0
Research Papers

Enhancing the Performance of a Safe Controller Via Supervised Learning for Truck Lateral Control

[+] Author and Article Information
Yuxiao Chen

Department of Mechanical and Civil Engineering,
California Institute of Technology,
Pasadena, CA 91106
e-mail: chenyx@caltech.edu

Ayonga Hereid

Department of Mechanical and
Aerospace Engineering,
Ohio State University,
Columbus, OH 43210
e-mail: hereid.1@osu.edu

Huei Peng

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: hpeng@umich.edu

Jessy Grizzle

Department of Electrical Engineering and
Computer Science,
University of Michigan,
Ann Arbor, MI 48109
e-mail: grizzle@umich.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 23, 2018; final manuscript received April 3, 2019; published online June 3, 2019. Assoc. Editor: Xuebo Zhang.

J. Dyn. Sys., Meas., Control 141(10), 101005 (Jun 03, 2019) (13 pages) Paper No: DS-18-1396; doi: 10.1115/1.4043487 History: Received August 23, 2018; Revised April 03, 2019

Correct-by-construction techniques, such as control barrier functions (CBFs), can be used to guarantee closed-loop safety by acting as a supervisor of an existing legacy controller. However, supervisory-control intervention typically compromises the performance of the closed-loop system. On the other hand, machine learning has been used to synthesize controllers that inherit good properties from a training dataset, though safety is typically not guaranteed due to the difficulty of analyzing the associated learning structure. In this paper, supervised learning is combined with CBFs to synthesize controllers that enjoy good performance with provable safety. A training set is generated by trajectory optimization that incorporates the CBF constraint for an interesting range of initial conditions of the truck model. A control policy is obtained via supervised learning that maps a feature representing the initial conditions to a parameterized desired trajectory. The learning-based controller is used as the performance controller and a CBF-based supervisory controller guarantees safety. A case study of lane keeping (LK) for articulated trucks shows that the controller trained by supervised learning inherits the good performance of the training set and rarely requires intervention by the CBF supervisor.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ames, A. D. , Grizzle, J. W. , and Tabuada, P. , 2014, “ Control Barrier Function Based Quadratic Programs With Application to Adaptive Cruise Control,” 53rd IEEE Conference on Decision and Control (CDC), Los Angeles, CA, Dec. 15–17, pp. 6271–6278.
Xu, X. , Grizzle, J. W. , Tabuada, P. , and Ames, A. D. , 2016, “ Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control,” preprint .
Hsu, S.-C. , Xu, X. , and Ames, A. D. , 2015, “ Control Barrier Function Based Quadratic Programs With Application to Bipedal Robotic Walking,” American Control Conference (ACC), Chicago, IL, July 1–3, pp. 4542–4548.
Chen, Y. , Peng, H. , and Grizzle, J. , 2017, “ Obstacle Avoidance for Low-Speed Autonomous Vehicles With Barrier Function,” IEEE Trans. Control Syst. Technol., 26(1), pp. 194–206. [CrossRef]
Ames, A. D. , Xu, X. , Grizzle, J. W. , and Tabuada, P. , 2016, “ Control Barrier Function Based Quadratic Programs With Application to Automotive Safety Systems,” preprint arXiv: 1609.06408.
Gomi, H. , and Kawato, M. , 1993, “ Neural Network Control for a Closed-Loop System Using Feedback-Error-Learning,” Neural Networks, 6(7), pp. 933–946. [CrossRef]
Da, X. , Hartley, R. , and Grizzle, J. W. , 2017, “ Supervised Learning for Stabilizing Underactuated Bipedal Robot Locomotion, With Outdoor Experiments on the Wave Field,” IEEE International Conference on Robotics and Automation (ICRA), Singapore, May 29—June 3, pp. 3476–3483.
Bojarski, M. , Del Testa, D. , Dworakowski, D. , Firner, B. , Flepp, B. , Goyal, P. , Jackel, L. D. , Monfort, M. , Muller, U. , Zhang, J. , Zhang, X. , Zhao, J. , and Zieba, K. , 2016, “ End to End Learning for Self-Driving Cars,” preprint .
Sallab, A. E. , Abdou, M. , Perot, E. , and Yogamani, S. , 2016, “ End-to-End Deep Reinforcement Learning for Lane Keeping Assist,” preprint .
Oh, S.-Y. , Lee, J.-H. , and Choi, D.-H. , 2000, “ A New Reinforcement Learning Vehicle Control Architecture for Vision-Based Road Following,” IEEE Trans. Veh. Technol., 49(3), pp. 997–1005. [CrossRef]
Bertsekas, D. , 1995, Dynamic Programming and Optimal Control, 1, Athena Scientific, Belmont, MA.
Gillula, J. H. , and Tomlin, C. J. , 2012, “ Guaranteed Safe Online Learning Via Reachability: Tracking a Ground Target Using a Quadrotor,” IEEE International Conference on Robotics and Automation (ICRA), St. Paul, MN, May 14–18, pp. 2723–2730.
Akametalu, A. K. , Fisac, J. F. , Gillula, J. H. , Kaynama, S. , Zeilinger, M. N. , and Tomlin, C. J. , 2014, “ Reachability-Based Safe Learning With Gaussian Processes,” IEEE 53rd Annual Conference on Decision and Control (CDC), Los Angeles, CA, Dec. 15–17, pp. 1424–1431.
Smit-Anseeuw, N. , Vasudevan, R. , and Remy, C. D. , 2017, “ Safe Online Learning Using Barrier Functions,” Proceedings of Dynamic Walking, Mariehamn, Finland, June 4–9.
Berkenkamp, F. , and Schoellig, A. P. , 2015, “ Safe and Robust Learning Control With Gaussian Processes,” European Control Conference (ECC), Linz, Austria, July 15–17, pp. 2496–2501.
Isidori, A. , 2013, Nonlinear Control Systems, Springer Science & Business Media, London.
Khalil, H. K. , 1996, Nonlinear Systems, Vol. 2, Prentice Hall, Upper Saddle River, NJ, pp. 5–1.
Westervelt, E. R. , Grizzle, J. W. , Chevallereau, C. , Choi, J. H. , and Morris, B. , 2007, Feedback Control of Dynamic Bipedal Robot Locomotion, CRC Press, Boca Raton, FL.
Shiriaev, A. , Perram, J. W. , and Canudas-de-Wit, C. , 2005, “ Constructive Tool for Orbital Stabilization of Underactuated Nonlinear Systems: Virtual Constraints Approach,” IEEE Trans. Autom. Control, 50(8), pp. 1164–1176. [CrossRef]
Maggiore, M. , and Consolini, L. , 2013, “ Virtual Holonomic Constraints for Euler–Lagrange Systems,” IEEE Trans. Autom. Control, 58(4), pp. 1001–1008. [CrossRef]
Grizzle, J. W. , Di Benedetto, M. D. , and Lamnabhi-Lagarrigue, F. , 1994, “ Necessary Conditions for Asymptotic Tracking in Nonlinear Systems,” IEEE Trans. Autom. Control, 39(9), pp. 1782–1794. [CrossRef]
Miege, A. J. , and Cebon, D. , 2005, “ Optimal Roll Control of an Articulated Vehicle: Theory and Model Validation,” Veh. Syst. Dyn., 43(12), pp. 867–884. [CrossRef]
Wong, J. Y. , 2008, Theory of Ground Vehicles, Wiley, Hoboken, NJ.
Xu, X. , Tabuada, P. , Grizzle, J. W. , and Ames, A. D. , 2015, “ Robustness of Control Barrier Functions for Safety Critical Control,” IFAC-PapersOnLine, 48(27), pp. 54–61. [CrossRef]
Parrilo, P. A. , 2003, “ Semidefinite Programming Relaxations for Semialgebraic Problems,” Math. Program., 96(2), pp. 293–320. [CrossRef]
Bochnak, J. , Coste, M. , and Roy, M.-F. , 2013, Real Algebraic Geometry, Vol. 36, Springer Science & Business Media, New York.
Stengle, G. , 1974, “ A Nullstellensatz and a Positivstellensatz in Semialgebraic Geometry,” Math. Ann., 207(2), pp. 87–97. [CrossRef]
Papachristodoulou, A. , and Prajna, S. , 2002, “ On the Construction of Lyapunov Functions Using the Sum of Squares Decomposition,” 41st IEEE Conference on Decision and Control (CDC), Las Vegas, NV, Dec. 10–13, pp. 3482–3487.
Prajna, S. , and Jadbabaie, A. , 2004, “ Safety Verification of Hybrid Systems Using Barrier Certificates,” International Workshop on Hybrid Systems: Computation and Control (HSCC), Philadelphia, PA, Mar. 25–27, pp. 477–492.
Prajna, S. , Papachristodoulou, A. , and Wu, F. , 2004, “ Nonlinear Control Synthesis by Sum of Squares Optimization: A Lyapunov-Based Approach,” Fifth Asian Control Conference (ASCC), Melbourne, Australia, July 20–23 , pp. 157–165.
Goh, K. C. , Turan, L. , Safonov, M. G. , Papavassilopoulos, G. P. , and Ly, J. H. , 1994, “ Biaffine Matrix Inequality Properties and Computational Methods,” American Control Conference (ACC), Baltimore, MD, June 29–July 1, pp. 850–855.
Chen, Y. , Peng, H. , and Grizzle, J. W. , 2018, “ Validating Noncooperative Control Designs Through a Lyapunov Approach,” IEEE Trans. Control Syst. Technol., 27(2), pp. 527–539. [CrossRef]
Betts, J. T. , 2010, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, SIAM, Philadelphia, PA.
Hereid, A. , Cousineau, E. A. , Hubicki, C. M. , and Ames, A. D. , 2016, “ 3D Dynamic Walking With Underactuated Humanoid Robots: A Direct Collocation Framework for Optimizing Hybrid Zero Dynamics,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 1447–1454.
Ames, A. D. , Xu, X. , Grizzle, J. W. , and Tabuada, P. , 2017, “ Control Barrier Function Based Quadratic Programs for Safety Critical Systems,” IEEE Trans. Autom. Control, 62(8), pp. 3861–3876. [CrossRef]
Stoer, J. , and Bulirsch, R. , 2013, Introduction to Numerical Analysis, Vol. 12, Springer Science & Business Media, New York.
Hereid, A. , and Ames, A. D. , 2017, “ FROST*: Fast Robot Optimization and Simulation Toolkit,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada, Sept. 24–28, pp. 719–726.
Abadi, M. , Agarwal, A. , Barham, P. , Brevdo, E. , Chen, Z. , Citro, C. , Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mane, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viegas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X., 2016, “ Tensorflow: Large-Scale Machine Learning on Heterogeneous Distributed Systems,” preprint arXiv: 1603.04467.
Frazzoli, E. , Dahleh, M. A. , and Feron, E. , 2002, “ Real-Time Motion Planning for Agile Autonomous Vehicles,” J. Guid., Control, Dyn., 25(1), pp. 116–129. [CrossRef]
Tabuada, P. , 2007, “ Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks,” IEEE Trans. Autom. Control, 52(9), pp. 1680–1685. [CrossRef]
Da, X. , and Grizzle, J. , 2017, “ Combining Trajectory Optimization, Supervised Machine Learning, and Model Structure for Mitigating the Curse of Dimensionality in the Control of Bipedal Robots,” preprint .
Arnol'd, V. I. , 2013, Mathematical Methods of Classical Mechanics, Vol. 60, Springer Science & Business Media, New York.

Figures

Grahic Jump Location
Fig. 1

Block diagram of CBF supervising a “student” controller

Grahic Jump Location
Fig. 2

Learning based trajectory generator

Grahic Jump Location
Fig. 3

Structure of the proposed supervisory control

Grahic Jump Location
Fig. 4

Lateral-yaw-roll model of articulated truck

Grahic Jump Location
Fig. 5

Preview deviation as output

Grahic Jump Location
Fig. 6

Synthesis of a CBF via SOS

Grahic Jump Location
Fig. 7

Example of trajectory optimization result

Grahic Jump Location
Fig. 8

Lower bound for b˙

Grahic Jump Location
Fig. 9

Animation with a 312 state model in trucksim

Grahic Jump Location
Fig. 10

Disturbance to the system

Grahic Jump Location
Fig. 11

Value of the CBF and key states during simulation

Grahic Jump Location
Fig. 12

Input and intervention of CBF during simulation

Grahic Jump Location
Fig. 13

Value of CBF and key states with large initial deviations

Grahic Jump Location
Fig. 14

Input and intervention of CBF with large initial deviations

Grahic Jump Location
Fig. 15

Simulation result with LQR as student controller

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In