Exploring implicit spaces for constrained sampling-based planning

We present a review and reformulation of manifold constrained sampling-based motion planning within a unifying framework, IMACS (implicit manifold configuration space). IMACS enables a broad class of motion planners to plan in the presence of manifold constraints, decoupling the choice of motion planning algorithm and method for constraint adherence into orthogonal choices. We show that implicit configuration spaces defined by constraints can be presented to sampling-based planners by addressing two key fundamental primitives, sampling and local planning, and that IMACS preserves theoretical properties of probabilistic completeness and asymptotic optimality through these primitives. Within IMACS, we implement projection- and continuation-based methods for constraint adherence, and demonstrate the framework on a range of planners with both methods in simulated and realistic scenarios. Our results show that the choice of method for constraint adherence depends on many factors and that novel combinations of planners and methods of constraint adherence can be more effective than previous approaches. Our implementation of IMACS is open source within the Open Motion Planning Library and is easily extended for novel planners and constraint spaces.

[1]  Matthew T. Mason,et al.  Compliance and Force Control for Computer Controlled Manipulators , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Robert O. Ambrose,et al.  Robonaut 2 - The first humanoid robot in space , 2011, 2011 IEEE International Conference on Robotics and Automation.

[3]  Werner C. Rheinboldt,et al.  On the existence and uniqueness of solutions of nonlinear semi-implicit differential-algebraic equations , 1991 .

[4]  G. Swaminathan Robot Motion Planning , 2006 .

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

[6]  Lydia E. Kavraki,et al.  Measure theoretic analysis of probabilistic path planning , 2004, IEEE Transactions on Robotics and Automation.

[7]  Mantian Li,et al.  Learning the Metric of Task Constraint Manifolds for Constrained Motion Planning , 2018 .

[8]  Milan Simic,et al.  Sampling-Based Robot Motion Planning: A Review , 2014, IEEE Access.

[9]  Kostas E. Bekris,et al.  Probabilistic Completeness of RRT for Geometric and Kinodynamic Planning With Forward Propagation , 2018, IEEE Robotics and Automation Letters.

[10]  Florent Lamiraux,et al.  Manipulation planning: building paths on constrained manifolds , 2016 .

[11]  Howie Choset,et al.  Principles of Robot Motion: Theory, Algorithms, and Implementation ERRATA!!!! 1 , 2007 .

[12]  Leslie Pack Kaelbling,et al.  Sampling-based methods for factored task and motion planning , 2018, Int. J. Robotics Res..

[13]  Léonard Jaillet,et al.  Asymptotically-optimal Path Planning on Manifolds , 2012, Robotics: Science and Systems.

[14]  Lydia E. Kavraki,et al.  Motion Planning in the Presence of Drift, Underactuation and Discrete System Changes , 2005, Robotics: Science and Systems.

[15]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[16]  Marilena Vendittelli,et al.  Task-constrained motion planning with moving obstacles , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[17]  Dmitry Berenson,et al.  No falls, no resets: Reliable humanoid behavior in the DARPA robotics challenge , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[18]  Mike Stilman,et al.  Global Manipulation Planning in Robot Joint Space With Task Constraints , 2010, IEEE Transactions on Robotics.

[19]  Kris K. Hauser,et al.  Unbiased, scalable sampling of protein loop conformations from probabilistic priors , 2013, BMC Structural Biology.

[20]  Timothy Bretl,et al.  Motion Planning for Legged Robots on Varied Terrain , 2008, Int. J. Robotics Res..

[21]  Troy McMahon,et al.  Sampling Based Motion Planning with Reachable Volumes , 2016 .

[22]  Joseph S. B. Mitchell,et al.  The Discrete Geodesic Problem , 1987, SIAM J. Comput..

[23]  W. Rheinboldt MANPAK: A set of algorithms for computations on implicitly defined manifolds , 1996 .

[24]  Lydia E. Kavraki,et al.  Mobile manipulation: Encoding motion planning options using task motion multigraphs , 2011, 2011 IEEE International Conference on Robotics and Automation.

[25]  Irina Voiculescu,et al.  Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms , 2009 .

[26]  Giuseppe Oriolo,et al.  Task-constrained motion planning for underactuated robots , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[27]  G. Stewart On the Continuity of the Generalized Inverse , 1969 .

[28]  Nicholas Roy,et al.  Asymptotically-Optimal Path Planning on Manifolds , 2013 .

[29]  Lydia E. Kavraki,et al.  The Open Motion Planning Library , 2012, IEEE Robotics & Automation Magazine.

[30]  Henry van den Bedem,et al.  Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs , 2015, PLoS Comput. Biol..

[31]  Oussama Khatib,et al.  Synthesis of Whole-Body Behaviors through Hierarchical Control of Behavioral Primitives , 2005, Int. J. Humanoid Robotics.

[32]  Bilge Mutlu,et al.  RelaxedIK: Real-time Synthesis of Accurate and Feasible Robot Arm Motion , 2018, Robotics: Science and Systems.

[33]  Jean-Claude Latombe,et al.  Multi-modal Motion Planning in Non-expansive Spaces , 2010, Int. J. Robotics Res..

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

[35]  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).

[36]  Nicolas Mansard,et al.  HPP: A new software for constrained motion planning , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

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

[38]  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).

[39]  Jan Awrejcewicz,et al.  Bifurcation and Chaos , 1995 .

[40]  Lydia E. Kavraki,et al.  Anytime solution optimization for sampling-based motion planning , 2013, 2013 IEEE International Conference on Robotics and Automation.

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

[42]  Siddhartha S. Srinivasa,et al.  CHOMP: Covariant Hamiltonian optimization for motion planning , 2013, Int. J. Robotics Res..

[43]  Marco Pavone,et al.  Fast marching tree: A fast marching sampling-based method for optimal motion planning in many dimensions , 2013, ISRR.

[44]  Lydia E. Kavraki,et al.  Decoupling Constraints from Sampling-Based Planners , 2019, ISRR.

[45]  Maren Bennewitz,et al.  Whole-body motion planning for manipulation of articulated objects , 2013, 2013 IEEE International Conference on Robotics and Automation.

[46]  Léonard Jaillet,et al.  The CUIK Suite: Analyzing the Motion Closed-Chain Multibody Systems , 2014, IEEE Robotics & Automation Magazine.

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

[48]  Lydia E. Kavraki,et al.  Kinodynamic Motion Planning by Interior-Exterior Cell Exploration , 2008, WAFR.

[49]  Siddhartha S. Srinivasa,et al.  Addressing cost-space chasms in manipulation planning , 2011, 2011 IEEE International Conference on Robotics and Automation.

[50]  Scott Kuindersma,et al.  An Architecture for Online Affordance‐based Perception and Whole‐body Planning , 2015, J. Field Robotics.

[51]  Leonidas J. Guibas,et al.  Visibility-polygon search and euclidean shortest paths , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

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

[53]  Léonard Jaillet,et al.  Path Planning Under Kinematic Constraints by Rapidly Exploring Manifolds , 2013, IEEE Transactions on Robotics.

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

[55]  Kris K. Hauser,et al.  An empirical study of optimal motion planning , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[56]  Twan Koolen,et al.  Team IHMC's Lessons Learned from the DARPA Robotics Challenge Trials , 2015, J. Field Robotics.

[57]  Pieter Abbeel,et al.  Combined task and motion planning through an extensible planner-independent interface layer , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[58]  L. W. Tsai,et al.  Robot Analysis: The Mechanics of Serial and Parallel Ma-nipulators , 1999 .

[59]  Kris K. Hauser,et al.  Fast Interpolation and Time-Optimization on Implicit Contact Submanifolds , 2013, Robotics: Science and Systems.

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

[61]  Li Han,et al.  Convexly Stratified Deformation Spaces and Efficient Path Planning for Planar Closed Chains with Revolute Joints , 2008, Int. J. Robotics Res..

[62]  Andreas Aristidou,et al.  FABRIK: A fast, iterative solver for the Inverse Kinematics problem , 2011, Graph. Model..

[63]  Frank Chongwoo Park,et al.  Tangent bundle RRT: A randomized algorithm for constrained motion planning , 2014, Robotica.

[64]  S. Buss Introduction to Inverse Kinematics with Jacobian Transpose , Pseudoinverse and Damped Least Squares methods , 2004 .

[65]  Florent Lamiraux,et al.  Handling implicit and explicit constraints in manipulation planning , 2018, Robotics: Science and Systems.

[66]  Léonard Jaillet,et al.  Efficient asymptotically-optimal path planning on manifolds , 2013, Robotics Auton. Syst..

[67]  E. Hairer,et al.  Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .

[68]  Siddhartha S. Srinivasa,et al.  Batch Informed Trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs , 2014, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[69]  Antonio Bicchi,et al.  Noninteracting constrained motion planning and control for robot manipulators , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[70]  Michael E. Henderson,et al.  Multiple Parameter Continuation: Computing Implicitly Defined k-Manifolds , 2002, Int. J. Bifurc. Chaos.

[71]  Victor Ng-Thow-Hing,et al.  Randomized multi-modal motion planning for a humanoid robot manipulation task , 2011, Int. J. Robotics Res..

[72]  M. Spivak A comprehensive introduction to differential geometry , 1979 .

[73]  Marilena Vendittelli,et al.  A control-based approach to task-constrained motion planning , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[75]  Josep M. Porta,et al.  Randomized Kinodynamic Planning for Constrained Systems , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[76]  Sachin Chitta,et al.  Motion planning with constraints using configuration space approximations , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[78]  Nancy M. Amato,et al.  A Kinematics-Based Probabilistic Roadmap Method for Closed Chain Systems , 2001 .

[79]  Rasmus Fonseca,et al.  Collision‐free poisson motion planning in ultra high‐dimensional molecular conformation spaces , 2016, J. Comput. Chem..

[80]  Swarat Chaudhuri,et al.  An incremental constraint-based framework for task and motion planning , 2018, Int. J. Robotics Res..

[81]  Oussama Khatib,et al.  A unified approach for motion and force control of robot manipulators: The operational space formulation , 1987, IEEE J. Robotics Autom..

[82]  Lydia E. Kavraki,et al.  Sampling-Based Methods for Motion Planning with Constraints , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[83]  Pieter Abbeel,et al.  Motion planning with sequential convex optimization and convex collision checking , 2014, Int. J. Robotics Res..

[84]  Robert R. Burridge,et al.  Prophetic goal-space planning for human-in-the-loop mobile manipulation , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[85]  Andreas Hofmann,et al.  Improving Trajectory Optimization Using a Roadmap Framework , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[86]  Kamal K. Gupta,et al.  Path planning with general end-effector constraints: using task space to guide configuration space search , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[88]  William H. Press,et al.  Numerical recipes: the art of scientific computing, 3rd Edition , 2007 .

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

[90]  Siddhartha S. Srinivasa,et al.  Randomized path planning for redundant manipulators without inverse kinematics , 2007, 2007 7th IEEE-RAS International Conference on Humanoid Robots.

[91]  Kostas E. Bekris,et al.  Sparse roadmap spanners for asymptotically near-optimal motion planning , 2014, Int. J. Robotics Res..

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

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

[94]  Lydia E. Kavraki,et al.  Atlas + X: Sampling-based Planners on Constraint Manifolds , 2017 .

[95]  Riccardo Bonalli,et al.  Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach , 2019, Robotics: Science and Systems.

[96]  Paul M. Griffin,et al.  Path planning for a mobile robot , 1992, IEEE Trans. Syst. Man Cybern..

[97]  Nicholas Roy,et al.  Asymptotically Optimal Planning under Piecewise-Analytic Constraints , 2016, WAFR.

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