Autonomous Parking Using Optimization-Based Collision Avoidance

We present an optimization-based approach for autonomous parking. Building on recent advances in the area of optimization-based collision avoidance (OBCA), we show that the autonomous parking problem can be formulated as a smooth non-convex optimization problem. Unfortunately, such problems are numerically challenging to solve in general and require appropriate warm-starting. To address this limitation, we propose a novel algorithm called Hierarchical OBCA (H-OBCA). The main idea is to first use a generic path planner, such as Hybrid A*, to compute a coarse trajectory using a simplified vehicle model and by discretizing the state-input space. This path is subsequently used to warm-start the OBCA algorithm, which optimizes and smoothens the coarse path using a full vehicle model and continuous optimization. Our studies indicate that the proposed H-OBCA parking algorithm combines Hybrid A*'s global path planning capability with OBCA's ability to generate smooth, collision-free, and dynamically feasible paths. Extensive simulations suggest that the proposed H-OBCA algorithm is robust and admits realtime parking for autonomous vehicles. Sample code is provided at https://github.com/XiaojingGeorgeZhang/H-OBCA.

[1]  Agus Budiyono,et al.  Model predictive control for obstacle avoidance as hybrid systems of small scale helicopter , 2013, 2013 3rd International Conference on Instrumentation Control and Automation (ICA).

[2]  Pierre-Brice Wieber,et al.  Fast Direct Multiple Shooting Algorithms for Optimal Robot Control , 2005 .

[3]  Mo Chen,et al.  FaSTrack: A modular framework for fast and guaranteed safe motion planning , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

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

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

[6]  John Lygeros,et al.  Racing miniature cars: Enhancing performance using Stochastic MPC and disturbance feedback , 2017, 2017 American Control Conference (ACC).

[7]  Sebastian Thrun,et al.  Path Planning for Autonomous Vehicles in Unknown Semi-structured Environments , 2010, Int. J. Robotics Res..

[8]  Hans Joachim Ferreau,et al.  Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation , 2009 .

[9]  P. Goulart,et al.  Trajectory Generation for Aircraft Avoidance Maneuvers Using Online Optimization , 2011 .

[10]  Zhijiang Shao,et al.  Time-Optimal Maneuver Planning in Automatic Parallel Parking Using a Simultaneous Dynamic Optimization Approach , 2016, IEEE Transactions on Intelligent Transportation Systems.

[11]  Masayoshi Tomizuka,et al.  The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning , 2017, SIAM J. Control. Optim..

[12]  Hadas Kress-Gazit,et al.  Valet parking without a valet , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  RaphaelBertram,et al.  Correction to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths" , 1972 .

[14]  Magnus Egerstedt,et al.  Autonomous driving in urban environments: approaches, lessons and challenges , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[16]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[17]  Nils J. Nilsson,et al.  Correction to "A Formal Basis for the Heuristic Determination of Minimum Cost Paths" , 1972, SGAR.

[18]  I. Grossmann.  Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques , 2002 .

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

[20]  Masahiro Ono,et al.  Chance-Constrained Optimal Path Planning With Obstacles , 2011, IEEE Transactions on Robotics.

[21]  I. Michael Ross,et al.  Direct trajectory optimization by a Chebyshev pseudospectral method , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[22]  F. Borrelli,et al.  Collision-free UAV formation flight using decentralized optimization and invariant sets , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[23]  Emilio Frazzoli,et al.  A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles , 2016, IEEE Transactions on Intelligent Vehicles.

[24]  Stephen M. Erlien,et al.  Collision Avoidance and Stabilization for Autonomous Vehicles in Emergency Scenarios , 2017, IEEE Transactions on Control Systems Technology.

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

[26]  Xiaojing Zhang,et al.  Optimization-Based Collision Avoidance , 2017, IEEE Transactions on Control Systems Technology.

[27]  John Lygeros,et al.  Efficient implementation of Randomized MPC for miniature race cars , 2016, 2016 European Control Conference (ECC).

[28]  Masayoshi Tomizuka,et al.  Real time trajectory optimization for nonlinear robotic systems: Relaxation and convexification , 2017, Syst. Control. Lett..

[29]  Manfred Morari,et al.  Optimization‐based autonomous racing of 1:43 scale RC cars , 2015, ArXiv.

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

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

[32]  Andrew G. Alleyne,et al.  Autonomous Vehicle Control: A Nonconvex Approach for Obstacle Avoidance , 2017, IEEE Transactions on Control Systems Technology.

[33]  Jonathan P. How,et al.  Aircraft trajectory planning with collision avoidance using mixed integer linear programming , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).