Motion Planning Algorithms for General Closed-Chain Mechanisms

A robot essentially acts by moving in a physical world. The motion planning capability is thus a fundamental issue for the autonomy of the system, and represents a very active area of research in Robotics. Furthermore, the interest in motion planning techniques goes beyond robotic applications. Currently, these techniques are applied in other very different domains such as : CAD/CAM, industrial logistics, graphic animation, or computational Biology. Complex articulated mechanisms containing closed kinematic chains appear in all these domains. This thesis treats motion planning for such systems. The first part contains our theoretical and technical work. We introduce samplingbased planners into a general formulation of the motion planning problem in presence of kinematic closure constraints. The algorithmic tools that we propose allow an efficient application of these techniques to complex closed-chain mechanisms. The second part deals with the different fields of application that we have investigated. In Robotics, our approach has been applied to motion synthesis of parallel robots, coordinated manipulation and manipulation planning. Finally, we discuss an original application to Structural Biology for the conformational analysis of protein loops. The results of our experiments prove the efficacy and the generality of the approach.

[1]  Alain Liégeois,et al.  A study of multiple manipulator inverse kinematic solutions with applications to trajectory planning and workspace determination , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[2]  Mark H. Overmars,et al.  A probabilistic learning approach to motion planning , 1995 .

[3]  Jean-Claude Latombe,et al.  Efficient maintenance and self-collision testing for Kinematic Chains , 2002, SCG '02.

[4]  J. Laumond,et al.  Trailer-truck trajectory optimization for Airbus A 380 component transportation , 2003 .

[5]  Jean-Claude Latombe,et al.  Capturing molecular energy landscapes with probabilistic conformational roadmaps , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[6]  Tsai-Yen Li,et al.  Assembly maintainability study with motion planning , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[7]  E. Primrose.  On the input-output equation of the general 7R-mechanism , 1986 .

[8]  Adrian A Canutescu,et al.  Cyclic coordinate descent: A robotics algorithm for protein loop closure , 2003, Protein science : a publication of the Protein Society.

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

[10]  C. Gosselin.  Determination of the Workspace of 6-DOF Parallel Manipulators , 1990 .

[11]  Marie-Françoise Roy,et al.  Real algebraic geometry , 1992 .

[12]  Bruno Siciliano,et al.  Kinematic control of redundant robot manipulators: A tutorial , 1990, J. Intell. Robotic Syst..

[13]  Jing Xiao,et al.  Planning motion compliant to complex contact states , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[14]  Mitul Saha,et al.  Exact Collision Checking of Robot Paths , 2002, WAFR.

[15]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[16]  Narsingh Deo,et al.  A parallel algorithm for bound-smoothing , 1999, Proceedings 13th International Parallel Processing Symposium and 10th Symposium on Parallel and Distributed Processing. IPPS/SPDP 1999.

[17]  S. LaValle,et al.  Motion Planning , 2008, Springer Handbook of Robotics.

[18]  Kamal K. Gupta,et al.  The kinematic roadmap: a motion planning based global approach for inverse kinematics of redundant robots , 1999, IEEE Trans. Robotics Autom..

[19]  S. N. Gottschlich,et al.  AMP-CAD: an assembly motion planning system , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[20]  Lydia E. Kavraki,et al.  A Random Sampling Scheme for Path Planning , 1997, Int. J. Robotics Res..

[21]  S. Agrawal,et al.  Inverse kinematic solution of robot manipulators using interval analysis , 1998 .

[22]  J. Latombe,et al.  Randomized Query Processing in Robot Motion Planning , 1998 .

[23]  Sandor Vajda,et al.  CAPRI: A Critical Assessment of PRedicted Interactions , 2003, Proteins.

[24]  Jean-Claude Latombe,et al.  Experiments in dual-arm manipulation planning , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[25]  Thierry Siméon,et al.  Visibility-based probabilistic roadmaps for motion planning , 2000, Adv. Robotics.

[26]  Jean-Pierre Merlet,et al.  Parallel Robots: Open Problems , 2000 .

[27]  Paul W. Fitzjohn,et al.  Comparative modelling: an essential methodology for protein structure prediction in the post-genomic era. , 2002, Applied bioinformatics.

[28]  D. Chablat.  Domaines d'unicite et parcourabilite pour les manipulateurs pleinement paralleles , 1998 .

[29]  Arthur G. Erdman,et al.  Mechanism Design : Analysis and Synthesis , 1984 .

[30]  Thierry Siméon,et al.  Probabilistic motion planning for parallel mechanisms , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[31]  Magali Remaud-Simeon,et al.  Oligosaccharide and Sucrose Complexes of Amylosucrase , 2002, The Journal of Biological Chemistry.

[32]  Robert E. Bruccoleri,et al.  Chain closure with bond angle variations , 1985 .

[33]  G. N. Ramachandran,et al.  Conformation of polypeptides and proteins. , 1968, Advances in protein chemistry.

[34]  Oussama Khatib,et al.  The augmented object model: cooperative manipulation and parallel mechanism dynamics , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[35]  M. Renaud,et al.  A SIMPLIFIED INVERSE KINEMATIC MODEL CALCULATION METHOD FOR ALL 6R TYPE MANIPULATORS , 2000 .

[36]  Nicholas M. Patrikalakis,et al.  Computation of the solutions of nonlinear polynomial systems , 1993, Comput. Aided Geom. Des..

[37]  Kostas E. Bekris,et al.  Probabilistic Roadmaps of Trees for Parallel Computation of Multiple Query Roadmaps , 2003, ISRR.

[38]  Lydia E. Kavraki,et al.  A two level fuzzy PRM for manipulation planning , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[39]  J. Trinkle,et al.  THE GEOMETRY OF CONFIGURATION SPACES FOR CLOSED CHAINS IN TWO AND THREE DIMENSIONS , 2004 .

[40]  Lydia E. Kavraki,et al.  A probabilistic roadmap approach for systems with closed kinematic chains , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[41]  S. Basu,et al.  COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY , 1999 .

[42]  Xuerong Ji,et al.  Automatic Generation of High-Level Contact State Space , 2001, Int. J. Robotics Res..

[43]  J. Angeles,et al.  DETERMINATION DU DEGRE DE LIBERTE DES CHAINES CINEMATIQUE , 1988 .

[44]  M. Karplus,et al.  PDB-based protein loop prediction: parameters for selection and methods for optimization. , 1997, Journal of molecular biology.

[45]  Dinesh Manocha,et al.  Collision and Proximity Queries , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[46]  Nancy M. Amato,et al.  Iterative relaxation of constraints: a framework for improving automated motion planning , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[47]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[48]  J.-P. Laumond,et al.  Mechanical part assembly planning with virtual mannequins , 2005, (ISATP 2005). The 6th IEEE International Symposium on Assembly and Task Planning: From Nano to Macro Assembly and Manufacturing, 2005..

[49]  Bruce Randall Donald,et al.  Algorithmic and Computational Robotics: New Directions , 2001 .

[50]  Victor Y. Pan,et al.  Solving a Polynomial Equation: Some History and Recent Progress , 1997, SIAM Rev..

[51]  Carme Torras,et al.  A branch-and-prune algorithm for solving systems of distance constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[52]  Carme Torras,et al.  A branch-and-prune solver for distance constraints , 2005, IEEE Transactions on Robotics.

[53]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[54]  Yong K. Hwang,et al.  Practical path planning among movable obstacles , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[55]  Carole Nissoux,et al.  Visibilite et methodes probabilistes pour la planification de mouvement en robotique , 1999 .

[56]  Steven M. LaValle,et al.  Reducing metric sensitivity in randomized trajectory design , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[57]  Steven M. LaValle,et al.  Incremental low-discrepancy lattice methods for motion planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[58]  Lydia E. Kavraki,et al.  A framework for using the workspace medial axis in PRM planners , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[59]  Sukhan Lee,et al.  Self-motion topology for redundant manipulators with joint limits , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[60]  Vijay Kumar,et al.  Motion planning for cooperating mobile manipulators , 1999, J. Field Robotics.

[61]  Thierry Siméon,et al.  Geometric algorithms for the conformational analysis of long protein loops , 2004, J. Comput. Chem..

[62]  El-Ghazali Talbi,et al.  The "Ariadne's clew" algorithm: global planning with local methods , 1993, Proceedings of 1993 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '93).

[63]  Federico Thomas.  The Self-Motion Manifolds of the N-bar Mechanism , 1993 .

[64]  Mark H. Overmars,et al.  The Gaussian sampling strategy for probabilistic roadmap planners , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[65]  Bernard Roth,et al.  Kinematic analysis of the 6R manipulator of general geometry , 1991 .

[66]  Steven M. LaValle,et al.  Resolution complete rapidly-exploring random trees , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[67]  Patrick A. O'Donnell,et al.  HANDEY: A Robot Task Planner , 1992 .

[68]  Gregory S. Chirikjian,et al.  A combinatorial approach to trajectory planning for binary manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[69]  M. Karplus,et al.  Prediction of the folding of short polypeptide segments by uniform conformational sampling , 1987, Biopolymers.

[70]  Mark H. Overmars,et al.  Probabilistic path planning , 1998 .

[71]  Carme Torras,et al.  Solving Multi-Loop Linkages by Iterating 2D Clippings , 2002 .

[72]  Eiichi Yoshida,et al.  Humanoid motion planning for dynamic tasks , 2005, 5th IEEE-RAS International Conference on Humanoid Robots, 2005..

[73]  David Hsu,et al.  Randomized single-query motion planning in expansive spaces , 2000 .

[74]  Kamal K. Gupta,et al.  A motion planning based approach for inverse kinematics of redundant robots: the kinematic roadmap , 1997, Proceedings of International Conference on Robotics and Automation.

[75]  Lydia E. Kavraki,et al.  Generalizing the analysis of PRM , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[76]  Steven M. LaValle,et al.  Efficient nearest neighbor searching for motion planning , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[77]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[78]  Jean-Paul Laumond,et al.  Robot Motion Planning and Control , 1998 .

[79]  Rajeev Motwani,et al.  Path planning in expansive configuration spaces , 1997, Proceedings of International Conference on Robotics and Automation.

[80]  Etienne Huens,et al.  Algorithms for Solving Non-Linear Constrained and Optimization Problems: The State of The Art , 2001 .

[81]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[82]  Rachid Alami,et al.  Playing with several roadmaps to solve manipulation problems , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[83]  E. Allgower,et al.  Numerical Continuation Methods , 1990 .

[84]  Jean-Pierre Merlet,et al.  Determination of the orientation workspace of parallel manipulators , 1995, J. Intell. Robotic Syst..

[85]  D. Stewart,et al.  A Platform with Six Degrees of Freedom , 1965 .

[86]  Donald Lee Pieper.  The kinematics of manipulators under computer control , 1968 .

[87]  Ying Zhang,et al.  Modular Reconfigurable Robots in Space Applications , 2003, Auton. Robots.

[88]  Jorge Angeles,et al.  Architecture singularities of platform manipulators , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[89]  Florent Lamiraux,et al.  Smooth motion planning for car-like vehicles , 2001, IEEE Trans. Robotics Autom..

[90]  Ming Zhang,et al.  A New Method for Fast and Accurate Derivation of Molecular Conformations , 2002, J. Chem. Inf. Comput. Sci..

[91]  Roger Bostelman,et al.  TOWARD NEXT-GENERATION CONSTRUCTION MACHINES , .

[92]  Jean-Pierre Merlet.  Trajectory Verification in the Workspace for Parallel Manipulators , 1994, Int. J. Robotics Res..

[93]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms , 1995 .

[94]  Thierry Fraichard,et al.  Trajectory planning in a dynamic workspace: a 'state-time space' approach , 1998, Adv. Robotics.

[95]  C. Levinthal,et al.  Predicting antibody hypervariable loop conformation. I. Ensembles of random conformations for ringlike structures , 1987, Biopolymers.

[96]  Lydia E. Kavraki,et al.  Geometry and the Discovery of New Ligands , 1996 .

[97]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[98]  Gordon M. Crippen,et al.  Exploring the conformation space of cycloalkanes by linearized embedding , 1992 .

[99]  Vladimir Andreevich Zinovʹev,et al.  Théorie des mécanismes et des machines , 1969 .

[100]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[101]  Clément Gosselin,et al.  Singularity analysis of closed-loop kinematic chains , 1990, IEEE Trans. Robotics Autom..

[102]  Jean-Claude Latombe,et al.  Planning motions with intentions , 1994, SIGGRAPH.

[103]  Florent Lamiraux.  Robots mobiles à remorque : de la planification de chemins à l'exécution de mouvements , 1997 .

[104]  Jean-Claude Latombe,et al.  Motion Planning: A Journey of Robots, Molecules, Digital Actors, and Other Artifacts , 1999, Int. J. Robotics Res..

[105]  Jean-Paul Laumond,et al.  Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints , 1986, IAS.

[106]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Autonomous Robot Vehicles.

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

[108]  Nancy M. Amato,et al.  Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures , 2002, RECOMB '02.

[109]  Dinesh Manocha,et al.  Conformational analysis of molecular chains using nano-kinematics , 1995, Comput. Appl. Biosci..

[110]  Nancy M. Amato,et al.  Ligand binding with OBPRM and user input , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[111]  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).

[112]  A. Castellet,et al.  An Algorithm for the Solution of Inverse Kinematics Problems Based on an Interval Method , 1998 .

[113]  Günter Hommel,et al.  On the Tangent-Half-Angle Substitution , 1993 .

[114]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[115]  Lydia E. Kavraki,et al.  Planning Paths for Elastic Objects under Manipulation Constraints , 2001, Int. J. Robotics Res..

[116]  Jean-Paul Laumond,et al.  Guidelines in nonholonomic motion planning for mobile robots , 1998 .

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

[118]  Jean-Claude Latombe,et al.  Randomized Kinodynamic Motion Planning with Moving Obstacles , 2002, Int. J. Robotics Res..

[119]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[120]  Lydia E. Kavraki,et al.  Path planning using lazy PRM , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[121]  Kevin M. Lynch,et al.  Stable Pushing: Mechanics, Controllability, and Planning , 1995, Int. J. Robotics Res..

[122]  Steven M. LaValle,et al.  On the Relationship between Classical Grid Search and Probabilistic Roadmaps , 2004, Int. J. Robotics Res..

[123]  Bernard Roth,et al.  Formulation and Solution for the Direct and Inverse Kinematics Problems for Mechanisms and Mechatronics Systems , 1998 .

[124]  Bhaskar Dasgupta,et al.  The Stewart platform manipulator: a review , 2000 .

[125]  Lydia E. Kavraki,et al.  A randomized kinematics-based approach to pharmacophore-constrained conformational search and database screening , 2000, J. Comput. Chem..

[126]  Stanley A. Schneider,et al.  Object impedance control for cooperative manipulation: theory and experimental results , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[127]  A. Bondi.  van der Waals Volumes and Radii , 1964 .

[128]  T Schlick,et al.  The loop opening/closing motion of the enzyme triosephosphate isomerase. , 1998, Biophysical journal.

[129]  Lydia E. Kavraki,et al.  Randomized path planning for linkages with closed kinematic chains , 2001, IEEE Trans. Robotics Autom..

[130]  Nancy M. Amato,et al.  A general framework for sampling on the medial axis of the free space , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[131]  Dinesh Manocha,et al.  Efficient inverse kinematics for general 6R manipulators , 1994, IEEE Trans. Robotics Autom..

[132]  Hong Y. Lee,et al.  Displacement analysis of the general spatial 7-link 7R mechanism , 1988 .

[133]  Lydia E. Kavraki,et al.  Planning Paths for a Flexible Surface Patch , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[134]  Sylvie Charentus.  Modélisation et commande d'un robot manipulateur redondant composé de plusieurs plateformes de Stewart , 1990 .

[135]  Thierry Siméon,et al.  A random loop generator for planning the motions of closed kinematic chains using PRM methods , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[136]  Jean-Pierre Merlet,et al.  A Parser for the Interval Evaluation of Analytical Functions and its Application to Engineering Problems , 2001, J. Symb. Comput..

[137]  Jing Xiao,et al.  Planning Motions Compliant to Complex Contact States , 2001, Int. J. Robotics Res..

[138]  Rachid Alami,et al.  A geometrical approach to planning manipulation tasks. The case of discrete placements and grasps , 1991 .

[139]  Ming C. Lin,et al.  Constraint-based motion planning for virtual prototyping , 2002, SMA '02.

[140]  John F. Canny,et al.  Geometric Problems in Molecular Biology and Robotics , 1994, ISMB.

[141]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[142]  Jean-Claude Latombe,et al.  On Delaying Collision Checking in PRM Planning: Application to Multi-Robot Coordination , 2002, Int. J. Robotics Res..

[143]  Lydia E. Kavraki,et al.  On finding narrow passages with probabilistic roadmap planners , 1998 .

[144]  J. Schwartz,et al.  On the Piano Movers''Problem V: The Case of a Rod Moving in Three-Dimensional Space amidst Polyhedra , 1984 .

[145]  Mark H. Overmars,et al.  A Comparative Study of Probabilistic Roadmap Planners , 2002, WAFR.

[146]  Oussama Khatib,et al.  Object manipulation in a multi-effector robot system , 1988 .

[147]  Nancy M. Amato,et al.  A kinematics-based probabilistic roadmap method for high DOF closed chain systems , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[148]  Jean-Claude Latombe,et al.  Autonomous agents for real-time animation , 1999 .

[149]  Lydia E. Kavraki,et al.  Random networks in configuration space for fast path planning , 1994 .

[150]  Gordon T. Wilfong.  Motion planning in the presence of movable obstacles , 1988, SCG '88.

[151]  Jeffrey C. Trinkle,et al.  Complete Path Planning for Closed Kinematic Chains with Spherical Joints , 2002, Int. J. Robotics Res..

[152]  Nancy M. Amato,et al.  MAPRM: a probabilistic roadmap planner with sampling on the medial axis of the free space , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[153]  J. Moult,et al.  An algorithm for determining the conformation of polypeptide segments in proteins by systematic search , 1986, Proteins.

[154]  N. Go,et al.  Ring Closure and Local Conformational Deformations of Chain Molecules , 1970 .

[155]  M. Gajhede,et al.  Amylosucrase, a Glucan-synthesizing Enzyme from the α-Amylase Family* , 2001, The Journal of Biological Chemistry.

[156]  Bernard Roth.  Computational Advances in Robot Kinematics , 1994 .

[157]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling: An Introduction , 1989 .

[158]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[159]  George N Sandor,et al.  Determination of the condition of existence of complete crank rotation and of the instantaneous efficiency of spatial four-bar mechanisms , 1985 .

[160]  Jean-Claude Latombe,et al.  A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking , 2001, ISRR.

[161]  Jean-Daniel Boissonnat,et al.  Motion Planning of Legged Robots , 2000, SIAM J. Comput..

[162]  Thierry Siméon,et al.  Computer aided motion: Move3D within MOLOG , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[163]  Nazareth Bedrossian,et al.  Classification of singular configurations for redundant manipulators , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[164]  Clément Gosselin,et al.  On the Determination of the Workspace of Complex Planar Robotic Manipulators , 1998 .

[165]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[166]  R Leplae,et al.  Analysis and assessment of comparative modeling predictions in CASP4 , 2001, Proteins.

[167]  M. Steiner,et al.  Configuration Spaces of Mechanical Linkages , 1999, Discret. Comput. Geom..

[168]  J. Hervé.  Analyse structurelle des mcanismes par groupe des dplacements , 1978 .

[169]  Thierry Siméon,et al.  Manipulation Planning with Probabilistic Roadmaps , 2004, Int. J. Robotics Res..

[170]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[171]  Kamal K. Gupta,et al.  Manipulation Planning for Redundant Robots: A Practical Approach , 1998, Int. J. Robotics Res..

[172]  Timothy F. Havel,et al.  Shortest-path problems and molecular conformation , 1988, Discret. Appl. Math..

[173]  Harold A. Scheraga,et al.  Conformational Analysis of Macromolecules. II. The Rotational Isomeric States of the Normal Hydrocarbons , 1966 .

[174]  Jean-Claude Latombe,et al.  On multi-arm manipulation planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[175]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[176]  Thierry Siméon,et al.  Planetary exploration by a mobile robot: Mission teleprogramming and autonomous navigation , 1995, Auton. Robots.

[177]  Thierry Siméon,et al.  BioCD : An Efficient Algorithm for Self-collision and Distance Computation between Highly Articulated Molecular Models , 2005, Robotics: Science and Systems.

[178]  Jing Xiao,et al.  Automatic Generation of High-Level Contact State Space , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[179]  A. Sali,et al.  Modeling of loops in protein structures , 2000, Protein science : a publication of the Protein Society.

[180]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[181]  Thierry Siméon,et al.  A path planning approach for computing large-amplitude motions of flexible molecules , 2005, ISMB.

[182]  Carme Torras,et al.  Collision detection algorithms for motion planning , 1998 .

[183]  Jean-Paul Laumond,et al.  Algorithms for Robotic Motion and Manipulation , 1997 .

[184]  Jean-Claude Latombe,et al.  Stochastic roadmap simulation: an efficient representation and algorithm for analyzing molecular motion , 2002, RECOMB '02.

[185]  Carme Torras,et al.  On Finding the Set of Inverse Kinematic Solutions for Redundant Manipulators , 1993 .

[186]  J. Laumond,et al.  Multi-Level Path Planning for Nonholonomic Robots using Semi-Holonomic Subsystems , 1996 .

[187]  Qiang Zheng,et al.  Loop closure via bond scaling and relaxation , 1993, J. Comput. Chem..

[188]  Steven M. LaValle,et al.  From Dynamic Programming to RRTs: Algorithmic Design of Feasible Trajectories , 2003, Control Problems in Robotics.

[189]  Jérôme Barraquand,et al.  A penalty function method for constrained motion planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[190]  Jian Wang,et al.  Workspace evaluation of Stewart platforms , 1994, Adv. Robotics.

[191]  Bhaskar Dasgupta,et al.  Singularity-free path planning for the Stewart platform manipulator , 1998 .

[192]  Steven M. LaValle,et al.  Algorithms for Computing Numerical Optimal Feedback Motion Strategies , 2001, Int. J. Robotics Res..

[193]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 2005, Algorithmica.

[194]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.

[195]  Rachid Alami,et al.  aSyMov: A Planner That Deals with Intricate Symbolic and Geometric Problems , 2003, ISRR.

[196]  C. V. Geem,et al.  KCD : a Collision Detector for Path Planning in Factory Models , 2001 .

[197]  Hong Y. Lee,et al.  A new vector theory for the analysis of spatial mechanisms , 1988 .

[198]  H. Kwakernaak,et al.  Polynomial J-spectral factorization , 1994, IEEE Trans. Autom. Control..

[199]  Thierry Siméon,et al.  A probabilistic algorithm for manipulation planning under continuous grasps and placements , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[200]  Juan Cortés Mastral.  Motion Planning Algorithms for General Closed-Chain Mechanisms , 2003 .

[201]  P E Wright,et al.  Backbone dynamics in dihydrofolate reductase complexes: role of loop flexibility in the catalytic mechanism. , 2001, Biochemistry.

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

[203]  Bud Mishra,et al.  Computational Real Algebraic Geometry , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[204]  Thierry Siméon,et al.  Sampling-Based Motion Planning under Kinematic Loop-Closure Constraints , 2004, WAFR.

[205]  J. Burdick.  On the inverse kinematics of redundant manipulators: characterization of the self-motion manifolds , 1989 .

[206]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[207]  Steven M. LaValle,et al.  Quasi-randomized path planning , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[208]  Leonidas J. Guibas,et al.  H-Walk: hierarchical distance computation for moving convex bodies , 1999, SCG '99.

[209]  H. Edelsbrunner.  Geometry for modeling biomolecules , 1998 .

[210]  Baldomero Oliva,et al.  An automated classification of the structure of protein loops. , 1997, Journal of molecular biology.

[211]  Jean-Claude Latombe,et al.  CARABEAMER: a treatment planner for a robotic radiosurgical system with general kinematics , 1999, Medical Image Anal..

[212]  B. Buchberger.  An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[213]  I. M. Gelʹfand,et al.  Discriminants, Resultants, and Multidimensional Determinants , 1994 .

[214]  J.-P. Laumond,et al.  Move3D: A generic platform for path planning , 2001, Proceedings of the 2001 IEEE International Symposium on Assembly and Task Planning (ISATP2001). Assembly and Disassembly in the Twenty-first Century. (Cat. No.01TH8560).

[215]  Nancy M. Amato,et al.  Choosing good distance metrics and local planners for probabilistic roadmap methods , 2000, IEEE Trans. Robotics Autom..

[216]  Rachid Alami,et al.  Two manipulation planning algorithms , 1995 .

[217]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[218]  Francis L. Merat,et al.  Introduction to robotics: Mechanics and control , 1987, IEEE J. Robotics Autom..

[219]  J. Laumond,et al.  Notes on Visibility Roadmaps and Path Planning , 2001 .

[220]  Nancy M. Amato,et al.  Probabilistic roadmaps-putting it all together , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[221]  Harold A. Scheraga,et al.  Exact analytical loop closure in proteins using polynomial equations , 1999, J. Comput. Chem..

[222]  Chris Welman,et al.  INVERSE KINEMATICS AND GEOMETRIC CONSTRAINTS FOR ARTICULATED FIGURE MANIPULATION , 1993 .

[223]  Jean-Paul Laumond,et al.  Animation Planning for Virtual Mannequin Cooperation , 2004 .

[224]  Lydia E. Kavraki,et al.  Capturing the Connectivity of High-Dimensional Geometric Spaces by Parallelizable Random Sampling Techniques , 1998, IPPS/SPDP Workshops.

[225]  Jean-Claude Latombe,et al.  Robot Motion Planning: A Distributed Representation Approach , 1991, Int. J. Robotics Res..

[226]  Norman I. Badler,et al.  Real-Time Inverse Kinematics Techniques for Anthropomorphic Limbs , 2000, Graph. Model..

[227]  Lydia E. Kavraki,et al.  Analysis of probabilistic roadmaps for path planning , 1998, IEEE Trans. Robotics Autom..

[228]  Jon Rigelsford,et al.  Modelling and Control of Robot Manipulators , 2000 .

[229]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[230]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[231]  Nancy M. Amato,et al.  Using motion planning to study protein folding pathways , 2001, J. Comput. Biol..

[232]  Jiří Novotný,et al.  Structure of antibody hypervariable loops reproduced by a conformational search algorithm , 1988, Nature.

[233]  Yong Yu,et al.  Sensor-based probabilistic roadmaps: experiments with an eye-in-hand system , 2000, Adv. Robotics.

[234]  Clément Gosselin,et al.  Workspaces of Planar Parallel Manipulators , 1998 .

[235]  K. Kreutz-Delgado,et al.  Inverse Kinematics of Dextrous Manipulators , 1997 .

[236]  Thierry Siméon,et al.  A manipulation planner for pick and place operations under continuous grasps and placements , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[237]  John H. Reif,et al.  Complexity of the mover's problem and generalizations , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).