Collision-free and smooth trajectory computation in cluttered environments

We present a novel trajectory computation algorithm to smooth piecewise linear collision-free trajectories computed by sample-based motion planners. Our approach uses cubic B-splines to generate trajectories that are C2 almost everywhere, except on a few isolated points. The algorithm performs local spline refinement to compute smooth, collision-free trajectories and it works well even in environments with narrow passages. We also present a fast and reliable algorithm for collision checking between a robot and the environment along the B-spline trajectories. We highlight the performance of our algorithm on complex benchmarks, including path computation for rigid and articulated models in cluttered environments.

[1]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[2]  Tony DeRose,et al.  Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines , 1988, TOGS.

[3]  Tony DeRose,et al.  Geometric continuity of parametric curves: three equivalent characterizations , 1989, IEEE Computer Graphics and Applications.

[4]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[5]  John F. Hughes,et al.  Smooth interpolation of orientations with angular velocity constraints using quaternions , 1992, SIGGRAPH.

[6]  Cyrille Froissart,et al.  On-line polynomial path planning in Cartesian space for robot manipulators , 1993, Robotica.

[7]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[8]  Hsuan Chang.  Motion planning in virtual prototyping: practical considerations , 1995, Proceedings. IEEE International Symposium on Assembly and Task Planning.

[9]  Timothy F. Havel,et al.  Derivatives of the Matrix Exponential and Their Computation , 1995 .

[10]  Sung Yong Shin,et al.  A general construction scheme for unit quaternion curves with simple high order derivatives , 1995, SIGGRAPH.

[11]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

[12]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[13]  Gerald E. Farin,et al.  Curves and surfaces for computer-aided geometric design - a practical guide, 4th Edition , 1997, Computer science and scientific computing.

[14]  N. Hogan,et al.  Robot-aided neurorehabilitation. , 1998, IEEE transactions on rehabilitation engineering : a publication of the IEEE Engineering in Medicine and Biology Society.

[15]  M. J. Kim,et al.  Real time motion fairing with unit quaternions , 1998, Comput. Aided Des..

[16]  Steven M. LaValle,et al.  RRT-connect: An efficient approach to single-query path planning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[17]  Oliver Brock,et al.  Elastic Strips: A Framework for Motion Generation in Human Environments , 2002, Int. J. Robotics Res..

[18]  Thierry Siméon,et al.  Planning human walk in virtual environments , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  O. Brock,et al.  Elastic Strips: A Framework for Motion Generation in Human Environments , 2002, Int. J. Robotics Res..

[20]  Katsu Yamane,et al.  Synthesizing animations of human manipulation tasks , 2004, ACM Trans. Graph..

[21]  Gregory M. Nielson,et al.  /spl nu/-Quaternion splines for the smooth interpolation of orientations , 2004, IEEE Transactions on Visualization and Computer Graphics.

[22]  Mark H. Overmars,et al.  Useful cycles in probabilistic roadmap graphs , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[23]  Dinesh Manocha,et al.  Fast continuous collision detection for articulated models , 2004, SM '04.

[24]  Katsu Yamane,et al.  Synthesizing animations of human manipulation tasks , 2004, SIGGRAPH 2004.

[25]  Ming C. Lin,et al.  Interactive collision detection between deformable models using chromatic decomposition , 2005, ACM Trans. Graph..

[26]  Dinesh Manocha,et al.  Interactive collision detection between deformable models using chromatic decomposition , 2005, SIGGRAPH 2005.

[27]  Frank Chongwoo Park,et al.  Newton-type algorithms for dynamics-based robot movement optimization , 2005, IEEE Transactions on Robotics.

[28]  Xinyu Zhang,et al.  Interactive continuous collision detection for non-convex polyhedra , 2006, The Visual Computer.

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

[30]  Marc Toussaint,et al.  Optimization of sequential attractor-based movement for compact behaviour generation , 2007, 2007 7th IEEE-RAS International Conference on Humanoid Robots.

[31]  Hiroshi Mizoguchi,et al.  Path shortening and smoothing of grid-based path planning with consideration of obstacles , 2007, 2007 IEEE International Conference on Systems, Man and Cybernetics.

[32]  Mark H. Overmars,et al.  Creating High-quality Paths for Motion Planning , 2007, Int. J. Robotics Res..

[33]  Young J. Kim,et al.  Continuous collision detection for articulated models using Taylor models and temporal culling , 2007, ACM Trans. Graph..

[34]  Jarek Rossignac,et al.  ScrewBender: Smoothing Piecewise Helical Motions , 2008, IEEE Computer Graphics and Applications.

[35]  Dinesh Manocha,et al.  D-Plan: Efficient Collision-Free Path Computation for Part Removal and Disassembly , 2008 .

[36]  D. Thalmann,et al.  Planning collision-free reaching motions for interactive object manipulation and grasping , 2008, SIGGRAPH '08.

[37]  Thierry Siméon,et al.  Path Deformation Roadmaps: Compact Graphs with Useful Cycles for Motion Planning , 2008, Int. J. Robotics Res..

[38]  Siddhartha S. Srinivasa,et al.  CHOMP: Gradient optimization techniques for efficient motion planning , 2009, 2009 IEEE International Conference on Robotics and Automation.

[39]  Eiichi Yoshida,et al.  Generation of dynamic multi-contact motions: 2D case studies , 2010, 2010 10th IEEE-RAS International Conference on Humanoid Robots.

[40]  Dinesh Manocha,et al.  CCQ: Efficient Local Planning Using Connection Collision Query , 2010, WAFR.

[41]  Victor Ng-Thow-Hing,et al.  Fast smoothing of manipulator trajectories using optimal bounded-acceleration shortcuts , 2010, 2010 IEEE International Conference on Robotics and Automation.

[42]  Dinesh Manocha,et al.  Retraction-based RRT planner for articulated models , 2010, 2010 IEEE International Conference on Robotics and Automation.

[43]  Salah Sukkarieh,et al.  An Analytical Continuous-Curvature Path-Smoothing Algorithm , 2010, IEEE Transactions on Robotics.

[44]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..

[45]  Kostas E. Bekris,et al.  Asymptotically Near-Optimal Is Good Enough for Motion Planning , 2011, ISRR.

[46]  Dinesh Manocha,et al.  FCL: A general purpose library for collision and proximity queries , 2012, 2012 IEEE International Conference on Robotics and Automation.

[47]  P. Abbeel,et al.  Collision-Free and Curvature-Continuous Path Smoothing in Cluttered Environments , 2012 .