1. Introduction
1.4 Dissertation Overview
The rest of this dissertation is organized as follows. Chapter 2 describes the overview of our vehicle platform, namely Taiwan iTS-1. The design of the lateral control system with lane-keeping and lane-change control are presented in Chapter 3. In Chapter 4, the modeling of vehicle longitudinal dynamics and the longitudinal control system design with CC, ACC, and stop-and-go are presented. Besides, the developed collision avoidance/warning scheme is also introduced. In Chapter 5, fuzzy modeling for a nonlinear 3-DOF vehicle dynamics is described and the combined longitudinal and lateral control is achieved by utilization of optimal fuzzy control design. Experimental results under real traffic environment are presented in Chapter 6 to demonstrate the system’s validness. Finally, conclusions are included in Chapter 7.
Chapter 2
Vehicle Overview
2.1. Automated Vehicular System
Fig. 2-1. System architecture of the test-bed vehicle, Taiwan iTS-1.
As shown in Fig. 2-1, Taiwan iTS-1 (a prototype of Mitsubishi Savrin wagon) is equipped with a throttle, a brake, and a steering-wheel (SW) actuating system. Two internal state sensors, namely the speedometer and an inertia measurements unit (IMU), are used to sense the vehicle’s velocity, acceleration and angular rate, respectively. Besides, the utilized primary sensors include a real-time kinematical differential GPS (RTK-DGPS), an image processor with a monochromatic CCD camera, and a laser range finder. Initially, the in-vehicle controller is developed in a dSPACE Microautobox (MABX), a real-time hardware with a rapid prototype for control design and verification [29]. At present, the in-vehicle controller is successfully realized by a DSP-based stand-alone board [30, 31]. The in-vehicle controller communicates with various sensors through an interface board, and can be
reprogrammed onboard with data analysis and calibration via a notebook. Through environmental perception from primary sensors, the in-vehicle controller runs the driving control algorithm and sends throttle, brake, and SW controlling commands to actuating motors to achieve vehicle longitudinal and lateral control.
An AC servomotor is installed in the SW column to enable automatic steering. The angle of SW is measured by a steering angle sensor which is set around the axis of SW. Both the vision system [18, 32] and RTK-DGPS can provide lateral information such as the deviation from the centerline and the orientation with respect to a reference trajectory. The vision system is a look-ahead sensor while RTK-DGPS is a look-down sensor, and the fundamental difference between these two sensors is the difference in the range of the lateral information.
The vision detects the lane-markings ahead of the subject-vehicle, and provides the look-ahead relative positions of the vehicle with respect to the lane center. Based on RTK-DGPS, the relative position data are compared with a digital map on which the target route has been previously specified to be tracked.
As for longitudinal control, a throttle valve is driven by a mounted DC servomotor avoiding any change to vehicle’s internal-components. A throttle position sensor (TPS) is composed of an A/D converter encoding an analog voltage into a normalized digital signal [33]. The brake pedal is automated by using a DC servomotor which is connected to a brailed steel cable via an electromagnet. Its position is measured in terms of voltage variation output from a linear position transducer [30]. The main sensor for longitudinal control is the range finder which provides the current headway distance between the subject-vehicle and a preceding-vehicle in the same lane.
The specification of Taiwan iTS-1 and the utilized sensors, signal processors, and actuators are given in Appendix A.
2.2. Automated Driving System Diagram
Fig. 2-2. Two-level hierarchy of the proposed automated driving system.
We use a two-level hierarchical architecture as shown in Fig. 2-2 to achieve automated driving or driver assistance in a highway/freeway and urban-road environment. Mimicking human driver observing the traffic situation and the course of the road, the upper-level control determines the driving modes, namely lane-keeping (LK), lane-change (LC), cruise control (CC), adaptive cruise control (ACC), and stop-and-go. This level is concerned with ensuring that the system fits the suitable driving to the existing road-condition and the traffic. After determination of driving mode, the upper-level control then provides the vehicle-body control with the reference velocity (for CC, ACC, and stop-and-go) and the reference trajectory (for LK and LC).
The vehicle-body control is the lowest level in the hierarchy, but has the highest priority at the same time because of the task of transforming the desired variables into suitable control values. As comparing sensory information to these reference data, vehicle-body control will generate SW-, throttle-, and brake-control commands to motor drivers. In addition to stability requirement, the vehicle-body control must handle uncertainties in vehicle subsystems such as engine, driveline and brake, and compensate for disturbances such as tire-road adhesion or changes in gradients. Another important factor is the transmission latency in transmitting data.
There are two major delays which come from (a) the sensor processing time such as image processing of the vision system and scanning period of the laser range finder, and (b) the actuation of servo motor. Since these delays are quite substantial, this factor have been explicitly considered into the upper-level control or the vehicle-body control design which depends on our designing approach.
Fig. 2-3. Structure of controller/vehicle system.
The two levels can be described with “controller/vehicle” system, as illustrated in Fig. 2-3.
In this figure, a division into longitudinal and lateral control is made. The upper-level control requires good knowledge about road-environment, while the vehicle-body control focuses on providing driver-comparable control behavior in carrying out the control of throttle pedal, brake pedal, and SW angle. The upper-level control is responsible for calculating the reference values of velocity (for CC, ACC, and stop-and-go) and trajectory (for LK and LC) for the longitudinal controller and lateral controller, respectively. The reference velocity changes frequently and is rather dependent upon the road traffic. The objective for the longitudinal controller is to keep the reference velocity as exactly as possible. The general task for the lateral controller is to keep the lateral error to zero, i.e., the reference trajectory is the centerline of the road. While LC mode is activated, the reference trajectory will be previously calculated in terms of desired values of lateral offset such that the vehicle can be steered from the current lane to an adjacent lane. It should be noted that either the upper-level control or the vehicle-body control is designed to be adaptive with vehicle states such as current velocity, real-time lateral error, and headway distance. In practice human drivers also
perform several driving tasks which are adaptive to these vehicle states.
By receiving the throttle-, brake-position, and SW-angle commands from the vehicle-body control, a proportional-integrate-differential (PID) controller is used to manage the AC-motor attached to the SW column to reach the target position for LK and LC mode, and another two PID controllers are used to drive DC-motors to adjust the throttle degree and the brake position for executing CC, ACC, and stop-and-go mode. This architecture, based on the cascade-control paradigm [34], is particularly useful to get over time-delay from controlling signals to action signals: rapid control can be achieved by intermediate signals which will provide faster response than the control signals.
2.3. Function-flow
Fig. 2-4. Function-flow of the upper-level control.
In Fig. 2-4, the function-flow between LK, LC, CC, ACC, and stop-and-go mode in the upper-level control is presented. This system will initially activate LK mode or CC mode, or both simultaneously according to on-line detected traffic condition. In LK mode, the system retrieves real-time sensory information, calculates the deviation from a reference trajectory, and then generates a SW-control command. In CC mode, the subject-vehicle tracks a desired velocity profile set up by a human driver or the limited highway-velocity. As the vehicle
velocity is more than 40 km/h, the control scenario in ACC mode includes both safety-distance and fixed-distance tracking control. The former operation guarantees the safety-spacing keeping from the vehicle ahead while the later operation keeps a constant inter-vehicle spacing for the purpose of increasing the capacity of traffic flow. As a new event is detected, switching from CC mode to ACC mode is automatically activated. The system is defaulted in CC mode for clearance at road-ahead, and switches to ACC mode as a valid-target is detected. A valid-target is defined to satisfy the following conditions:
(a) it is in a designated range which is well defined to the feasible field of the utilized laser range finder;
(b) the velocity of a valid-target is slower than that of the subject-vehicle.
In ACC mode, the safety-distance is derived from constant headway-time policy. The value of fixed-distance can be set according to roadway control [35]. While the vehicle is driven under the velocity 40 km/h, it is reasonably to be assumed that the subject-vehicle is moving in an urban environment or a situation of heavy traffic such that stop-and-go mode will be activated if a valid-target is detected ahead. The preceding-vehicle might come to a complete stop owing to a traffic jam or a stop light. The modes-selection logic scheme is constructed in the upper-level control. The desired reference velocity in each mode will be filtered out, and then passed onto the vehicle-body control.
While the request of LC mode is given by the driver, the system steers the subject-vehicle from the current lane to an adjacent lane. The autonomous changing lane for overtaking a slower vehicle or an obstacle will be further developed in our system. Two schemes of lane-change maneuvers (GPS-guided lane-change and free lane-change) using RTK-DGPS and the vision system, respectively, are developed in our system. In the GPS-guided lane-change scenario, the reference trajectory calculated in the upper-level control is directly added on the lateral position of a specified route on the GPS map. This scheme guarantees the reference path-tracking stability issue, but limits the lane-change maneuver to specific locations where the map must be obtained beforehand. In the free lane-change scenario, the reference trajectory is transformed into the reference steering command that causes the subject-vehicle to track that reference. Without requiring the map information, however, the major difficulty in the free lane-change scenario is the extreme sensitivity of the system performance with respect to sensor noises and parameters variations in vehicle/road model.
Chapter 3
Lateral Control System Design
3.1. Vehicle Lateral Dynamics
In this chapter, the model for vehicle lateral dynamics is introduced to design the lane-keeping and lane-change control. As stated in [16, 32][36], the longitudinal and the lateral dynamics can be separated if the moving velocity does not vary too much. If roll movement is neglected, the vehicle lateral dynamics can be well represented by the so-called
“bicycle model”. The bicycle model which dominates the lateral and yaw dynamics is useful in designing the steering controller to stabilize the vehicle keeping within the lane. As shown in Fig. 3-1, the bicycle model couples two front and two rear wheels together by assuming that the vehicle body is symmetric about the longitudinal plane, and the roll and pitch motion of vehicle are neglected.
Fig. 3-1. Bicycle model for front-steering vehicles.
From Newton’s law, the net lateral forces and the net torque at the center of gravity (CG) of the vehicle can be obtained as
( y x ) yf cos f yr
m v + ⋅v γ =F δ +F (3-1)
z yf yr
I γ=F ⋅ +a F ⋅b (3-2) Based on the assumption of the small steering angle (cosδf ≈ 1) and the linear tire model, the lateral force of tire can be taken as linear proportional to the slip angle with a constant proportionality called cornering stiffness as
yf f f The cornering stiffness of front and rear tire Cf, r considered here is the slope of side force characteristics at the origin on a normal road condition. The slip angles αf and αr can be approximated as the functions of the vehicle’s kinematic parameters
y
The state equation of bicycle model can be rewritten in the following 1 2 1 constant. In reality, it is found that the lateral tire force will initially increase with tire slip angle, and then saturate for a given tire/road friction condition [55-57], as shown in Fig. 3-2.
To capture the saturation property of lateral tire/road friction, several nonlinear tire models were proposed. Bakker and Pacejka proposed a famous “magic formula” which represents that the lateral tire force not only depends on its slip angle but also on vehicle side slip angel αf , r , steering angle δf , and yaw rate γ. Without assuming small angles, the stability condition and bifurcation phenomenon with varying cornering stiffness and different velocities are presented in our previous work [57]. Besides, the front-wheel steering vehicle will become unstable due to the existence of saddle-node bifurcation which is derived in [57] and heavily depends on the rear-tire cornering force characteristics [55].
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Fig. 3-2. Exampled cornering characteristics of front and rear tires. (Dotted line: high friction road, and dashed line: low friction road)
To validate the bicycle model with the real vehicle dynamics is critical to obtain precise tracking results of steering control. The bicycle model in (3-5) varies with the vehicle speed vx. Notably, the actual input to our vehicle platform is the SW angle δSW rather than the front-wheel angle δf . According to vehicular steering mechanics [37], the SW angle can be expressed as a product of the steering ratio isr and the front-wheel angle δf
SW isr f
δ = ⋅δ (3-6) Because the compliance and steering torque gradients vary with increasing steering angles and load on the front tires, tire pressure, coefficient of friction, etc, in general, isr is not a fixed value for the power steering of the vehicle. However, the constant ratio can be practically used for control design. The steering ratio isr can then be adjusted slightly to yield a response that is more similar to that of the real vehicle platform. The measured SW angle was used as the input to the model. Besides yaw rate, the predicted lateral acceleration from the model can be approximately calculated by
y x y
a ≅ v ⋅ − γ v (3-7) The average errors between the measurements and the model with respect to isr are illustrated in Fig. 3-3, and the minimum point is in the case of isr = 26. Figure 3-4 compares experimental results with the bicycle model predictions for a transient maneuver at around 60 km/h. The lateral acceleration of model agrees with the obtained experimental data in Fig.
3-4(a), and the predicted yaw rate of the vehicle also shows consistent correlation with the
experimental results in Fig. 3-4(b). Several other quantities were also measured and compared with the bicycle model. Results show that the bicycle model (3-5) can faithfully represent the lateral dynamics of the vehicle platform (Taiwan iTS-1).
Fig. 3-3. The relation between the steering ratio and the average error of measurements.
0 5 10 15 20 25 30 35 40 45 50
-0.4 -0.2 0 0.2 0.4
lateral acceleration (g-unit)
0 5 10 15 20 25 30 35 40 45 50
-10 -5 0 5 10
yaw rate (deg/s)
time (sec) (a)
(b)
Fig. 3-4. The states signal for verification between the model and the vehicle in the case of isr
= 26. (solid line: model output; dashed line: measured)
3.2. Lane-keeping Control Design
Fig. 3-5. Vehicle lateral dynamics with respect to road geometry.
The relationship between the lateral dynamics of the vehicle and the desired previewed navigation at a look-ahead distance Ld is plotted in Fig. 3-5. The valid amount of Ld is determined from the vision system [18, 32]. The previewed dynamics can be described as
Ld y d x Ld
y =v +L ⋅ +γ v ⋅ε (3-8)
Ld vx Ld
ε = − ⋅γ ρ (3-9) where the parameters have been defined in Nomenclature.
The bicycle model (3-5) is combined with the previewed dynamics (3-8) and (3-9) to form a linear state-space equation curvature ρLd is viewed as an exogenous disturbance of the system.
The linear system in (3-10) is parameterized with the longitudinal vehicle speed vx . As vx
increases, the poles of the system move toward the imaginary axis, reducing the stability.
Notably, changing the look-ahead distance Ld does not affect the poles location in the transfer function from δf to the previewed lateral offset yLd . If Ld is regarded as being close to the front of the vehicle, then the damping of the zeros in system (3-10) declines drastically and a
high-gain controller drives the closed-loop poles toward the zeros, resulting in a poorly damped closed-loop system. However, Ld can not be chosen too distant from the reliable field of the vision system. The image resolution at far look-ahead distance will be degraded such that collected data includes more errors. As the result of numerous experimental verifications, the reliable value of Ld is chosen as 10 ~ 15 m according to the developed vision system [18].
The control objective for vehicle lane-keeping is to regulate the offset at the look-ahead yLd
to zero. Moreover, the controller is well anticipated to ensure that the vehicle lateral acceleration does not exceed 0.4g (g is 9.8 m/s2) during the control process, such that smooth responses and the comfort of the passengers can be achieved. Given the vehicle model as (3-10), the state feedback control seems to be naturally applied with u =− Kfb x where
[ y Ld Ld]
fb v y
K = k kγ k kε . Here the pole-placement design approach is adopted to consider that the control effort required is related to how far the open-loop poles are moved by the feedback. The objective of pole-placement aims to fix specifically the undesirable aspects of the open-loop response, and avoids either large increases in bandwidth or efforts while poles are moved [38]. Moreover, it typically allows smaller gains and thus smaller control efforts by moving poles that are near zeros rather than arbitrarily assigning all the poles. The closed-loop poles for the system with high order (>2) can be chosen as a desired pair of dominant second-order poles with the rest poles which correspond to sufficiently damped modes, so that the system will mimic a second-order response with the reasonable balance between system errors and control effort. The closed-loop bandwidth for the look-ahead lateral offset is chosen at 5.35 rad/s to mimic human responses [16]. As for comfort requirement, the corresponding closed-loop poles are chosen to ensure that the lateral acceleration above 0.5 Hz will not be amplified during the steering path. Besides, the pole-selection can also be specified by the bandwidth requirement with regard to the transfer function yLd (s)/ρLd (s) with the maximal allowable yLd to reasonable step changes of ρLd [3-6].
From the computer simulations for the closed-loop system response with the step change in curvature, it is found that the complex poles with a damping ratioζ =0.707 will meet the constraint of lateral acceleration. Therefore, the natural frequency ωn of the prototype second-order system can be determined by [39]
1 / 2
2 4 2
BW =ωn⎡⎣(1 2− ζ )+ 4ζ −4ζ +2⎤⎦ , (3-11) and then we have the conjugate dominant poles as s1,2 =−3.58±3.58j. The other two poles are chosen as those in the original system. Notably, increasing the speed will reduce the stability
of the closed-loop system since the poles move close to the imaginary axis.
Recall the system matrix A in (3-10) is time-varying with the longitudinal vehicle velocity vx. The feedback control is supposed to be designed under the highest speed of interest such that the stability for lower velocities can be guaranteed by applying the convex nature of the
Recall the system matrix A in (3-10) is time-varying with the longitudinal vehicle velocity vx. The feedback control is supposed to be designed under the highest speed of interest such that the stability for lower velocities can be guaranteed by applying the convex nature of the