Real-time motion planning for agile autonomous vehicles

Planning the path of an autonomous, agile vehicle in a dynamic environment is a very complex problem, especially when the vehicle is required to use its full maneuvering capabilities. Recent efforts aimed at using randomized algorithms for planning the path of kinematic and dynamic vehicles have demonstrated considerable potential for implementation on future autonomous platforms. This paper builds upon these efforts by proposing a randomized motion planning architecture for dynamical systems in the presence of fixed and moving obstacles. This architecture addresses the dynamic constraints on the vehicle's motion, and it provides at the same time a consistent decoupling between low-level control and motion planning. Simulation examples involving a ground robot and a small autonomous helicopter, are presented and discussed.

[1]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[2]  J. Davenport.  Editor , 1960 .

[3]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[4]  E. Blum,et al.  The Mathematical Theory of Optimal Processes. , 1963 .

[5]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[6]  R. Bellman.  Dynamic programming. , 1957, Science.

[7]  Michael Athans,et al.  Optimal Control , 1966 .

[8]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[9]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[10]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

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

[12]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[14]  Tomás Lozano-Pérez,et al.  Automatic Planning of Manipulator Transfer Movements , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[16]  Robert L. Shaw,et al.  Fighter Combat: Tactics and Maneuvering , 1985 .

[17]  Chee-Keng Yap,et al.  A "Retraction" Method for Planning the Motion of a Disc , 1985, J. Algorithms.

[18]  Editors , 1986, Brain Research Bulletin.

[19]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1986 .

[20]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

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

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

[23]  Michael Lewis,et al.  Game theory for automated maneuvering during air-to-air combat , 1990 .

[24]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[25]  Jean-Claude Latombe,et al.  Numerical potential field techniques for robot path planning , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

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

[27]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[28]  Narendra Ahuja,et al.  A potential field approach to path planning , 1992, IEEE Trans. Robotics Autom..

[29]  J. Canny,et al.  Nonholonomic Motion Planning , 1992 .

[30]  M. Fliess,et al.  Sur les systèmes non linéaires différentiellement plats , 1992 .

[31]  J. Marsden.  Lectures on Mechanics , 1992 .

[32]  Gerardo Lafferriere,et al.  A Differential Geometric Approach to Motion Planning , 1993 .

[33]  Jean-Paul Laumond,et al.  Singularities and Topological Aspects in Nonholonomic Motion Planning , 1993 .

[34]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[35]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

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

[37]  M. H. Overmars,et al.  A paradigm for probabilistic path planning , 1995 .

[38]  Kurt Mehlhorn,et al.  LEDA: a platform for combinatorial and geometric computing , 1997, CACM.

[39]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[40]  Lydia E. Kavraki,et al.  Randomized query processing in robot path planning , 1995, STOC '95.

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

[42]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[43]  Richard M. Murray,et al.  Real Time Trajectory Generation for Differentially Flat Systems , 1996 .

[44]  Lydia E. Kavraki,et al.  Analysis of probabilistic roadmaps for path planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[45]  Nancy M. Amato,et al.  A randomized roadmap method for path and manipulation planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

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

[47]  Alexander Leonessa,et al.  Globally stabilizing controllers for multi-mode axial flow compressors via equilibria-dependent Lyapunov functions , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[48]  Kurt Mehlhorn,et al.  The LEDA Platform of Combinatorial and Geometric Computing , 1997, ICALP.

[49]  Douglas Thomson,et al.  Mathematical Definition of Helicopter Maneuvers , 1997 .

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

[51]  S. Sastry,et al.  Output tracking control design of a helicopter model based on approximate linearization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

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

[54]  Lydia E. Kavraki,et al.  Randomized Query Processing in Robot Path Planning , 1998, J. Comput. Syst. Sci..

[55]  Lydia E. Kavraki,et al.  Probabilistic Roadmaps for Robot Path Planning , 1998 .

[56]  R. Murray,et al.  Real‐time trajectory generation for differentially flat systems , 1998 .

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

[58]  Philippe Souères,et al.  Optimal trajectories for nonholonomic mobile robots , 1998 .

[59]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

[60]  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).

[61]  Emilio Frazzoli,et al.  A hybrid control architecture for aggressive maneuvering of autonomous helicopters , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[62]  Gregory E. Chamitoff,et al.  Autonomous Maneuver Tracking for Self-Piloted Vehicles , 1999 .

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

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

[65]  F. Bullo.  Stabilization of relative equilibria for systems on Riemannian manifolds , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[66]  Rajeev Motwani,et al.  Path Planning in Expansive Configuration Spaces , 1999, Int. J. Comput. Geom. Appl..

[67]  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).

[68]  Emilio Frazzoli,et al.  Real-Time Motion Planning for Agile Autonomous Vehicles , 2000 .

[69]  E. Feron,et al.  Robust hybrid control for autonomous vehicle motion planning , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[70]  Munther A. Dahleh,et al.  A computationally efficient Lyapunov-based scheduling procedure for control of nonlinear systems with stability guarantees , 2000, IEEE Trans. Autom. Control..

[71]  Mark B. Milam,et al.  A new computational approach to real-time trajectory generation for constrained mechanical systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[72]  Emilio Frazzoli,et al.  Trajectory tracking control design for autonomous helicopters using a backstepping algorithm , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[73]  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).

[74]  R. Murray,et al.  Trajectory Planning of Differentially Flat Systems with Dynamics and Inequalities , 2000 .

[75]  Emilio Frazzoli,et al.  A RANDOMIZED ATTITUDE SLEW PLANNING ALGORITHM FOR AUTONOMOUS SPACECRAFT , 2001 .

[76]  Kevin M. Lynch,et al.  Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems , 2001, IEEE Trans. Robotics Autom..

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