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Nonlinear Model Predictive Control for Autonomous Vehicles.pdf

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    Sommario
    Abstract
    List of publications
    1 Simplified Vehicle Models
    1.1 Four Wheels Model
    1.2 The Bicycle Model
    1.3 Tire Model
    1.3.1 Basics of Static Tire Model
    1.3.2 Pacejka Tire Model
    1.4 Bicycle Model Based on Small Angles Approximation and Linear Tire Model
    1.5 Point Mass Vehicle Model
    1.6 A Static Model for Tire Normal Force Calculation
    2 Model Predictive Control. Problem Formulation
    2.1 Nonlinear MPC
    2.2 Linear Time Varying (LTV) MPC
    2.3 Stability Analysis
    2.3.1 Stability of a State Trajectory
    2.4 Alternative Approaches to Suboptimal MPC Schemes
    3 VDC via Guidance and Navigation Control Systems
    3.1 Hierarchical Framework for Autonomous Guidance
    3.2 Path Planning Problem Formulation
    3.3 Concluding Remarks
    4 Active Front Steering Control in Autonomous Vehicles
    4.1 Nonlinear Model Predictive Active Front Steering Control (NMPC)
    4.2 LTV-MPC Active Front Steering Control Problem
    4.2.1 Active Front Steering via LTV MPC and Stability Condition (2.24)
    4.3 Double Lane Change on Snow Using Active Front Steering
    4.3.1 Trajectory generation
    4.4 Simulation and Experimental Results
    4.4.1 NMPC Active Front Steering Controller
    4.4.2 LTV MPC Active Front Steering Controller
    4.4.3 Low Complexity LTV MPC Active Front Steering Controller
    4.4.4 LTV MPC Active Front Steering Controller with Stability Condition. Simulations results
    4.5 Concluding Remarks
    5 Combined Steering, Braking and Active Differential Control in Autonomous Vehicles
    5.1 Combined AFS and Braking NMPC
    5.1.1 Slip-Based Steering and Braking NMPC
    5.1.2 Torque-Based Steering and Braking NMPC
    5.2 Combined AFS and Braking LTV MPC
    5.2.1 Slip-Based Steering and Braking LTV MPC
    5.2.2 Torque-Based Steering and Braking LTV MPC
    5.2.3 Discretization of the Linearized Vehicle Model
    5.2.4 Reduced Order Discrete-Time Linearized Vehicle Model
    5.2.5 LTV MPC Based on a Reduced Vehicle Linear Model
    5.3 Double Lane Change on Snow Using Combined AFS and Braking
    5.4 Simulation and Experimental Results
    5.4.1 Controller A
    5.4.2 Controller B
    5.4.3 Controller C
    5.5 Concluding Remarks
    6 Real time implementation of the Model Predictive Vehicle Dynamics Control
    6.1 Sensing System and Actuators
    6.2 The dSPACE Experimental Setup
    6.2.1 Hardware
    6.2.2 Software
    6.3 The Labview Experimental Setup
    Bibliography
    A Modeling
    A.1 Four Wheels Vehicle Model Validation
    A.2 Understeering and Oversteering
    B Formulation of The QP Problems
    B.1 Prediction model
    B.2 Problem formulation
    List of figures
    List of tables
    Nonlinear Model Predictive Control for Autonomous Vehicles Paolo Falcone Department of Engineering University of Sannio, Benevento June 2007 cPaolo Falcone
    A mamma, pap`a, Giusy e Rossella
    Sommario In questo lavoro di tesi sono stati considerati i problemi del progetto e dell’ implementazione di algoritmi di controllo delle dinamiche del veicolo basati su tecniche di controllo ottimo predittivo (MPC). Per questa classe di sistemi, le nonlinearit`a del modello matematico e i bassi tempi di campionamento limitano l’implementazione in real-time di algoritmi di controllo MPC a regioni dello spazio di stato e ingresso dove il comportamento del sistema `e lineare. Questa limitazione diventa ancora pi`u stringente quando, per la validazione sperimen- tale, vengono utilizzati sistemi di prototipazione standard con bassa capacit`a di calcolo. In questa tesi sono stati inizialmente progettati e implementati controllori MPC non lineari per il controllo di sistemi di sterzata attiva (AFS). In questa classe di controllori, nota la traiettoria di riferimento su un orizzonte temporale finito, il controllore calcola l’angolo di sterzata delle ruote anteriori in modo tale da seguire la traiettoria di riferimento alla pi`u elevata velocit`a possibile su superfici a basso coefficiente di attrito. Mediante test sperimentali `e stato dimostrato che l’esecuzione in real-time di tali controllori, su un sistema di prototipazione rapida dSPACE c alla frequenza di 20 Hz, `e limitata a basse velocit`a del veicolo. Per tale motivo sono stati proposti algoritmi di controllo MPC a bassa com- plessit`a computazionale in grado di operare su ampie regioni degli spazi di stato e di ingresso (elevate velocit`a del veicolo ed elevati angoli di deriva). Gli algo- ritmi di controllo MPC proposti sono basati su linearizzazioni successive (LTV MPC) del modello non lineare del veicolo. Le prestazioni e la stabilit`a dei controllori LTV MPC proposti sono stati ulteriore oggetto di interesse e di studio. In particolare, per migliorare le prestazioni del controllore sono stati proposti vincoli nello spazio di stato e 1
    2 ingresso, derivanti da un attento studio delle dinamiche non lineari del veicolo. La stabilit`a del sistema, invece, `e imposta mediante vincoli convessi aggiunti al problema di ottimizzazione su tempo finito . Gli algoritmi di controllo MPC proposti sono stati utilizzati sia per il pro- getto di controllori della sola sterzata attiva sia per il progetto di controllori che combinano la sterzata e le frenate indipendenti alle quattro ruote. Questi controllori sono stati validati con esperimenti su una vettura equipaggiata con un sistema di prototipazione rapida dSPACE. Gli esperimenti sono stati effet- tuati presso un centro di test dotato di piste ricoperte di ghiaccio e neve. `E stato dimostrato che i controllori proposti possono stabilizzare il veicolo lungo la traiettoria desiderata fino a 75 Km/h su una superficie ghiacciata. Questa attivit`a di ricerca `e stata sponsorizzata dai Laboratori di Ricerca Ford in Dearborn, Michigan, USA.
    Abstract In this thesis we consider the problem of designing and implementing Model Predictive Controllers (MPC) for stabilizing the dynamics of an autonomous ground vehicle. For such a class of systems, the non-linear dynamics and the fast sampling time limit the real-time implementation of MPC algorithms to local and linear operating regions. This phenomenon becomes more relevant when using the limited computational resources of a standard rapid prototyping system for automotive applications. In this thesis we first study the design and the implementation of a nonlinear MPC controller for an Active Font Steering (AFS) problem. At each time step a trajectory is assumed to be known over a finite horizon, and the nonlinear MPC controller computes the front steering angle in order to follow the trajectory on slippery roads at the highest possible entry speed. We demonstrate that experimental tests can be performed only at low vehicle speed on a dSPACE rapid prototyping system with a frequency of 20 Hz. Then, we propose a low complexity MPC algorithm which is real-time capa- ble for a wider operating range of the state and input space (i.e., high vehicle speed and large slip angles). The MPC control algorithm is based on successive on-line linearizations of the nonlinear vehicle model (LTV MPC). We study per- formance and stability of the proposed MPC scheme. Performance is improved through an ad hoc stabilizing state and input constraints arising from a careful study of the vehicle nonlinearities. The stability of the LTV MPC is enforced by means of an additional convex constraint to the finite time optimization problem. We used the proposed LTV MPC algorithm in order to design AFS con- trollers and combined steering and braking controllers. We validated the pro- posed AFS and combined steering and braking MPC algorithms in real-time, 3
    4 on a passenger vehicle equipped with a DSPACE rapid prototyping system. Ex- periments have been performed in a testing center equipped with snowy and icy tracks. For both controllers we showed that vehicle stabilization can be achieved at high speed (up to 75 Kph) on icy covered roads. This research activity has been supported by Ford Research Laboratories, in Dearborn, MI, USA.
    List of publications List of the publications of the candidate [1] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Linear Time Varying Model Predictive Control and its Application to Active Steering Systems: Stability Analysis and Experimental Validation”, To appear on International Journal of Robust and Nonlinear Control 2007. [2] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Predictive Active Steering Control for Autonomous Vehicle Systems”. IEEE Tans- actions on Control Systems Technology, vol. 15 , no. 3 , May 2007 , p. 566-580. [3] F. Borrelli , P. Falcone , C. Del Vecchio, “Event-Based Receding Horizon Control for Two-Stages Multi-Product Production Plants”. To appear on on Control Engineering Practice 2007. [4] F. Borrelli, P. Falcone, T. Keviczky, J. Asgari, E. H. Tseng, D. Hrovat, “MPC-based approach to active steering for autonomous vehicle systems”. International Journal on Vehicle Autonomous Systems, vol. 3, no. 2/3/4, November 2005 , p. 265-291. [5] P. Falcone, G. Fiengo, L. Glielmo, “New Strategy for Torque Estimators”. dSPACE News, June 2005. [6] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Predictive Autonomous Vehicles: a Linear Time Varying Model Predictive Control Approach”. Submitted to 46th Conference on Decision and Control. 5
    6 [7] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “A Model Predictive Control Approach for Combined Braking and Steering in Au- tonomous Vehicles”. 15th Mediterranean Conference on Control and Au- tomation, Athens, Greece, June 2007. [8] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Integrated Braking and Steering Model Predictive Control Approach in Autonomous Vehicles”. 5th IFAC Symposium on Advances in Automotive Control, Monterey Coast, CA, USA, 2007 [9] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “MPC-Based Yaw Stabilization Via Active Front Steering and Braking”. Submitted to 20th International Symposium: Dynamics of Vehicles on Roads and Tracks, UC Berkeley, CA, USA, 2007. [10] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “A Real-Time Model Predictive Control Approach for Autonomous Active Steering”. First IFAC International workshop on NMPC for Fast Systems, Grenoble, France, October 2006. [11] P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Model Predic- tive Control Approach for Autonomous Active Steering Based on Succes- sive On-Line Linearizations”. 8th International Symposium on Advanced Vehicle Control , Taipei, Taiwan, August 2006. [12] F. Borrelli , P. Falcone , C. Del Vecchio, “Event-Based Receding Hori- zon Control for Two-Stages Multi-Product Production Plants”. American Control Conference, Minneapolis, Minnesota. June 2006. [13] T. Keviczky, P. Falcone, F. Borrelli, J. Asgari, E. H. Tseng, D. Hrovat, “Predictive Control Approach to Autonomous Vehicle Steering”. Ameri- can Control Conference, Minneapolis, Minnesota, June 2006. [14] F. Borrelli , P. Falcone , C. Del Vecchio, M. Cibardo, S. Canto,“Receding horizon control for two-stages multi-product production plants”. ANIPLA 2005, Napoli, Italy, November 2005. [15] P. Falcone, G. Fiengo, L. Glielmo, “Nicely Nonlinear Engine Torque Esti- mator”. 16th IFAC World Congress 2005, Prague, Czech Republic.
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