew J. Davison,et al.  DTAM: Dense tracking and mapping in real-time , 2011, 2011 International Conference on Computer Vision.

[68]  梶田 尚志,et al.  IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'97) , 1998 .

[69]  Wolfram Burgard,et al.  A Bayesian regression approach to terrain mapping and an application to legged robot locomotion , 2009, J. Field Robotics.

[70]  S. Gruber,et al.  Robot hands and the mechanics of manipulation , 1987, Proceedings of the IEEE.

[71]  Satoshi Kagami,et al.  Autonomous navigation of a humanoid robot over unknown rough terrain using a laser range sensor , 2012, Int. J. Robotics Res..

[72]  Marsette Vona,et al.  Curved surface contact patches with quantified uncertainty , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[73]  M. Maimone,et al.  Overview of the Mars Exploration Rovers ’ Autonomous Mobility and Vision Capabilities , 2007 .

[74]  Kia Ng,et al.  Hybrid Approach to the Construction of Triangulated 3D Models of Building Interiors , 1999, ICVS.

[75]  RusuRadu Bogdan,et al.  Towards 3D Point cloud based object maps for household environments , 2008 .

[76]  Gabriel Taubin,et al.  Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[77]  Thomas S. Huang,et al.  A fast two-dimensional median filtering algorithm , 1979 .

[78]  Chitra Dorai,et al.  Optimal Registration of Object Views Using Range Data , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[79]  Sven Behnke,et al.  Humanoid Robots - From Fiction to Reality? , 2008, Künstliche Intell..

[80]  Jizhong Xiao,et al.  Fast visual odometry and mapping from RGB-D data , 2013, 2013 IEEE International Conference on Robotics and Automation.

[81]  F. Sebastian Grassia,et al.  Practical Parameterization of Rotations Using the Exponential Map , 1998, J. Graphics, GPU, & Game Tools.

[82]  Michael Beetz,et al.  Fault-tolerant 3D Mapping with Application to an Orchard Robot , 2009 .

[83]  Nicholas Roy,et al.  Collision detection in legged locomotion using supervised learning , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[84]  Masahiro Fujita,et al.  Stair climbing for humanoid robots using stereo vision , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

[85]  Wolfram Burgard,et al.  An evaluation of the RGB-D SLAM system , 2012, 2012 IEEE International Conference on Robotics and Automation.

[86]  Aftab E. Patla,et al.  Review article Understanding the roles of vision in the control of human locomotion , 1997 .

[87]  Masahiro Fujita,et al.  Real-Time Path Planning for Humanoid Robot Navigation , 2005, IJCAI.

[88]  David W. Murray,et al.  Parallel Tracking and Mapping on a camera phone , 2009, 2009 8th IEEE International Symposium on Mixed and Augmented Reality.

[89]  Andreas Birk,et al.  Revisiting uncertainty analysis for optimum planes extracted from 3D range sensor point-clouds , 2009, 2009 IEEE International Conference on Robotics and Automation.

[90]  Michael Beetz,et al.  Perception for mobile manipulation and grasping using active stereo , 2009, 2009 9th IEEE-RAS International Conference on Humanoid Robots.

[91]  Frank P. Ferrie,et al.  From uncertainty to visual exploration , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[92]  Nico Blodow,et al.  Towards 3D Point cloud based object maps for household environments , 2008, Robotics Auton. Syst..

[93]  Friedrich Fraundorfer,et al.  Visual Odometry Part I: The First 30 Years and Fundamentals , 2022 .

[94]  Masayuki Inaba,et al.  Plane segment finder: algorithm, implementation and applications , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[95]  Gabriel Taubin,et al.  An improved algorithm for algebraic curve and surface fitting , 1993, 1993 (4th) International Conference on Computer Vision.

[96]  Kevin Blankespoor,et al.  BigDog, the Rough-Terrain Quadruped Robot , 2008 .

[97]  Andrew Howard,et al.  Real-time stereo visual odometry for autonomous ground vehicles , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[98]  D. Marigold Role of Peripheral Visual Cues in Online Visual Guidance of Locomotion , 2008, Exercise and sport sciences reviews.

[99]  A. E. Patla,et al.  Gaze fixation patterns for negotiating complex ground terrain , 2007, Neuroscience.

[100]  Wolfram Burgard,et al.  Point feature extraction on 3D range scans taking into account object boundaries , 2011, 2011 IEEE International Conference on Robotics and Automation.

[101]  D. Holz,et al.  3 D Pose Estimation and Mapping with Time-of-Flight Cameras , 2008 .

[102]  G. Klein,et al.  Parallel Tracking and Mapping for Small AR Workspaces , 2007, 2007 6th IEEE and ACM International Symposium on Mixed and Augmented Reality.

[103]  Ian D. Reid,et al.  Locally Planar Patch Features for Real-Time Structure from Motion , 2004, BMVC.

[104]  Marc Levoy,et al.  A volumetric method for building complex models from range images , 1996, SIGGRAPH.

[105]  Marsette Vona,et al.  Bio-inspired rough terrain contact patch perception , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[106]  Simon Lacroix,et al.  Using planar facets for stereovision SLAM , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[107]  Andrew E. Johnson,et al.  Registration and integration of textured 3-D data , 1997, Proceedings. International Conference on Recent Advances in 3-D Digital Imaging and Modeling (Cat. No.97TB100134).

[108]  Alfred A. Rizzi,et al.  Autonomous navigation for BigDog , 2010, 2010 IEEE International Conference on Robotics and Automation.

[109]  Larry H. Matthies,et al.  Error modeling in stereo navigation , 1986, IEEE J. Robotics Autom..

[110]  Shuuji Kajita,et al.  Humanoid Robots in the Future , 2009, Adv. Robotics.

[111]  Castro Gomez,et al.  Sensing with a 3-toe foot for a mini biped robot = Midiendo con un pie de 3 dedos para mini robots bipedos , 2014 .

[112]  A E Patla,et al.  Where and when do we look as we approach and step over an obstacle in the travel path? , 1997, Neuroreport.

[113]  金谷 健一 Statistical optimization for geometric computation : theory and practice , 2005 .

[114]  Andrew W. Fitzgibbon,et al.  KinectFusion: real-time 3D reconstruction and interaction using a moving depth camera , 2011, UIST.

[115]  Daniel Cremers,et al.  Large-Scale Multi-resolution Surface Reconstruction from RGB-D Sequences , 2013, 2013 IEEE International Conference on Computer Vision.

[116]  Peter C. Cheeseman,et al.  Estimating uncertain spatial relationships in robotics , 1986, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[117]  Andrew Y. Ng,et al.  Stereo vision and terrain modeling for quadruped robots , 2009, 2009 IEEE International Conference on Robotics and Automation.

[118]  Peter Secretan Learning , 1965, Mental Health.

[119]  Luiz Velho,et al.  Image moments-based structuring and tracking of objects , 2002, Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing.

[120]  Marsette Vona,et al.  Moving Volume KinectFusion , 2012, BMVC.

[121]  Daniel Maier,et al.  Monte Carlo Localization for Humanoid Robot Navigation in Complex Indoor Environments , 2014, Int. J. Humanoid Robotics.

[122]  Patrick Hébert,et al.  Median Filtering in Constant Time , 2007, IEEE Transactions on Image Processing.

[123]  Michael Garland,et al.  Fair morse functions for extracting the topological structure of a surface mesh , 2004, ACM Trans. Graph..

[124]  Stefan Schaal,et al.  Learning, planning, and control for quadruped locomotion over challenging terrain , 2011, Int. J. Robotics Res..

[125]  Tomás Pajdla,et al.  3D with Kinect , 2011, 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops).

[126]  Ross T. Whitaker,et al.  Cramer-Rao bounds for nonparametric surface reconstruction from range data , 2003, Fourth International Conference on 3-D Digital Imaging and Modeling, 2003. 3DIM 2003. Proceedings..

[127]  Heiko Hirschmüller,et al.  Stereo-vision-based navigation of a six-legged walking robot in unknown rough terrain , 2012, Int. J. Robotics Res..

[128]  Michael A. Greenspan,et al.  On the Repeatability of 3D Point Cloud Segmentation Based on Interest Points , 2012, 2012 Ninth Conference on Computer and Robot Vision.

[129]  Min Dai,et al.  Least-squares-based fitting of paraboloids , 2007, Pattern Recognit..

[130]  Andreas Birk,et al.  Online 3D SLAM by Registration of Large Planar Surface Segments and Closed Form Pose-Graph Relaxation , 2010 .

[131]  Piotr Skrzypczynski,et al.  Map-based adaptive foothold planning for unstructured terrain walking , 2010, 2010 IEEE International Conference on Robotics and Automation.

[132]  Hajime Asama,et al.  Development of open humanoid platform DARwIn-OP , 2011, SICE Annual Conference 2011.

[133]  Leonidas J. Guibas,et al.  Uncertainty and Variability in Point Cloud Surface Data , 2004, PBG.

[134]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .

[135]  Reid G. Simmons,et al.  Perception, Planning, and Control for Autonomous Walking With the Ambler Planetary Rover , 1996, Int. J. Robotics Res..

[136]  Christopher K. Rhea,et al.  Control of adaptive locomotion: effect of visual obstruction and visual cues in the environment , 2006, Experimental Brain Research.

[137]  Masayuki Inaba,et al.  Autonomous 3D walking system for a humanoid robot based on visual step recognition and 3D foot step planner , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[138]  Peter Cheeseman,et al.  On the Representation and Estimation of Spatial Uncertainty , 1986 .

[139]  David W. Jacobs,et al.  Mesh saliency , 2005, ACM Trans. Graph..

[140]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[141]  Daniel Cremers,et al.  Volumetric 3D mapping in real-time on a CPU , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[142]  Daniel Maier,et al.  Search-Based Footstep Planning , 2013 .

[143]  Roberto Manduchi,et al.  Bilateral filtering for gray and color images , 1998, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271).

[144]  Rama Chellappa,et al.  Estimation of Object Motion Parameters from Noisy Images , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[145]  Olivier Stasse,et al.  Toward Reactive Vision-Guided Walking on Rough Terrain: An Inverse-Dynamics Based Approach , 2014, Int. J. Humanoid Robotics.

[146]  Ilan Shimshoni,et al.  Estimating the principal curvatures and the Darboux frame from real 3D range data , 2002, Proceedings. First International Symposium on 3D Data Processing Visualization and Transmission.

[147]  Radu Bogdan Rusu,et al.  3D is here: Point Cloud Library (PCL) , 2011, 2011 IEEE International Conference on Robotics and Automation.

[148]  Caihua Wang,et al.  Comparison of local plane fitting methods for range data , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[149]  Satoshi Kagami,et al.  Biped navigation in rough environments using on-board sensing , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[150]  Roland Siegwart,et al.  3D SLAM using planar segments , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[151]  Andrew W. Fitzgibbon,et al.  KinectFusion: Real-time dense surface mapping and tracking , 2011, 2011 10th IEEE International Symposium on Mixed and Augmented Reality.

[152]  Masahiro Fujita,et al.  3D Perception and Environment Map Generation for Humanoid Robot Navigation , 2008, Int. J. Robotics Res..

[153]  Horst Bunke,et al.  Comparing Curved-Surface Range Image Segmenters , 1998, ICCV.

[154]  Henrik I. Christensen,et al.  Planar surface SLAM with 3D and 2D sensors , 2012, 2012 IEEE International Conference on Robotics and Automation.

[155]  Robert B. Fisher,et al.  Estimating 3-D rigid body transformations: a comparison of four major algorithms , 1997, Machine Vision and Applications.

[156]  Daniel Maier,et al.  Real-time navigation in 3D environments based on depth camera data , 2012, 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012).

[157]  Masayuki Inaba,et al.  Walking navigation system of humanoid robot using stereo vision based floor recognition and path planning with multi-layered body image , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).