車輛轉向輔助系統之適應性控制

行政院國家科學委員會專題研究計畫 成果報告

車輛轉向輔助系統之適應性控制

計畫類別： 個別型計畫

計畫編號： NSC93-2212-E-011-038-

執行期間： 93 年 09 月 01 日至 94 年 07 月 31 日 執行單位： 國立臺灣科技大學機械工程系

計畫主持人： 陳亮光

計畫參與人員： 林宏達、胡東暘、許聖勇、黃液權

報告類型： 精簡報告

處理方式： 本計畫可公開查詢

中 華 民 國 94 年 10 月 31 日

Final Report

Adaptive Control of Vehicle Steering Assist System

I Introduction

Safety is the single most important issue in vehicle driving. In [1], Jones states that

“Every minute, on average, at least one person somewhere in the world dies in a car crash.”

The economic costs associated with vehicle crashes total almost 3% of the world’s gross domestic product (GDP) annually. This fact motivates significant research effort to build

“safer” vehicles. Many advanced vehicle control systems (AVCS) are designed to improve driving safety. Within the category of AVCS, active safety systems are generally termed as systems that function while the driver is still in command of the vehicle. In contrast to passive systems, active safety systems issue some form of signal to affect vehicle motions (e.g., warning, braking, or steering augmentation) to prevent vehicle crashes. For systems that directly affect vehicle motion, the driver-controller interactions become challenging problems, since both the driver and the control system are controlling vehicle motion. Single vehicle road departure (SVRD) accidents are selected as the scenario problem to investigate.

National Highway Traffic Safety Administration (NHTSA) reports that in 1999 the SVRD accidents account for more than 40 percent of fatalities, and approximately 20 percent of all vehicle crashes [2]. The high frequency and severity of the SVRD accidents call for the need of safety systems to prevent them. To design active safety systems for steering assist control, and thus reduce the occurrence of SVRD accidents, proper representation of driver steering behavior is needed. Many driver steering models are available in the literature; however, these models are not exact and model uncertainty is expected. An approach to estimate driver model uncertainty from driving simulator data has been presented in [3]. The uncertainty results show that although the average driver model exhibits acceptable performance, (e.g., in terms of phase margin, gain margin, and crossover frequency), the driver can perform very poorly during a long driving task. The driver degradation observed from the identified driver models may be an indication of the low alertness level of the driver.

A robust control approach has been investigated to handle the observed driver model uncertainty [4]. However, the large uncertainty attributed to the driver makes robust performance un-achievable. Therefore, in this project, it is proposed to use adaptive control approach to reduce the effect of the large driver model uncertainty.

II Literature Review

Due to vast advances in AVCS research, trying to construct a thorough yet concise review of the literature is a daunting task. Instead, the review described here focus on the steering assist controller design with respect to driver variation. Steering control AVCS has been extensively studied in the literature. A thorough review of the research activities of AVCS before 1995 is presented in [5]. This survey paper provides thorough background information on many aspects of AVCS. The driver-controller interaction research is a relatively new arena in the AVCS community, and the literature presented will be limited to steering assist systems. Naab and Reichart [6] report on the driver assistance system developed by BMW in the framework of PROMETHEUS. They implemented a parallel steering wheel control by comparing the calculated steering wheel angle generated from computer vision system with the driver’s steering angle. The controller then uses this information to provide steering correction with limited authority. A similar approach to provide steering assist has been reported by [7-8]. Birch [9] described a steering assist system designed by Jaguar/Lucas. Their system used an opto-electronic torque sensor to monitor driver inputs. Steering aids are introduced by power steering. A warning is issued if the car starts to move off course. The system is deactivated if a turn indicator is used or sufficient steering wheel movement is detected.

For vehicle lateral control, the steering wheel angle is the primary mean for control actuation. In the literature, many driver models try to approximate the real driver’s road tracking performance, assuming certain driver inputs and outputs (e.g., [10-14]). A well-known result from human factors research is the “crossover” model [10-11]. One of the implications from the crossover model states that the open loop frequency response of the driver-vehicle combination approximates that of a transfer function

ω

/s near the crossover

ω

Although these models approximate the driver behavior well, no driver model is expected to completely represent the real driver. Furthermore, for the purpose of controller design, it is common practice to use a low-order driver model. Therefore, it is reasonable to expect that significant driver model uncertainty exists. The driver model uncertainty reported in [3] includes two parts. The unstructured uncertainty represents the un-modeled dynamics due to causes such as nonlinearity and mode order. The second part of the uncertainty model represents the driver’s time-varying behavior during a long driving course. Very little has been done in the literature with respect to quantitatively address the effects of driver model uncertainty and possible countermeasures that are applicable to this problem. The article [4]

reports the analysis results of using a serial robust controller to ensure robust performance. It is found that driver’s behavior varies significantly with time, and robust performance is not achievable due to the fundamental tradeoff between robustness and performance.

III Research Approach and Results

The research work to implement adaptive control for vehicle steering assist is divided into three parts. First an on-line driver steering model estimation algorithm is developed.

Second the adaptive control design is investigated with respect to simplified driver model parametric variations. Finally, as a testing facility, the scaled vehicle set up is constructed and serve as an evaluation platform for the safety systems developed in this research. The progress of each task is presented in the following sections.

III.1 On-line driver steering model estimation

Vehicle crashes are serious problems that induce significant loss to the society. Among all the possible causes of vehicle crashes, human error is believed to be the primary factor that is responsible for most crashes. Therefore, many active safety systems are being developed to prevent traffic accidents. The vehicle active safety research has a rich and well-developed literature. Many successful ideas have been implemented on vehicles in the market, for example, the anti-lock braking system (ABS) and electronic stability program (ESP).

However, no matter how the active safety systems influence the vehicle motions, eventually the system is to function with driver still in the control loop, unless an automated highway system is employed. The human driver behavior is notorious for its varying and unpredictable nature. How the active safety systems perform effectively with the human together becomes an important issue. An appropriate representation will be essential for the development and functioning of the active safety systems. An online driver model estimation algorithm aimed to provide useful clues to the active systems is proposed in this research.

The vehicle steering control is the problem of interest in this research. There are many driver steering control models in the literature, e.g., the crossover principle model, optimal control model, and neural network model, to name a few [10-14]. However, these models are developed to emulate human driver’s behavior. They are generally used in simulation and analysis, and seldom used in controller design or on-line testing. These models are also expected to have uncertainty.

There are also articles discuss obtaining driver model parameters from experimental data, as in [15-16]. The data are usually obtained from field tests or driving simulator with human drivers. The potential benefit of this approach is the hope to implement the modeling in real-time and thus reducing the driver model uncertainty and providing essential clues to the controller. However, there are several underlying limitations. For example, the vehicle driving

is a closed loop system, and identification in closed loop is generally hindered by the monotony of the data. Furthermore, the driver behavior is highly un-predictable and this may invalidate the model structure for some of the data. On-line estimation of driver model parameters has been reported in the literature. Soma and Hiramatsu [15] use AR model to represent driver steering behavior. The on-line estimation of driver longitudinal control model has also been reported by Lee and Peng [16] and Kuhn and Heidinger [17]. In this research, it is proposed to use ARMAX structure to model driver steering behavior, and investigate the performance of this modeling approach on-line. This algorithm is first evaluated using existing driving simulator data, and finally will be tested on-line with human driver on a PC based driving simulator.

Off-line simulations and results

A set of driving simulator data from 12 drivers, each driving the simulator for 2 hours, is used in the beginning phase of this work. The data is collected by Dr. Pilutti at Ford Motor Company [18]. First the model parameters are computed in an off-line manner, the on-line algorithm based on extended recursive least square (ERLS) method is investigated afterwards.

It is noted that the driver behavior is very complicated and the model structure used here is an over-simplified one. The estimated model parameters may not represent the driver behavior correctly, and outliers always exist. The objective of this research is to investigate the interpretation of the identification results and how to produce meaningful results for the controller.

In [3], Chen and Ulsoy concluded that, compared with ARX, the choice of ARMAX model structure for driver steering behavior can satisfy the model assumption more closely.

The ARMAX model is used to represent input-output relationship between lateral position error (ye) and driver steering command (

δ

Fig. 1: Input and output of driver model Driver

) (t

y_e δ(t)

ARMAX Window 30 1

t (sec, fs=10Hz)

ARMAX Window ARMAX Window

ARMAX Window

: get result

30 31 32 33 34 0 1

Fig. 2: ARMAX with moving window

Figure 3 shows the raw data that is used in this study, and the standard deviation of the lateral position error is also included.

Fig. 3: Sample driving simulator data

Fig. 4: Standard deviation and absolute value of lateral position error

From crossover principle it is observed that manual control systems generally have similar pattern of frequency response, especially around crossover frequency (see, e.g., [13]).

The identified driver models have to conform to such principle. Therefore, it is concluded that the estimated driver model must provide sufficient phase lead around crossover frequency. It is conjectured that this can be used as an indication of whether the estimated driver model is reasonable.

Delay is an important factor in the driver model. For the model structure considered in this research, a constant one sampling time of delay (0.1 sec) is used. However, it is well-accepted

that the driver delay is actually not constant. Therefore, for comparison purpose, an extra flexibility that considers several possible amount of delay is introduced. At present only two candidate values are considered, i.e., 0.1 sec and 0.2 sec. The criterion to determine which value to use is the resulting DC gain and phase lead of the identified driver models. The results show that this mechanism significantly reduces the abrupt changes in the identified driver models among consecutive data. Consequently it is more possible to derive consistent and meaningful conclusions from the estimated models. Figures 5 and 6 show a set of sample plots of the computed DC gain and phase lead of the driver models using this method. The phase lead used here corresponds to the maximum phase angle of the computed driver model frequency response. Compared with fixed delay case (not shown for brevity), the abrupt changes in DC gain and phase lead are greatly reduced.

Fundamental control discipline suggests that higher gain results in faster tracking response, but correspondingly requires larger phase lead to ensure stability. From the example plot shown in Fig. 5, it is observed that there are evidences of this suggestion, although the separation cannot be clearly defined. There are also portions of data that generate negative DC gain, indicating an unstable system. It is found that this usually corresponds to a portion of data that the driver behavior is slightly “panic”. Therefore, the off-line analyses show that the proposed algorithm to evaluate the driver performance using DC gain and phase lead from the estimated driver models is reasonable.

Fig. 5: Driver model DC gain

Fig. 6: Driver model phase lead

On-line simulations and results

In this part the algorithm is implemented in an on-line manner. That is, the data is fed into the computation as if it comes from human driver’s input and output signal during driving.

However, the moving window size of 300 samples involve large amount of computations, and is more difficult to implement in a real-time experiment. Therefore, the ERLS method with a forgetting factor of 0.985 is used in the following algorithm.

As indicated in [19], the ARMAX model is a non-space-linear regression model and the standard recursive least square (RLS) method cannot be applied for system identification. The ERLS method is introduced especially for this type of problem and results in a pseudo-space-linear regression model. This method is briefly summarized as below. The model is

y

t

q

B

q

u

t

A

q

y

t

C

q

ε

t

e

t

)

| ˆ ( ) ( )

|

(

ε

t = y t − y t

In matrix form, we have ˆ(t) T(t) (t)

y

ξ θ

e

)]

1, - (t ), n - 2 - u(t ), n - 1 - u(t , 2) - y(t - , 1) - [-y(t

(k) _{d d}

T

ε θ

ξ

T 1 2 1 2

1,a ,b,b ,c]

=[a

θ

ε (t): prediction error

With the forgetting factor

λ

⎪⎩

⎪⎨

⎧

ˆ (N)]

1) (N - 1) 1)[y(N K(N

ˆ (N) 1) ˆ (N

1)P(N)]

(N 1) K(N - [P(N) 1) 1

P(N

1)]

(N 1)P(N) (N

[ / 1) (N P(N) 1)

K(N

T T

T

θ ξ

θ θ

λ ξ

ξ ξ

λ ξ

+ +

+ +

= +

+ +

= +

+ +

+ +

= +

(3)

This way the driver model parameters can thus be computed.

Results and Discussions

The same data set used in section 2 is fed into the ERLS algorithm, and the results are shown in Fig. 7. The switching of driver model delay is also considered in this on-line version.

However, the results are quite different, as the effect of this flexibility is significantly less obvious than before. The reasons behind this observation is that the recursive algorithm computes the new model parameters based on the previous model result, while the methodology in section 2 does not have this feature. Therefore, the driver model delay is fixed at 0.1 sec in this section.

Fig. 7: Phase lead estimate and DC gain

Although other data sets are also investigated, due to space constraints only one sample plot is presented. Nonetheless, the following observations are verified on other portions of the original data as well. Firstly, the DC gain plot resembles the plot in section 2 very well. This implies that the driver models computed in the on-line manner are consistent with the off-line method. However, the phase plots are not very consistent because in the on-line method, the computation involved in finding the maximum phase angle of the driver model is avoided.

Instead, the ratio between the discrete time zero and the dominant pole is computed as a rough estimation of the possible phase lead of the driver model. This decision again is made to simplify the on-line computation. Consequently, the phase angle estimates alone cannot yield much meaningful conclusions.

The DC gain level again is highly indicative of driver’s steering performance. Between 560 sec and 610 sec the DC gain is approximately at a higher level, and the corresponding phase lead estimates are slightly higher (in comparison with the data between 640 sec and 720 sec). In the raw data it is observed that this section of data has lower level of lateral position errors.

Between 540 sec and 570 sec the DC gain gradually increases. In the raw data it is seen that the steering angle changes rapidly and the steering performance improves. It is conjectured in this period the driver is trying to correct the lateral position error by increasing his steering effort.

The DC gain becomes negative in several section of Fig. 7. In the raw data it is seen that these events correspond to portions of data where the driver overreacts to the error and the steering performance becomes very poor. As this observation is found in several parts of the original data, it is conjectured that this can be used as an indication of a “panic” driver.

Conclusion

The objective of this research is to develop an on-line driver model parameters estimation algorithm and provide meaningful clues for the vehicle active safety systems. It is believed that these outputs will be helpful to the development and functioning of active safety systems. Although there are still many issues to address to correctly interpret the computed results, the preliminary results show that this approach is promising. The on-line algorithm has been tested and compared with off-line results, and its validity is verified in simulation. Currently a PC based driving simulator is being developed and human-in-the-loop driving simulator experiments will be performed next to verify this algorithm experimentally. The results of this section have been submitted to Advanced Vehicle Control Conference 2006 for presentation.

III.2 Adaptive steering controller design

Without doubt there is a certain level of uncertainty between the real human steering behavior and the steering model used. Among which when the human model parameters vary, it may correspond to change in driver’s steering performance. This change in performance may lead to accidents if the performance degrades significantly. Therefore, it is desired to develop safety systems such that the degradation of driver’s performance can be alleviated.

Adaptive control is particular effective with respect to systems with unknown or slow varying parameters. The problem associated with driver’s steering performance variations may be formulated under the framework of the adaptive control. The adaptive control is expected to compensate for the human model parametric variations. Thus an acceptable steering performance level may be achieved and maintained. Therefore, the objective of this

section is to investigate whether it is possible to apply the adaptive control algorithm to the vehicle steering assist controller design, and evaluate the effectiveness of such controller in dealing with degradation caused by driver model parametric variations.

To simplify the algorithm, only the proportional gain of the system is estimated and adapted. The adaptive control used here is an integration algorithm that has been proposed in [20]. The nominal system G_d

G

G

G

G

= k

G ˆ

k

δ - δ

δ

δ

δ

k ˆ

G

e

-y, where y

is the

∫

=

e e dt

k

γ

γ

δ

The controller gain K_c is adjusted using a similar integration algorithm. Define another error as e_c

=k

-k

K

∫

=

e e dt

K

γ

γ

The γi, i=1,…,4 in the integrands are adaptation gains that need to be tuned to achieve acceptable performance. The two integrations ensure that at steady state, e and e_c will both approach zero. This implies that k_e equal k_p and k_e

K

- +

G

K

G

G

er u y

yr

Fig. 8: Adaptive control structure

Adaptive control has been extensively applied to vehicle safety system design. Model reference adaptive control (MRAC) has been modified to improve vehicle steering motion control and tracking in [21-22]. In [23], Qu et al. consider the cornering stiffness between

front and rear axle and external disturbance as model uncertainty, and applied adaptive control to handle these uncertainty. The nonlinearity of tires has been considered in [24] and treated with MRAC using steer-by-wire approach. Self-tuning control (STC) has also been utilized in vehicle safety system design. The vehicle dynamic uncertainty from road curvature change and side wind has been addressed using STC in [25]. Clearly uncertainty in vehicle dynamics is a suitable topic for adaptive control.

For the vehicle driving, another source of model uncertainty is the driver model uncertainty. Although the literature about driver steering model is abundant, the research about driver model uncertainty is significantly less. In [3], the driver model parametric uncertainty has been used to represent driver’s change of steering behavior during a long driving task. The authors used robust controller to achieve steering assist with respect to this driver model uncertainty. A simple self-tuning controller has also been simulated with respect to driver model’s proportional gain variation. In this research, it is proposed to investigate applying adaptive control techniques to address driver model uncertainty in all parameters.

Theoretical background

In order to formulate the design problem, a driver steering behavior model must be assumed. For the purpose of controller design and analysis, it is desired to have a low order and simple driver model structure. Therefore, a PD with delay type driver model is selected as the model for driver steering behavior. Furthermore, such a simple model has higher potential to be implemented on-line. Within the structure of the driver model, first a nominal driver model is assumed to represent a degraded driver steering behavior.

PD with delay Gd:

) 1 )(

1 (

) 1 (

2 1

3

+ +

= ⁻ +

s s

s Gd Kde

sT

τ τ

τ

nominal Gd parameters:

Kd = 0 . 0033

τ

= 0 . 1

τ

= 0 . 01

τ

T = 0 . 1

In the same time, assume a reference driver model to represent a well-behaved driver as the baseline driver model. The purpose of the adaptive control is to improve the overall system response with the nominal driver model so that the compensated system is similar to the response of the system with the reference driver model.

Let the reference driver model be:

) 1 )(

1 (

) 1 (

2 1

3

+ +

= ⁻ +

s s

s e

Gd Kd

m m

m sT m

m

τ τ

τ

where

Kd

τ

τ

τ

T = 0 . 1

It is seen that the nominal driver is characterized by its twice as large DC gain value, compared with the reference driver model.

As a starting point, it is assumed that the driver model parameters are not known but fixed at constants. However, in reality driver’s steering behavior differs from the model and the model parameters may be time varying. These two factors contribute to most of the driver model uncertainty. At present driver model uncertainty is still under-developed in the literature. Consequently, in this work the driver model uncertainty results from [3] is adopted and simplified as the uncertainty model to be addressed. The model parameters are tuned to mimic the driver steering behavior found in the literature.

In the vehicle driving, the human driver serves as the primary controller of the vehicle.

To illustrate the nature of the driver model used, a vehicle model is needed. For simplicity it is assumed that the vehicle lateral dynamics can be modeled by a bicycle vehicle model. The following is the bicycle model in state space form:

2 2

0 1 0 0

0 0

0 0 0 1 0

0 0

v af ar ar af v af

ar af af ar af

z z

u

y C C bC aC y C

v mu mu u v m

bC aC a C b C aC

r r

l u mu l

ψ ψ δ

⎡ ⎤ ⎡ ⎤

⎢ + − ⎥ ⎢ ⎥

⎡ ⎤ ⎢ − − ⎥⎡ ⎤ ⎢ ⎥

⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥

⎢ ⎥=⎢ ⎥⎢ ⎥+⎢ ⎥

⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥

⎢ ⎥ ⎢ − + ⎥⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎢ − ⎥⎣ ⎦ ⎢ ⎥

⎣ ⎦

⎣ ⎦









(8)

[^{1 0 0 0}]

y

y v

r ψ

⎡ ⎤⎢ ⎥

= ⎢ ⎥

⎢ ⎥⎢ ⎥

⎣ ⎦ where

y

v: course angle ψ

r: yaw rate δ

The performance of the two assumed driver models can be easily verified by simulations.

It is observed that in general, with a lane change type maneuver, the steering performance of the nominal driver model is more oscillatory and has larger overshoot, due to its higher DC gain. The adaptive controller is expected to compensate for this effect and make the system behave like the reference model.

In this research a previous designed adaptive robust controller has been evaluated using

simulation. Next a model reference adaptive control (MRAC) is investigated to address model parametric variations in all the model parameters.

The input to the plant (Gd) is modified by the two adaptive control gains (G and F in the block diagram). The two adaptive controller gains (G and F) are designed based on Lyapunov Stability concept. The derivations of the control laws are summarized below:

From the block diagram it is seen that, u = G(R+Fx_p) If we let the model matching condition be

⎪⎩

⎪⎨

⎧

= +

=

m p

p

m p

A F G B A

B G B

*

*

*

, where G* and F* are the solutions to the model matching condition.

Then the closed loop system becomes:

GR B x GF B A

x

R B x A

x

Derive the error state dynamics as:

R G B B x GF B A A e A x x

e

R

G B B x GF B F B e

A

=

R G B B GFx B Fx B x F F B e

A

=

GR G G B GFx G

G B x F F B e

A

=

) (

) (

)

(

F

F x B G

G

G Fx R B

e

A

= ^{− −}

+

+

+ -

+

Ref model

Plant

Adaptive law G

F u

R

Let

G ^~ = G

− G

F

F

F

and substitute into the above equation, we have )

~ (

~

x B G G Fx R F

B e A

e

Now define ~]

~, [

F G

φ

_⎥

⎦

⎢ ⎤

⎣

⎡

= +

)

(

p

Fx R G

Z x

state dynamics can be simplified as

Z B e A

e

φ

Based on Lyapunov Stability Criterion, if we choose the Lyapunov function of the form 0

] 2[

1 ₁

>

Γ +

=

e

Pe tr

V φ φ

where Γ is the adaptation gain matrix to be tuned, the time derivative of V is ])

[ 2(

1 _{T T 1 T 1 T}

tr e P e Pe e

V

φ

φ

φ

φ

1 1

1(( ) ( ) [ ])

2

T T T T T T T T

m m m m

V

e A

Z φ B Pe

e P A e

B φ Z

tr φ φ

φ φ

]) [

) (

2 (

1

m T T

m T T m

T m

T

A P PA e Z B Pe e PB Z tr

e

V ^ = + +

+

+

^ Γ

+

Γ

^

⎩⎨

⎧

Γ

= Γ

=

−

− T T

T T

T T T

tr tr

Z B P e e P B Z

φ φ φ

φ

φ φ



 ^{1 1}

T

m m

A P

PA

Q

Substitute these equalities into the time derivative of V, yield 2 0

1 2

1 ₁

≤

−

= Γ + +

−

=

e Qe trB PeZ tr

e Qe

V

φ

φ

φ

If we let

Γ

−

= B

PeZ

φ ^

Equation (*) becomes negative definite. By the definition of φ, and

Γ = Γ [

Γ

]

1

~=−

B

Pex

F

) 2

~ (

Γ +

−

=

B

Pe R Fx

G

G

Finally, from the equality,

G

G

G

G

Γ1

=

B

Pex

F

G G Fx R Pe GB

G

Γ determines the parameters tracking speed, P is a symmetric positive definite matrix that can be found by solving the Lyapunov equation

A

P

PA

Q

Q.

Adaptive Control Simulations:

Consider the MRAC structure shown below, the original system with vehicle model driver by the controller Gd is simulated, as shown in the following figures.

0 10 20 30 40 50 60 70 80 90 100

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Gd model , vehicle lateral position

time(sec)

position(m)

After fine tuning with the adaptation gains, we choose the adaptation gain for F as

⎥ ⎥

⎥

⎦

⎤

⎢ ⎢

⎢

⎣

⎡

= Γ

01 . 0 0 0

0 01 . 0 0

0 0 01 . 0

1 , and for G as

Γ

= 1

-

u +

+

+

+ -

+

Ref model

Gd

Adaptive law G

F e

Gv

0 10 20 30 40 50 60 70 80 90 100 -0.2

0 0.2 0.4 0.6 0.8 1 1.2

Gd model , vehicle lateral position

time(sec)

position(m)

0 10 20 30 40 50 60 70 80 90 100

0.65 0.7 0.75 0.8 0.85 0.9 0.95

1 G

time(sec)

magnitude

0 10 20 30 40 50 60 70 80 90 100

-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005

0.01 F

time(sec)

magnitude

F1 F2 F3

It is seen that the adaptive controller effectively adjust the steering performance to the response similar to that of the reference driver model. It is then concluded that the MRAC can compensate for the driver model parametric variations effectively, at least preliminarily in simulations.

Observer

The previous developed MRAC requires full state feedback of driver model. However, the driver states do not correspond to physical variables and it is futile trying to measure them.

Therefore, it is proposed to use an observer to mathematically estimate the internal states that will be used in the MRAC algorithm. The block diagram structure is modified as below:

To simulate a practical situation, the driver model Gd used in the observer is chosen to be the reference driver model, as there is no way to determine a true driver model.

Let observer pole be

[ − 50 − 80 + 50 i − 80 − 50 i ]

L

The performance of this observer can be visualized in the following three plots. It is seen that this observer yields acceptable results for the state estimates.

+

+

+ + -

Ref model

Gd

Adaptive law G

F e u

Gv r

-

Observer

0 10 20 30 40 50 60 70 80 90 100 -0.015

-0.01 -0.005 0 0.005 0.01

0.015 Pole placement observer

time

x1 xhat1

0 10 20 30 40 50 60 70 80 90 100

-6 -4 -2 0 2 4

6 Pole placement observer

time

x2 xhat2

0 10 20 30 40 50 60 70 80 90 100 -80

-60 -40 -20 0 20 40 60

80 Pole placement observer

time

x3 xhat3

After the observer is designed, the following simulations are performed to evaluate the results of using this observer with the adaptive controller. It is seen that the actual simulated state variables differ from the estimated states from the observer. Consequently, using the estimated state variable may degrade the performance of the adaptive control.

Simulated results of mismatched observer with adaptive control

F:

⎥ ⎥

⎥

⎦

⎤

⎢ ⎢

⎢

⎣

⎡

= Γ

000001 .

0 0

0

0 000001

. 0 0

0 0

000001 .

0

1 G:

Γ

= 0 . 001

0 20 40 60 80 100 120 140 160 180 200

-0.2 0 0.2 0.4 0.6 0.8 1

1.2 Gd model , vehicle lateral position

time(sec)

position(m)

0 20 40 60 80 100 120 140 160 180 200

1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2

0 20 40 60 80 100 120 140 160 180 200 -8

-6 -4 -2 0 2 4 6 8x 10^-3

From the simulation results it can be concluded that the observer does have effect on the adaptive controller. With the observer, the high frequency oscillation in the lateral position error response and the variation in the F and G controller gains are more evident and with larger amplitude.

In this section we evaluate the performance of the adaptive system with the observer. In general it is not possible to know the exact model of the plant, therefore, a mismatched observer result. Larger estimation error is expected, and it is natural that the adaptive controller will be affected.

Introducing the noise and disturbance

While the observer model mismatch is one source of the performance degradation, the external noise and disturbance will also influence the system performance. The Kalman filter is designed specifically to deal with the input and output disturbance. In this section the effectiveness of Kalman filter in improving state estimates under external disturbance and noise is investigated.

Luenberger observer state estimates:

0 10 20 30 40 50 60 70 80 90 100 -0.02

0 0.02

Pole placement observer

0 10 20 30 40 50 60 70 80 90 100

-10 0 10

0 10 20 30 40 50 60 70 80 90 100

-100 0 100

time

x1 xhat1

x2 xhat2

x3 xhat3

Kalman filter state estimates:

0 10 20 30 40 50 60 70 80 90 100

-0.02 0 0.02

Kalman filter

0 10 20 30 40 50 60 70 80 90 100

-10 0 10

0 10 20 30 40 50 60 70 80 90 100

-100 0 100

time

x1 xhat1

x2 xhat2

x3 xhat3

From the comparison it can be concluded that Kalman filter performs better in suppressing the effect of the noise and disturbance.

Adaptive control with Luenberger observer

F:

⎥ ⎥

⎥

⎦

⎤

⎢ ⎢

⎢

⎣

⎡

= Γ

000001 .

0 0

0

0 000001

. 0 0

0 0

000001 .

0

1 G:

Γ

= 0 . 001

0 20 40 60 80 100 120 140 160 180 200

-0.2 0 0.2 0.4 0.6 0.8 1

1.2 Gd model , vehicle lateral position

time(sec)

position(m)

0 20 40 60 80 100 120 140 160 180 200 0.8

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

0 20 40 60 80 100 120 140 160 180 200

-8 -6 -4 -2 0 2 4 6 8x 10^-3

Adaptive control with Kalman filter

F:

⎥ ⎥

⎥

⎦

⎤

⎢ ⎢

⎢

⎣

⎡

= Γ

001 . 0 0 0

0 001 . 0 0

0 0

001 . 0

1 G:

Γ

= 0 . 01

0 20 40 60 80 100 120 140 160 180 200

-0.2 0 0.2 0.4 0.6 0.8 1 1.2

Gd model , vehicle lateral position

time(sec)

position(m)

0 20 40 60 80 100 120 140 160 180 200 0.75

0.8 0.85 0.9 0.95 1 1.05

1.1 G

time(sec)

magnitude

0 20 40 60 80 100 120 140 160 180 200

-0.02 -0.015 -0.01 -0.005 0 0.005

0.01 F

time(sec)

magnitude

F1 F2 F3

Once the plant suffers from noise and disturbance, the steering performance shows the expected oscillation. In MRAC this issue is not considered at all. It is expected that a robust adaptive control approach may enhance the robustness of the system.

Comparing the Kalman filter with the Luenberger type observer, it is seen that the Kalman is more effective in reducing the effect of noise and disturbance. This is due to the characteristics of the Kalman filter and is natural.

Conclusions

The simulation results show that the MRAC controller is effective to compensate for the parametric variations in driver model. It is also observed that the Kalman filter performs better in contaminated measurements. The performance of the MRAC with the observer is still acceptable, albeit slightly degraded than the perfect measurements cases. The results in this section have been submitted to the Advanced Vehicle Control Conference, 2006 for presentation.

III.3 Scaled vehicle testbed

There are several existing examples of using scaled vehicle as the testing facility for vehicle safety system design, e.g., Longoria, A1-Sharif, and Patil at Univ. of Texas at Austin construct a 1/5 scale vehicle testing system for ABS (Anti-lock Braking System) evaluations, and they emphasize on the difference in tire-ground contact effect between scaled vehicles full size vehicles [26]. Kachroo at the Virginia Institute of Technology applies their FLASH (Flexible Low-cost Automated Scaled Highway) system to the ITS (Intelligent Transportation System) investigations. The author employs several sensors on the scaled vehicle and successfully commands the scaled vehicle to follow prescribed trajectory [27]. Brennan and Alleyne, and their colleagues at the University of Illinois at Urbana-Champaign, develop the IRS (Illinois Roadway Simulator) system, and conclude the dynamic similitude between scaled vehicle and full size vehicle [28]. The scaled vehicle is controlled by the PC through the real-time kernel running on the CPU. The vehicle’s longitudinal motion is countered by the motion of the conveyer belt. They also report the evaluation of active safety system using the scaled vehicle testbed [29].

In this project it is proposed to construct a similar test-bed to conduct vehicle simulation experiments to evaluate the designed safety systems. Furthermore, it is planned to enhance the setup to incorporate human steering control interface so that a simulated experiment with both human driver and hardware (scaled vehicle) in the loop can be performed. The proposed adaptive steering assist controller will be evaluated on the scaled vehicle using different testing scenarios. The results will be compared with the PC-based driving simulator results.

The system consists of three parts: the roadway simulator (treadmill), the position measurement system, and the scaled vehicle. A Delta Electronics VFD-M controller is used to control the speed of the treadmill, and the controller set point can be adjusted via an interface with the PC. The position measurement is accomplished by the angles of serial-link arms, as has been done in [28]. The treadmill and the arms are shown in the photo below.

The computation can be illustrated in the figure below. From the angles measured by the encoders, using simple geometry, the following equations yield the desired vehicle position.

θ θ ψ θ

θ θ θ

θ θ θ

3 2 1

2 1 2 1 1

2 1 2

1 1

) sin(

. ) sin(

.

) cos(

. ) cos(

. + +

=

+ +

=

+ +

=

l y l

l x l

The scaled vehicle

The Tamiya Mercedes-Benz CLK-DTM 1/10 is the basis of the vehicle body. The vehicle is modified to be rear wheel driven, and the DC motor is replaced with a more suitable model.

In steering control an Oriental Motor CFK545AP2 Stepper Motor has been employed to replace the original steering servo, as the dynamic behavior significantly improve the steering actuation. The modified vehicle is shown in the following picture.

The DC motors are first tested with its speed control. The results are shown below:

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2

2.5 Vehicle Velocity Control

Time

Vehicle Velocity (m/s)

Vehicle Velocity Target Velocity

The steering command is achieved by a stepper motor. The stepper motor will be commanded to steer the front wheels to the desired value by a series of pulse train. The following plot shows the testing of the positioning control of the stepper motor. This corresponds to the