HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY MASTER THESIS Adaptive tracking control for autonomous vehicles with system constraints NGUYEN NHU TOAN toan.vn Control Engineering and Automation Supervisor: Assoc. PhD Nguyen Tung Lam Advisor’ signature School: School of Electrical and Electronic Engineering HANOI, 10/2023 ACKNOWLEDGEMENTS I would like to take a moment to extend my deep gratitude to the esteemed individuals who have played pivotal roles in shaping the trajectory of my academic journey and, ultimately, in the successful completion of this comprehensive report. Foremost among these remarkable individuals is Assoc. Tung Lam Nguyen, whose steadfast support and mentorship have been indispensable throughout this endeavor.
His unwavering dedication to my academic growth and his profound commitment to my development as a researcher have been a wellspring of inspira- tion. Tung Lam’s insightful guidance and his willingness to generously share his extensive expertise have proven invaluable, equipping me with the essential tools to navigate the challenges and surmount the obstacles encountered along this academic journey. It is through his unwavering mentorship that I have been able to chart a course toward academic excellence. I would also like to express my heartfelt appreciation to Dr.
Danh Huy Nguyen, whose contributions and support have added significant depth and perspective to my work. Danh Huy’s involvement and mentorship have been instrumental in enriching my academic experience. In the broader context, I wish to convey my profound gratitude for the unwa- vering support of my family. Their unwavering belief in my capabilities and their steadfast encouragement, provided during both the peaks of success and the val- leys of challenges in this academic pursuit, have served as my unwavering driving force.
Their unshakable faith, constant encouragement, and the sacrifices they have made are the bedrock of my motivation, and I am deeply indebted to them for their enduring presence in my life. Lastly, I extend my heartfelt acknowledgment to the broader academic com- munity, my peers, and fellow researchers who have generously provided valuable insights and diverse perspectives that have significantly enriched my work. The dy- namic exchange of ideas and collaborative discussions within this academic com- munity have not only broadened my horizons but have also profoundly shaped my understanding of the subject matter, contributing significantly to the depth and breadth of this report. As I pause to reflect upon this remarkable journey, my heart is filled with profound gratitude for these exceptional individuals who have contributed to the fruition of this report.
For this, I am truly and profoundly thankful. ABSTRACT This thesis investigates the lane following and changing maneuvers of au- tonomous vehicles in the presence of unknown disturbances, taking into account the dynamic system states and input constraints. The integrated longitudinal-lateral and yaw rate dynamics of the vehicle are simultaneously considered to improve the tracking accuracy and system stability when navigating under critical conditions. Then, a novel adaptive asymmetric time-varying integral barrier Lyapunov control scheme is developed to design the steering controller, longitudinal controller, and direct yaw moment control controller, which is capable of constraining the system states and control signals within the predefined boundary.
In addition, the radius basis function neural network is employed to estimate the lumped disturbances caused by the parametric uncertainties, external disturbances, and unmodeled dy- namics, and the command filter system is used to avoid the explosion of terms phenomenon. The optimization-based method is then implemented to effectively allocate the driving/braking torque to each in-wheel motor so as to improve vehicle performance. The stability of the closed-loop system is comprehensively demon- strated by means of the Lyapunov theory. Finally, the quantitative and qualitative comparisons in different driving scenarios using the Carim-Simulink joint environ- ment are carried out to illustrate the effectiveness and validation of the proposed method.
Student’s signature TABLE OF CONTENTS LIST OF FIGURES i LIST OF TABLES ii LIST OF SYMBOLS iii CHAPTER 1. VEHICLE DYNAMIC MODEL 5 CHAPTER 3.1 Steering control formulation .2 Longitudinal and direct yaw control formulation .1 Active front steering control .2 Longitudinal control and Direct yaw moment control. IMPLEMENTATION AND EVALUATION 23 5.3 Results of scenario 1: Double lane change maneuver with constant longitudinal velocity .4 Results of scenario 2: Double lane change maneuver with varying longitudinal speed .5 Results of scenario 3: On curved road. CONCLUSION 39 LIST OF PUBLICATIONS 40 REFERENCES 41 APPENDIX 48 APPENDIX OF CONTROL DESIGN 49 A.1 Proof of Lemma 1 .3 Proof of Theorem 2.
50 APPENDIX OF SLIDING MODE CONTROL 54 LIST OF FIGURES Figure 1.1 Lane changing maneuver in autonomous vehicles .1 Planar vehicle model .1 Double lane change trajectory .2 Curved road trajectory .1 Structure diagram of the proposed Carsim-Simulink co- simulation .3 Wind forces provided by Carsim .5 Yaw rate error (Scenario 1) .11 Rate of steering angle (Scenario 1) .13 Yaw rate error (Scenario 2) .19 Rate of steering angle (Scenario 2) .21 Yaw rate error (Scenario 3) .26 Rate of steering angle (Scenario 3). 38 i LIST OF TABLES Table 1.1 Literature review on the control method and objective .1 The control performance benchmark of three controllers un- der three scenarios. 38 ii LIST OF SYMBOLS Symbols Meaning m Vehicle mass Iz Inertial moment around the yaw axis lf Distance from the front axle to the COG lr Distances from the rear axle to the COG Fx Longitudinal tyre force Fy Lateral tyre force tw Distance from the left to the right tire Mz Direct yaw moment ax Longitudinal acceleration of the COG ay Lateral acceleration of the COG Fres Total resistance force Faero Aerodynamic drag force Froll Rolling resistance force AF Effective frontal area of the vehicle ρ Air density Cd Aerodynamic drag coefficient Crr Rolling friction coefficient h Center of gravity height Iw Moment of inertia of the wheel ω Wheel velocity rw Effective wheel radius Td Total traction torque executed on each wheel Tb Total braking torque executed on each wheel µτ,ε Friction coefficient Cαi j Tire cornering stiffness Cα f Front axle cornering stiffness Cαr Rear axle cornering stiffness Cκi j Longitudinal slip stiffness λxτ,ε Slip ratio of each wheel in longitudinal direction λyτ,ε Slip ratio of each wheel in lateral direction ατ,ε Slip angle of each tire ∆Tτ,ε Lumped disturbances of torque balance equation ∆Fkτ,ε Lumped disturbances of tire force equation iii CHAPTER 1. INTRODUCTION In recent years, the research on the development and application of the Ad- vanced Driver Assistance System (ADAS) has been gaining increasing attraction in many countries, technology companies, and education institutes.
ADAS is con- sidered a breakthrough in the car automation industry because of its significant ad- vantages, including lower energy consumption, the diminution of air pollution, and the improvement of passengers’ comfort. Especially this system plays a crucial role in decreasing car accidents caused mostly by human errors, thus enhancing overall road safety [1,2]. ADAS, in general, composes of a breadth of technologies such as Figure 1.1 Lane changing maneuver in autonomous vehicles lane departure warning, adaptive cruise control, automatic emergency braking, lane change assistance, traction control system, etc, which all incorporate to level up the driving experience [3]. Path tracking control (PTC) and stability handling are es- sential areas of research in ADAS that aim to improve vehicle safety and stability by utilizing the vehicle’s longitudinal, lateral, and yaw dynamics.
While stability handling primarily focuses on the application of active front steering (AFS) and di- rect yaw moment (DYC) control to provide additional control input for improving vehicle stability, path tracking control is designed to minimize the tracking error to precisely follow the path specified by the motion planning layer, thereby ensuring optimal safety, ride comfort, and stability [4–6]. Different control strategies can be found in the literature, as summarized in Figure 1. In a majority of studies, the path tracking control is generally approached as a problem of solely steering, neglecting other complexities of vehicle motion [7,27]. Although the aforementioned works achieve important results, there exists a strong 1 X-Y Plane Motion Control Longitudinal Lateral Control Control Slip ratio Velocity Path Stability control control tracking handling Lateral Yaw rate Slip angle deviation control control Figure 1.2 Control objective Table 1.1 Literature review on the control method and objective References Type Control method Pros Cons [7–10] AFS Fast response, robust to disturbance; It has the problem of chattering; [11–13] AFS+DYC Easily adapt with adaptive mechanisms SMC The system’s states and input signals to eliminate disturbances and enhance [14] PTC+DYC constraints are not concerned control performance.
The tracking error is guaranteed to be It has the problem of chattering; [15, 16] AFS BLF+SMC bounded;Robust to disturbances. The input constraints are not concerned. [6, 17] PTC+DYC It has a complicated solution Robust to disturbance with the H ∞ construction and theoretical derivation; H∞ performance; The parameter uncertainties The system constraints are not concerned; [18–20] AFS+DYC are handled by fuzzy rules. The performance highly depends on the number of fuzzy rules and scheduling variables.
[4, 21, 22] AFS Difficult to analyze system stability; Strong in handling system constraints; Computational burden, especially when [23–26] PTC+DYC The control action is optimized and can the size of the dynamic model increase; MPC adapt to sudden change based on the The prediction process is negatively impacted prediction process. by disturbances, degrading the system [23–26] PTC+DTC+TC performance. interdependence between the lateral and longitudinal motions of a vehicle, and the neglect of either one will adversely impact the vehicle’s performance [28, 29]. Therefore, it is necessary to take into account both the longitudinal and lateral con- trol simultaneously to enhance the control performance in a wide range of driving conditions.
In [29], the interval type-2 fuzzy sets control approach is developed for the integrated dynamic model, enabling the vehicle to robustly track the desired longitudinal speed and reference path simultaneously. Moreover, when navigating through adverse road conditions such as wet roads, or during critical maneuvers such as high-speed lane changes or high-curved roads, the tires will be slipped and express highly nonlinear characteristics, and the dy- 2 namic coupling effects between the longitudinal and lateral motions will be inten- sified. In these cases, direct yaw moment control is proven to be one of the most effective strategies to maintain vehicle stability and passenger comfort [14,31]. It is developed to exert the longitudinal force of each tire such that changes the distribu- tion of the driving/braking torque.
The authors in [14] develop the super-twisting sliding mode controller for path-following maneuvers of the vehicle using the DYC and active front steering integration systems, which enhances the accuracy and sta- bility of the vehicle and eliminates the chattering phenomenon of the traditional SMC method. In [18], the integration model of DYC and AFS are controlled by the Takagi-Sugeno fuzzy control method considering the norm-bounded uncertainties of tire forces and time-varying longitudinal velocity to improve vehicle stability and achieve the H-infinity performance. On the other hand, in practice, autonomous vehicles typically operate under a variety of constraints, stemming from the limitations of actuators such as steer- ing, braking, and throttling systems, as well as the dynamic states of the vehicle, such as speed, acceleration, and yaw rate, in order to meet safety standards and ensure passenger comfort. Disregarding the system constraints can significantly impair the performance of the controller and potentially lead to system instabil- ity [32, 33].
However, in most previous works, these limitations are not taken into account. To deal with the constraints problem, the MPC method is typically consid- ered a promising strategy. The authors in [34] present an improved MPC strategy, which adaptively adjusted the weight of the cost function via the fuzzy system, and the magnitude of the steering angle and its rate are also constrained such that the tracking accuracy and driving comfort is enhanced. In [35], the MPC method is de- veloped for lateral-longitudinal dynamic control problem, which takes into account the constraints of side slip angle and the control signals, hence improving the vehi- cle stability and control smoothness.