# Vehicle Rollover Stability and Path Planning in ADAS Using Model Predictive Control.pdf

VEHICLE ROLLOVER STABILITY AND PATH PLANNING IN ADAS USING MODEL PREDICTIVE CONTROL by XINYUE ZHANG THESIS Submitted to the Graduate School of Wayne State University, Detroit, Michigan in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE 2019 MAJOR: ELECTRIC-DRIVE VEHICLE ENGINEERING Approved By: ____________________________________ Advisor Date ____________________________________ Co-advisor Date ProQuest Number: All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest Published by ProQuest LLC ( ). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 13861828 13861828 2019 ii ACKNOWLEDGEMENTS I would like to express the greatest appreciation to my thesis advisors Dr. Caisheng Wang and Dr. Chin-An Tan for their continuous guidance and academic support during the past year. I would like to thank them for spending time to meet with me weekly and helping me have a clear timeline so that I can write my thesis continuously and finish it on time. They provided tons of suggestions for my thesis in the whole process, including how to schedule my timeline reasonably since it needs to have good self-control rather than fixed class time; how to better organize different sections and materials for the thesis. I really appreciate the opportunities to present my work in weekly meetings so that I can improve my presentation skills. I would also like to thank Dr. Liao for serving as my committee member and providing me with valuable comments and suggestions. My appreciation also goes to TASS International for providing free trial of PreScan. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS .ii LIST OF FIGURES . v LIST OF TABLES . vii CHAPTER 1 INTRODUCTION 1 1.1 Motivation 2 1.2 Overview of ADAS System . 4 1.3 Literature Review 6 CHAPTER 2 SCENARIO ANALYSIS 10 CHAPTER 3 MODELING OF VEHICLE DYNAMICS 15 3.1 Vehicle Coordinate Systems 16 3.2 Vehicle Chassis Model 18 3.3 Suspension Model . 27 3.4 Tire model . 28 3.5 State Space Model . 34 CHAPTER 4 MOTION CONTROL 38 4.1 Optimization . 39 4.2 Solution for Nonlinear Model Predictive Control 41 iv CHAPTER 5 RESULTS the other is by changing to another lane along a safe trajectory. The condition for the vehicle to choose one method over the other is determined by difference between the relative distance and a calculated safe distance. As all of the scenarios are under unusual situations, meaning that radar and other sensors are impossible to detect the obstacle beforehand, and the AEB is relatively ineffective because there is not enough distance and time for the vehicle to stop safely without any collision. Hence, more in deepth research on rollover prevention is needed for sudden lane changing. Highway traffic and safety engineers have already developed general standards for vehicle stopping distance and time [32]. If a road surface is dry, a light truck can safely reduce its speed with reasonably good tires at a rate of 15 ft/s2. A good controller system can perform as well as a skilled driver who can significantly reduce the stopping distance and time, and the deceleration rate could exceed 20 ft/s2. The table below shows the braking 11 distances regarding to different initial velocities. Table 2. Braking / Stopping Distance MPH Ft./Sec. Braking Deceleration Distance Perception Reaction Distance Total Stopping Distance 55 80.7 144 feet 43.9 m 8.1 feet 2.5 m 152.1 feet 46.4 m 60 88 172 feet 52.5 m 8.8 feet 2.7 m 180.8 feet 55.1 m 65 95.3 202 feet 61.6 m 9.6 feet 3.0 m 211.6 feet 64.5 m 70 102.7 234 feet 71.3 m 10.3 feet 3.2 m 244.3 feet 74.5 m 75 110 268 feet 81.7 m 11 feet 3.4 m 279 feet 85.1 m 80 117.3 305 feet 93.0 m 11.8 feet 3.6 m 316.8 feet 96.6 m It is noted that trucks need more time and longer distance to stop fully than common cars. Described below are four common scenarios that we will consider in the simulation. The first three cases vary by increasing the number of lanes and number of vehicles occupying the lanes. 12 Case 1. Sudden stop of the leading vehicle in the original lane Figure 2. Case 1: Leading vehicle in the original lane stops suddenly There are two possible ways for the ego vehicle to avoid a rear crash in this case: either stop straightforward or change lane to avoid the preceding vehicle if the ego vehicle cannot stop safely. For example, if the distance that the sensor detects the preceding car is smaller than 64.5 meters when the speed is 104 kph and above, it is impossible for the ego vehicle to stop safely even using the AEB (see Table 2. Braking / Stopping Distance). Thus, the only choice is to change to another lane, supposing that there are no other unexpected vehicles. Case 2. Sudden stop of the Preceding vehicle in the initial lane plus vehicles in the adjacent lane. There are also two possible approaches for the ego vehicle to make a decision in this case: either stop straightforward or change lane to avoid the preceding vehicle if the ego 13 vehicle cannot stop safely. However, the difference from case 1 is that the system needs to plan a best path to avoid the collision with the vehicle in the adjacent lane. Thus, not only the relative distance and velocity between the ego car and the preceding car are important, but also the relative distance and velocity between the ego car and the car in adjacent lane. All these factors impact the path / trajectory planning. The challenge of case 2 is that it requires more powerful sensors and computation ability of systems. Figure 3. Case 2: Preceding vehicle in the initial lane stops suddenly plus vehicles in adjacent lane Case 3. More complicated scenario 14 Figure 4. Case 3: Multiple obstacles scenario Case 3 is the most complicated situation among the first three cases, because more inputs from the environment should be considered and detected, which requires a more robust algorithm and more powerful hardware that could handle varying parameters in the environment and assist the vehicle to make a proper decision. In Figure 4, there are three possible ways for the ego vehicle to avoid collision as well as rollover. The difficulty is that it may take more time for the system to process inputs and the situation is varying all the time. If the system is not robust enough, a wrong and dangerous decision can be made. There are other possible scenarios, for example, there is no possible path planning that could prevent rollover and collision at the same time. Under these situations, a trade-off between rollover and collision avoidance has to be made. Many researchers have focused on unavoidable collisions and worked on how to reduce the risk. However, it is still a major research. Thus, it will not be discussed in this thesis. All the cases discussed can be built in PreScan by adding trajectory, actuators, and sensors. 15 CHAPTER 3 MODELING OF VEHICLE DYNAMICS A vehicle model as a rigid body has six degree-of-freedom (DOF), i.e., motions in three translational directions and three rotational directions. The translational motions are longitudinal, lateral and vertical motions, and the rotational motions are roll, pitch and yaw motions. Each motion represents a DOF. However, the rigid body model is too simplistic and does not account for the modeling of suspension, tires and other lumped mass units of the vehicle. On the other hand, it is not cost-effective to model every single aspect of the vehicle. Modelling a comprehensive vehicle model could also lead to high nonlinearity. Thus, different degrees of freedom of vehicle dynamic models have been developed for different purposes. In the rollover prevention problem, the wheels should be treated separately different from the chassis body. The lumped mass of body is the “sprung mass”, and the wheels are denoted as “unsprung masses” [15]. Moreover, pitch and vertical motions can be neglected since they are less important in this research. Similar to typical passenger cars, most buses have two axles, while each axle has one or more pairs of wheels. However, some heavy trucks have several different numbers of axles, varying with two to six or more axles. Since the center of gravity of heavy trucks are usually higher than passenger vehicles, there is higher possibility that it will rollover. Therefore, height of center of gravity is a significant factor that leads a heavy truck to roll over. Higher center of gravity has greater significance in causing the vehicle to rollover than the number of axles. In this research, we will take a two-axle, four-tire, single-unit truck as the research subject, which can make the results more general. The model can be further extended and applied to SUVs and buses with high center of gravity. Moreover, there is no difference 16 between a two-axle truck and a passenger car in the overall analysis. In Figure 5, a two- axle, four-tire, single-unit truck and its trailer is shown as, Figure 5. Two-axle, four-tire, single-unit truck and its trailer 3.1 Vehicle Coordinate Systems To describe the motion of the vehicle, it is necessary to select an appropriate coordinate system for derivation of the equation of motion. A moving body can be treated as a reference frame that constantly provide reference coordinate for the observation of motion. Sprung mass and unsprung mass can be considered as coordinate system 1 and coordinate system 2, respectively. Coordinate system 1 is also called the body-fixed coordinate, as the starting point is fixed in the center of gravity of vehicle. It is noted that the mass of vehicle is concentrated in the sprung mass. The space-fixed coordinate X-Y-Z is used here as a reference frame. The space-fixed coordinate, X-Y-Z, is a rectangular Cartesian coordinate, 17 which follows right-hand rule, hence is usually defined as inertial coordinate system. Figure 6. The relationships of three coordinate systems 18 X-Y-Z: inertial coordinate system; x-y-z: body-fixed coordinate system (coordinate system 1); x’-y’-z’: unsprung mass coordinate system (coordinate system 2). φ: roll angle; θ: pitch angle; Ψ: yaw angle. 𝑟𝑢 and 𝑟𝑠 stand for the position of unsprung mass with respect to the unsprung mass coordinate system, and the position of sprung mass with respect to the body-fixed coordinate system, respectively. The unsprung mass coordinate system is obtained by rotating the inertial coordinate system through the yaw angle Ψ. The body-fixed coordinate system is obtained by 1) rotating the inertial coordinate system through the yaw angle Ψ, then 2) rotating the pitch angle θ, and finally 3) rotating the roll angle φ. In other words, the body-fixed coordinate system is obtained by rotating the unsprung mass coordinate system through the pitch angle θ then the roll angle φ. 3.2 Vehicle Chassis Model The vehicle chassis model contains the sprung mass and the unsprung mass, as mentioned before. The vehicle chassis model has lateral, longitudinal, yaw and roll motions after ignoring the pitch rotational motion and vertical translational motion. Therefore, we can consider the chassis as a four-degree-of-freedom model as presented below. Figure 7 shows a top view of the vehicle in the inertial frame, presenting the lateral, longitudinal, and yaw motions. 𝐹𝑦𝑟𝑙,𝐹𝑦𝑟𝑟,𝐹𝑦𝑓𝑙,𝐹𝑦𝑓𝑟 denote the lateral forces of left rear wheel, right rear wheel, left front wheel and right front wheel, respectively. 𝐹𝑥𝑟𝑙,𝐹𝑥𝑟𝑟,𝐹𝑥𝑓𝑙,𝐹𝑥𝑓𝑟 stand for the longitudinal forces of left rear wheel, right rear wheel, left front wheel and right front wheel, respectively. 19 Figure 7. Top view of the vehicle chassis model Since the coordinate system 2 is obtained by rotating inertial coordinate system through yaw angle, the angular velocities of unsprung mass and sprung mass with respect to the inertial coordinate system XYZ are, [𝜔𝑂𝑢] = { 0 0 𝜓̇ },[𝜔𝑂𝑠] = { 𝜑̇ 0 𝜓̇ } 3.1 While the translational velocities of unsprung mass can be represented under the coordinate system 2 with vertical velocity along the z-axis neglected, [𝑟̇𝑢] = { 𝑣𝑥 𝑣𝑦 0 } 3.2 Figure 8 shows a rear view of the vehicle, presenting the roll motion. 𝐹𝑧𝑙,𝐹𝑧𝑟 the vertical forces of left wheels and right wheels. δ denotes the steering angle of front wheels. Assume the steering angles of front wheels are same. Ψ̇ the yaw rate [rad/s], φ the roll angle [rad]. 20 𝑣𝑥 and 𝑣𝑦 are the longitudinal and lateral velocities of the unsprung mass with respect to coordinate system 2. The velocity of unsprung mass can easily be measured compared with sprung mass. RC the roll center along the centerline of the track at the ground level. CG the center of gravity. 𝑚𝑠 the sprung mass, the whole vehicle mass as well. 𝐻𝐶𝐺 the original height of center of gravity, h the actual height of center of gravity; 𝐿𝑟,𝐿𝑓 denote the distances of rear and front wheels from center of gravity, 𝐿𝑤 is the vehicle width. Figure 8. Rear view of the vehicle chassis model The acceleration of the unsprung mass is, [𝑟̈𝑢] = 𝐷[𝑟̇𝑢]𝐷𝑡 = 𝑑[𝑟̇𝑢]𝑑𝑡 +[𝜔𝑂𝑢] × [𝑟̇𝑢] 3.3 21 The first term on the right side of Eq. 3.3 is the partial derivative of time respect to the unsprung coordinate system, 𝑑[𝑟̇𝑢] 𝑑𝑡 = [𝑣̇𝑥 𝑣̇𝑦 0] 𝑇 3.4 The second term on the right side of Eq. 3.3 is the cross-product of the angular velocity and the longitudinal velocity, representing the rotation of the unsprung mass with respect to the space-fixed coordinate system, [𝜔𝑂𝑢] × [𝑟̇𝑢] = | 𝑖 𝑗 𝑘 0 0 𝜓̇ 𝑣𝑥 𝑣𝑦 0 | 𝑇 = [−𝑣𝑦𝜓̇ 𝑣𝑥𝜓̇ 0]𝑇 3.5 Subtracting Eq. 3.4 and 3.5 into Eq. 3.3 leads to the following result, [𝑟̈𝑢] = [𝑣̇𝑥 −𝑣𝑦𝜓̇ 𝑣̇𝑦 +𝑣𝑥𝜓̇ 0]𝑇 3.6 After getting the position, velocity and acceleration of the unsprung mass, those of the sprung mass can be presented in coordinate system 2, [𝑟𝑠/𝑢] = {0 𝐻𝐶𝐺 sinφ 0}𝑇 3.7 The velocity of the sprung mass is [𝑟̇𝑠/𝑢] = 𝐷[𝑟𝑠/𝑢]𝐷𝑡 = 𝑑[𝑟𝑠/𝑢]𝑑𝑡 +[𝜔𝑂𝑢] × [𝑟𝑠/𝑢] 3.8 The first term on the right side of Eq. 3.8 is the partial derivative of time with respect to the unsprung coordinate system, 𝑑[𝑟𝑠/𝑢] 𝑑𝑡 = [0 𝜑̇𝐻𝐶𝐺 cos𝜑 0] 3.9 22 The second term on the right side of Eq. 3.8 is the cross-product of angular velocity and longitudinal velocity, representing the rotation of the sprung mass with respect to the unsprung coordinate system, [𝜔𝑂𝑢] × [𝑟𝑠/𝑢] = | 𝑖 𝑗 𝑘 0 0 𝜓̇ 0 𝐻𝐶𝐺𝑠𝑖𝑛𝜑 𝐻𝐶𝐺𝑐𝑜𝑠𝜑 | 𝑇 = [−𝐻𝐶𝐺 sin𝜑𝜓̇ 0 0]𝑇 3.10 Subtracting Eq. 3.9 and 3.10 into Eq. 3.8 leads to