Reducing Computation Times for Planning of Reference Trajectories in Cooperative Autonomous Driving

This paper considers the problem of planning reference trajectories for cooperating autonomous vehicles. Our previous work [1] relied on mixed-integer quadratic programming (MIQP) for planning, while controllable sets of hybrid automata were used to assess feasibility. In this paper, we supersede MIQP in the online part and obtain plans by directly making use of controllable sets and adapting ideas from approximate multi-parametric programming. The run-time of the algorithm is not only lower, but also more predictable than that of MIQP solvers, which is crucial for real-time operation. Even though it returns suboptimal solutions, the algorithm also enables the use of smaller sampling times or longer planning horizons.

[1]  Manfred Morari,et al.  Polytopic Approximation of Explicit Model Predictive Controllers , 2010, IEEE Transactions on Automatic Control.

[2]  Olaf Stursberg,et al.  Optimization-Based Maneuver Automata for Cooperative Trajectory Planning of Autonomous Vehicles , 2018, 2018 European Control Conference (ECC).

[3]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[4]  Matthias Althoff,et al.  Convex Interpolation Control with Formal Guarantees for Disturbed and Constrained Nonlinear Systems , 2017, HSCC.

[5]  Mathieu Desbrun,et al.  Barycentric coordinates for convex sets , 2007, Adv. Comput. Math..

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

[7]  D. Bertsekas,et al.  On the minimax reachability of target sets and target tubes , 1971 .

[8]  B. Moor,et al.  Mixed integer programming for multi-vehicle path planning , 2001, 2001 European Control Conference (ECC).

[9]  Alberto Bemporad,et al.  Predictive Control for Linear and Hybrid Systems , 2017 .

[10]  Julius Ziegler,et al.  The combinatorial aspect of motion planning: Maneuver variants in structured environments , 2015, 2015 IEEE Intelligent Vehicles Symposium (IV).

[11]  Thi Xuan Thao Dang Verification and Synthesis of Hybrid Systems , 2000 .

[12]  Colas Le Guernic Reachability Analysis of Hybrid Systems with Linear Continuous Dynamics. (Calcul d'Atteignabilité des Systèmes Hybrides à Partie Continue Linéaire) , 2009 .

[13]  Florent Altché,et al.  Partitioning of the free space-time for on-road navigation of autonomous ground vehicles , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[14]  Karl Iagnemma,et al.  Homotopy-Based Divide-and-Conquer Strategy for Optimal Trajectory Planning via Mixed-Integer Programming , 2015, IEEE Transactions on Robotics.

[15]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[16]  Martin Lauer,et al.  Cooperative Multiple Vehicle Trajectory Planning using MIQP , 2018, 2018 21st International Conference on Intelligent Transportation Systems (ITSC).

[17]  Alberto Bemporad,et al.  An Algorithm for Approximate Multiparametric Convex Programming , 2006, Comput. Optim. Appl..

[18]  Matthias Althoff,et al.  Formal verification of maneuver automata for parameterized motion primitives , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Olaf Stursberg,et al.  Fast optimizing control for non-convex state constraints using homotopy properties , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[20]  Jonas Sjöberg,et al.  Strategic decision making for automated driving on two-lane, one way roads using model predictive control , 2013, 2013 IEEE Intelligent Vehicles Symposium (IV).

[21]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[22]  Florent Altché,et al.  Optimal trajectory planning for autonomous driving integrating logical constraints: An MIQP perspective , 2016, 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC).

[23]  Russ Tedrake,et al.  Sampling-Based Polytopic Trees for Approximate Optimal Control of Piecewise Affine Systems , 2018, 2019 International Conference on Robotics and Automation (ICRA).

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

[25]  Matthias Althoff,et al.  Closed-form expressions of convex combinations , 2016, 2016 American Control Conference (ACC).

[26]  Olaf Stursberg,et al.  Cooperative driving using a hierarchy of mixed-integer programming and tracking control , 2017, 2017 IEEE Intelligent Vehicles Symposium (IV).