A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles

Self-driving vehicles are a maturing technology with the potential to reshape mobility by enhancing the safety, accessibility, efficiency, and convenience of automotive transportation. Safety-critical tasks that must be executed by a self-driving vehicle include planning of motions through a dynamic environment shared with other vehicles and pedestrians, and their robust executions via feedback control. The objective of this paper is to survey the current state of the art on planning and control algorithms with particular regard to the urban setting. A selection of proposed techniques is reviewed along with a discussion of their effectiveness. The surveyed approaches differ in the vehicle mobility model used, in assumptions on the structure of the environment, and in computational requirements. The side by side comparison presented in this survey helps to gain insight into the strengths and limitations of the reviewed approaches and assists with system level design choices.

[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]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

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

[4]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[5]  Nils J. Nilsson,et al.  A mobius automation: an application of artificial intelligence techniques , 1969, IJCAI 1969.

[6]  Nils J. Nilsson,et al.  A Mobile Automaton: An Application of Artificial Intelligence Techniques , 1969, IJCAI.

[7]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[8]  E. Polak An historical survey of computational methods in optimal control. , 1973 .

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

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

[11]  J. W. Humberston Classical mechanics , 1980, Nature.

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

[13]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[14]  Micha Sharir,et al.  Motion Planning in the Presence of Moving Obstacles , 1985, FOCS.

[15]  Takeo Kanade,et al.  First Results in Robot Road-Following , 1985, IJCAI.

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

[17]  Hans B. Pacejka,et al.  Tyre Modelling for Use in Vehicle Dynamics Studies , 1987 .

[18]  John F. Canny,et al.  New lower bound techniques for robot motion planning problems , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[19]  Mark H. Overmars,et al.  New methods for computing visibility graphs , 1988, SCG '88.

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

[21]  Osamu Takahashi,et al.  Motion planning in a plane using generalized Voronoi diagrams , 1989, IEEE Trans. Robotics Autom..

[22]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[23]  John F. Canny,et al.  Planning smooth paths for mobile robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

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

[25]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[26]  Bruce Randall Donald,et al.  Real-time robot motion planning using rasterizing computer graphics hardware , 1990, SIGGRAPH.

[27]  Fumio Miyazaki,et al.  A stable tracking control method for an autonomous mobile robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[28]  Charles E. Thorpe,et al.  Integrated mobile robot control , 1991 .

[29]  A. Ollero,et al.  Predictive path tracking of mobile robots. Application to the CMU NavLab , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[30]  R. C. Coulter,et al.  Implementation of the Pure Pursuit Path Tracking Algorithm , 1992 .

[31]  Jean-Paul Laumond,et al.  Primitives for smoothing mobile robot trajectories , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[32]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[33]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[34]  James A. Storer,et al.  Shortest paths in the plane with polygonal obstacles , 1994, JACM.

[35]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[36]  C. Samson Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[37]  Anthony Stentz,et al.  The Focussed D* Algorithm for Real-Time Replanning , 1995, IJCAI.

[38]  Georges Bastin,et al.  Control of Nonholonomic Wheeled Mobile Robots by State Feedback Linearization , 1995, Int. J. Robotics Res..

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

[40]  Carl D. Crane,et al.  Autonomous path-planning navigation system for site characterization , 1996, Defense, Security, and Sensing.

[41]  Pankaj K. Agarwal,et al.  Approximation algorithms for curvature-constrained shortest paths , 1996, SODA '96.

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

[43]  Ernst D. Dickmanns,et al.  Vehicles Capable of Dynamic Vision , 1997, IJCAI.

[44]  Henk Nijmeijer,et al.  Tracking Control of Mobile Robots: A Case Study in Backstepping , 1997, Autom..

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

[46]  Hongyan Wang,et al.  The complexity of the two dimensional curvature-constrained shortest-path problem , 1998 .

[47]  Thierry Fraichard,et al.  Path planning with uncertainty for car-like robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[48]  J. Betts Survey of Numerical Methods for Trajectory Optimization , 1998 .

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

[50]  Giuseppe Oriolo,et al.  Feedback control of a nonholonomic car-like robot , 1998 .

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

[52]  D. Hennessy,et al.  Traffic congestion, driver stress, and driver aggression , 1999 .

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

[54]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[55]  J. Christian Gerdes,et al.  A Unified Approach to Driver Assistance Systems Based on Artificial Potential Fields , 1999, Dynamic Systems and Control.

[56]  Subhash Suri,et al.  Curvature-Constrained Shortest Paths in a Convex Polygon , 2002, SIAM J. Comput..

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

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

[59]  Jean-Daniel Boissonnat,et al.  A Polynomial-Time Algorithm for Computing Shortest Paths of Bounded Curvature AmidstModerate Obstacles , 2003, Int. J. Comput. Geom. Appl..

[60]  Marko Bacic,et al.  Model predictive control , 2003 .

[61]  Sebastian Thrun,et al.  ARA*: Anytime A* with Provable Bounds on Sub-Optimality , 2003, NIPS.

[62]  Azim Eskandarian,et al.  Research advances in intelligent collision avoidance and adaptive cruise control , 2003, IEEE Trans. Intell. Transp. Syst..

[63]  Florent Lamiraux,et al.  Kinodynamic motion planning: connecting exploration trees using trajectory optimization Methods , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[64]  Carl D. Crane,et al.  Autonomous ground vehicle path tracking , 2004, J. Field Robotics.

[65]  Emilio Frazzoli,et al.  Incremental Search Methods for Reachability Analysis of Continuous and Hybrid Systems , 2004, HSCC.

[66]  Thierry Fraichard,et al.  Safe motion planning in dynamic environments , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[67]  Gordon T. Wilfong,et al.  Planning constrained motion , 1991, Annals of Mathematics and Artificial Intelligence.

[68]  M. Tomizuka,et al.  LTV controller design for vehicle lateral control under fault in rear sensors , 2005, IEEE/ASME Transactions on Mechatronics.

[69]  Z. Szabo,et al.  The Design of an Integrated Control System in Heavy Vehicles Based on an LPV Method , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[70]  Rajesh Rajamani,et al.  Vehicle dynamics and control , 2005 .

[71]  E. Velenis,et al.  Minimum Time vs Maximum Exit Velocity Path Optimization During Cornering , 2005, Proceedings of the IEEE International Symposium on Industrial Electronics, 2005. ISIE 2005..

[72]  Volker Graefe,et al.  Dynamic monocular machine vision , 1988, Machine Vision and Applications.

[73]  João Pedro Hespanha,et al.  Path-following for nonminimum phase systems removes performance limitations , 2005, IEEE Transactions on Automatic Control.

[74]  Volker Graefe,et al.  Applications of dynamic monocular machine vision , 1988, Machine Vision and Applications.

[75]  Andrew V. Goldberg,et al.  Computing the shortest path: A search meets graph theory , 2005, SODA '05.

[76]  Sven Koenig,et al.  Fast replanning for navigation in unknown terrain , 2005, IEEE Transactions on Robotics.

[77]  Sebastian Thrun,et al.  Anytime Dynamic A*: An Anytime, Replanning Algorithm , 2005, ICAPS.

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

[79]  Florent Lamiraux,et al.  Trajectory deformation applied to kinodynamic motion planning for a realistic car model , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[80]  Sebastian Thrun,et al.  Stanley: The robot that won the DARPA Grand Challenge , 2006, J. Field Robotics.

[81]  Anthony Stentz,et al.  Using interpolation to improve path planning: The Field D* algorithm , 2006, J. Field Robotics.

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

[83]  Francesco Borrelli,et al.  A linear time varying model predictive control approach to the integrated vehicle dynamics control problem in autonomous systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[84]  Manfred Morari,et al.  Hybrid Parameter-Varying Model Predictive Control for lateral vehicle stabilization , 2007, 2007 European Control Conference (ECC).

[85]  P. Tsiotras,et al.  Aggressive maneuvers on loose surfaces: Data analysis and input parametrization , 2007, 2007 Mediterranean Conference on Control & Automation.

[86]  João P. Hespanha,et al.  Trajectory-Tracking and Path-Following of Underactuated Autonomous Vehicles With Parametric Modeling Uncertainty , 2007, IEEE Transactions on Automatic Control.

[87]  Ariel Felner,et al.  Theta*: Any-Angle Path Planning on Grids , 2007, AAAI.

[88]  Sanjiv Singh,et al.  The 2005 DARPA Grand Challenge , 2007 .

[89]  Charles Poussot-Vassal,et al.  Towards global chassis control by integrating the brake and suspension systems , 2007 .

[90]  Sanjiv Singh,et al.  The 2005 DARPA Grand Challenge: The Great Robot Race , 2007 .

[91]  Eric A. Hansen,et al.  Anytime Heuristic Search , 2011, J. Artif. Intell. Res..

[92]  Francesco Borrelli,et al.  Predictive Active Steering Control for Autonomous Vehicle Systems , 2007, IEEE Transactions on Control Systems Technology.

[93]  David G. Kirkpatrick,et al.  Finding curvature-constrained paths that avoid polygonal obstacles , 2007, SCG '07.

[94]  Charles Poussot-Vassal,et al.  A new semi-active suspension control strategy through LPV technique , 2008 .

[95]  Luke Fletcher,et al.  A perception‐driven autonomous urban vehicle , 2008, J. Field Robotics.

[96]  D. Dolgov Practical Search Techniques in Path Planning for Autonomous Driving , 2008 .

[97]  Luke Fletcher,et al.  A perception-driven autonomous urban vehicle , 2008 .

[98]  Francesco Borrelli,et al.  Linear time‐varying model predictive control and its application to active steering systems: Stability analysis and experimental validation , 2008 .

[99]  Peter King,et al.  Odin: Team VictorTango's entry in the DARPA Urban Challenge , 2008, J. Field Robotics.

[100]  Luke Fletcher,et al.  A perception‐driven autonomous urban vehicle , 2008, J. Field Robotics.

[101]  Sanjiv Singh,et al.  The DARPA Urban Challenge: Autonomous Vehicles in City Traffic, George Air Force Base, Victorville, California, USA , 2009, The DARPA Urban Challenge.

[102]  Peter King,et al.  Odin: Team VictorTango's Entry in the DARPA Urban Challenge , 2009, The DARPA Urban Challenge.

[103]  Ross A. Knepper,et al.  Differentially constrained mobile robot motion planning in state lattices , 2009, J. Field Robotics.

[104]  S. Shankar Sastry,et al.  Model-predictive active steering and obstacle avoidance for autonomous ground vehicles , 2009 .

[105]  Manfred Morari,et al.  Autonomous vehicle steering using explicit LPV-MPC , 2009, 2009 European Control Conference (ECC).

[106]  Guilherme V. Raffo,et al.  A Predictive Controller for Autonomous Vehicle Path Tracking , 2009, IEEE Transactions on Intelligent Transportation Systems.

[107]  William Whittaker,et al.  Autonomous driving in urban environments: Boss and the Urban Challenge , 2008, J. Field Robotics.

[108]  Jonathan P. How,et al.  Real-Time Motion Planning With Applications to Autonomous Urban Driving , 2009, IEEE Transactions on Control Systems Technology.

[109]  I. Emre Köse,et al.  Gain-scheduled integrated active steering and differential control for vehicle handling improvement , 2009 .

[110]  Russ Tedrake,et al.  A quadratic regulator-based heuristic for rapidly exploring state space , 2010, 2010 IEEE International Conference on Robotics and Automation.

[111]  Péter Gáspár,et al.  LPV design of fault-tolerant control for road vehicles , 2012, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[112]  David Gerónimo Gómez,et al.  Survey of Pedestrian Detection for Advanced Driver Assistance Systems , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[113]  Yuval Tassa,et al.  Control-limited differential dynamic programming , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[114]  Emilio Frazzoli,et al.  Optimal kinodynamic motion planning using incremental sampling-based methods , 2010, 49th IEEE Conference on Decision and Control (CDC).

[115]  Jonas Sjöberg,et al.  Model-Based Threat Assessment for Avoiding Arbitrary Vehicle Collisions , 2010, IEEE Transactions on Intelligent Transportation Systems.

[116]  Sven Koenig,et al.  Lazy Theta*: Any-Angle Path Planning and Path Length Analysis in 3D , 2010, SOCS.

[117]  Dongwook Kim,et al.  Computer vision at the hyundai autonomous challenge , 2011, 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[118]  Rüdiger Dillmann,et al.  Probabilistic MDP-behavior planning for cars , 2011, 2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC).

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

[120]  W. Hager,et al.  An hp‐adaptive pseudospectral method for solving optimal control problems , 2011 .

[121]  Ilya V. Kolmanovsky,et al.  A Conjugate Gradient-Based BPTT-Like Optimal Control Algorithm With Vehicle Dynamics Control Application , 2009, IEEE Transactions on Control Systems Technology.

[122]  Julius Ziegler,et al.  StereoScan: Dense 3d reconstruction in real-time , 2011, 2011 IEEE Intelligent Vehicles Symposium (IV).

[123]  R. Verma,et al.  Semiautonomous Multivehicle Safety , 2011, IEEE Robotics & Automation Magazine.

[124]  Jonathan Schaeffer,et al.  Block A*: Database-Driven Search with Applications in Any-Angle Path-Planning , 2011, AAAI.

[125]  Panganamala Ramana Kumar,et al.  Provable Systemwide Safety in Intelligent Intersections , 2011, IEEE Transactions on Vehicular Technology.

[126]  Emilio Frazzoli,et al.  Differential flatness of a front-steered vehicle with tire force control , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[127]  Domitilla Del Vecchio,et al.  Efficient algorithms for collision avoidance at intersections , 2012, HSCC '12.

[128]  Peter Sanders,et al.  Exact Routing in Large Road Networks Using Contraction Hierarchies , 2012, Transp. Sci..

[129]  Emilio Frazzoli,et al.  Intention-Aware Motion Planning , 2013, WAFR.

[130]  G. Ros,et al.  Visual SLAM for Driverless Cars : A Brief Survey , 2012 .

[131]  Alessandro Rucco,et al.  Computing minimum lap-time trajectories for a single-track car with load transfer , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[132]  Alberto Broggi,et al.  The VisLab Intercontinental Autonomous Challenge: An Extensive Test for a Platoon of Intelligent Vehicles , 2012 .

[133]  Azim Eskandarian,et al.  Handbook of Intelligent Vehicles , 2012 .

[134]  Leslie Pack Kaelbling,et al.  LQR-RRT*: Optimal sampling-based motion planning with automatically derived extension heuristics , 2012, 2012 IEEE International Conference on Robotics and Automation.

[135]  Carlos Bordons Alba,et al.  Model Predictive Control , 2012 .

[136]  Péter Gáspár,et al.  Robust Control and Linear Parameter Varying approaches: Application to Vehicle Dynamics , 2013 .

[137]  Jur P. van den Berg,et al.  Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics , 2013, 2013 IEEE International Conference on Robotics and Automation.

[138]  Péter Gáspár,et al.  Integrated vehicle dynamics control via coordination of active front steering and rear braking , 2013, Eur. J. Control.

[139]  Markus Maurer,et al.  Probabilistic online POMDP decision making for lane changes in fully automated driving , 2013, 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013).

[140]  Quan Hung Tran,et al.  Modelling of traffic situations at urban intersections with probabilistic non-parametric regression , 2013, 2013 IEEE Intelligent Vehicles Symposium (IV).

[141]  Emilio Frazzoli,et al.  Optimal motion planning with the half-car dynamical model for autonomous high-speed driving , 2013, 2013 American Control Conference.

[142]  P. Olver Nonlinear Systems , 2013 .

[143]  Domitilla Del Vecchio,et al.  Cooperative Collision Avoidance at Intersections: Algorithms and Experiments , 2013, IEEE Transactions on Intelligent Transportation Systems.

[144]  Emilio Frazzoli,et al.  Sampling-based optimal motion planning for non-holonomic dynamical systems , 2013, 2013 IEEE International Conference on Robotics and Automation.

[145]  Rüdiger Dillmann,et al.  Probabilistic decision-making under uncertainty for autonomous driving using continuous POMDPs , 2014, 17th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[146]  Mark E. Campbell,et al.  Discrete and Continuous, Probabilistic Anticipation for Autonomous Robots in Urban Environments , 2010, IEEE Transactions on Robotics.

[147]  E. Kim,et al.  Model predictive control strategy for smooth path tracking of autonomous vehicles with steering actuator dynamics , 2014 .

[148]  Kostas E. Bekris,et al.  Sparse Methods for Efficient Asymptotically Optimal Kinodynamic Planning , 2014, WAFR.

[149]  Emilio Frazzoli,et al.  Generalized innovation and inference algorithms for hidden mode switched linear stochastic systems with unknown inputs , 2014, 53rd IEEE Conference on Decision and Control.

[150]  Emilio Frazzoli,et al.  RRTX: Real-Time Motion Planning/Replanning for Environments with Unpredictable Obstacles , 2014, WAFR.

[151]  Julius Ziegler,et al.  Making Bertha Drive—An Autonomous Journey on a Historic Route , 2014, IEEE Intelligent Transportation Systems Magazine.

[152]  Mike Stilman,et al.  Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete , 2014, WAFR.

[153]  Sertac Karaman,et al.  Polling-systems-based control of high-performance provably-safe autonomous intersections , 2014, 53rd IEEE Conference on Decision and Control.

[154]  Santokh Singh,et al.  Critical Reasons for Crashes Investigated in the National Motor Vehicle Crash Causation Survey , 2015 .

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

[156]  Fang Zhou,et al.  Parsimonious shooting heuristic for trajectory control of connected automated traffic part I: Theoretical analysis with generalized time geography , 2015, ArXiv.

[157]  Edwin Olson,et al.  Multipolicy decision-making for autonomous driving via changepoint-based behavior prediction: Theory and experiment , 2015, Autonomous Robots.

[158]  Alberto Broggi,et al.  PROUD—Public Road Urban Driverless-Car Test , 2015, IEEE Transactions on Intelligent Transportation Systems.

[159]  Marco Pavone,et al.  Optimal sampling-based motion planning under differential constraints: The driftless case , 2014, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[160]  Andrew V. Goldberg,et al.  Route Planning in Transportation Networks , 2015, Algorithm Engineering.

[161]  Peng Liu,et al.  Classification of Highway Lane Change Behavior to Detect Dangerous Cut-in Maneuvers , 2016 .