Robust Real-time Optimal Autonomous Highway Driving Control System: Development and Implementation

Transcription

1 Preprints of the 9th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 24-29, 24 Robust Real-time Optimal Autonomous Highway Driing Control System: Deelopment and Implementation Seung-Hi Lee Youngseop Son Chung Choo Chung Di. of Electrical and Computer Engineering, Hanyang Uniersity, Korea ( Global R&D Center, MANDO Corporation, Korea ( Di. of Electrical and Computer Engineering, Hanyang Uniersity, Korea ( Abstract: This paper deelops a systems approach for robust real-time optimal autonomous driing system deelopment. An autonomous ehicle system framework is proposed to dissect an automotie system into some sub-systems in which physical systems and softwares are communicating. To attain robustness, a robust on-road ehicle localization scheme is proposed applying multi sensor-data fusion with the results of multirate decentralized state estimation and the clothoidal road model constraint. Control block and block topology are proposed to utilize block-wise perception of enironment and ehicle localization and to produce a trajectory command ia a irtual lane cure for longitudinal/lateral ehicle. To attain real-time optimality, we apply the multileel approximate predictie deeloped by the authors. Performance of the proposed autonomous driing system is demonstrated through some track test results.. INTRODUCTION Autonomous driing ehicles are said to be the future of automotie ehicles that proide safety, comfortability, conenience for driers. Autonomous ehicles accordingly become a ery important research topic in the automotie industry. Autonomous driing requires much more adanced technologies oer adaptie cruise and lane keeping which assist the drier s driing action by getting the information of road enironment and ehicle s states. Autonomous driing thus requires lateral as well as longitudinal motion. Many articles considered lateral design such as automated lane change steering (see e.g. Falcone et al. (27); Guldner et al. (999); Hatipoglu et al. (23)). It is howeer hard to find designs that consider both lateral and longitudinal motion, whilst there has been so much work on lane keeping/changing design. It is our experience that adjusting the longitudinal elocity according to the ehicle s yaw rate and/or speed tends to proide more efficient driing (e.g. lane changing). Almost no article considers longitudinal elocity in the lane changing. Longitudinal ehicle was mostly for intelligent ehicle highway system (IVHS) (see e.g., Hedrick et al. (99); Pham et al. (994)). In This work was supported by National Research Foundation of Korea Grant funded by the Korean Goernment (22RAA244762). This work was also supported by the Industrial Source Technology Deelopment Program(4462, Automatic lane change system for noice driers) funded by the Ministry of Trade, Industry and Energy(MOTIE, Korea). Pham et al. (994), combined lateral and longitudinal was presented for IVHS. In Rajamani et al. (2), integrated longitudinal and lateral was presented. Cruise (see e.g., Ioannou et al. (993); Möbus et al. (23)) is also an interesting ehicle longitudinal problem. Multirate sensing is inherent in autonomous ehicles and it causes system design to become challenging. Recent trends in the lane keeping/changing system research are using ision systems to obtain optical lane recognition (Dickmanns (22)) which are slow. Whilst, other measurements such as the yaw rate and the longitudinal elocity are aailable at a fast rate through the ehicle s electronic unit (ECU). It is well known that the performance of a digital system is limited by the applied sampling rate. Nonetheless, the approach of conentional lateral is to generate a command at the same slow rate of the ision processing. The problem of a slow update rate as well as the time delay of ision processing systems causes inaccurate and undesirable lateral behaior such as oscillatory responses due to the loss of damping. Applying predictie is prospectie for real-time optimality in the presence of arious constraints (e.g. steering angle limit and its rate limit, yaw rate limit, etc.), proided it can be soled in real-time. No other methods can consider such arious constraints. In this regard, the authors proposed an innoatie approximate explicit model predictie (MPC) strategy applying multileel approximation scheme (Lee and Chung (23)). The scheme achieed a significant improement of Copyright 24 IFAC 76

2 9th IFAC World Congress Cape Town, South Africa. August 24-29, 24 computation time and approximation quality oer other approximate predictie methods. Applications of MPC to ehicle motion are ery promising and numerous successful results hae been reported so far (see e.g. Falcone et al. (27); Li et al. (2)). The paper deelops an autonomous driing system in a systems approach, with robust lane cure estimation and performance optimality. We will propose a new paradigm for autonomous driing system design, and deelop a set of sub-system modelings. We are to introduce innoatie methods for block-wise perception of enironment around the ehicle and for determining admissible maneuering to design trajectory commands. Robust real-time optimality is to be attained by deeloping a robust road lane estimation scheme and by applying predictie scheme deeloped by the authors Lee and Chung (23). We are also to demonstrate the performance of the proposed autonomous driing system through in-ehicle tests and some track test results. NOMENCLATURE {XY Z} inertial coordinate frame {xyz} local coordinate frame O the center of turn (CT) x a front fixed longitudinal position in {xyz} y lateral position of the origin of {xyz} to CT y des lateral position of the lane center to CT ẋ = V x longitudinal elocity at the center of graity (CG) ẏ = V y lateral elocity at CG of ehicle ψ yaw, heading, angle of ehicle in {XY Z} ψ des yaw, heading, angle of the lane center in {XY Z} β ehicle side slip angle at CG α f (α r ) front (rear) tire slip angle ψ yaw rate of ehicle δ f (δ r ) front (rear) steering angle C α (C αf, C αr ) cornering stiffness of (front, rear) tire F y (F yf, F yr ) lateral force on (front, rear) tire θ V tire elocity angle in {xyz} φ road bank angle µ Tire-road friction coefficient R turn radius of ehicle or radius of road L look-ahead distance e y = y y des lateral position error in {xyz} e ψ = ψ des ψ heading angle error in {xyz} N steering ratio m total mass of ehicle I z yaw moment of inertia of ehicle l f (l r ) longitudinal distance: CG to front (rear) tire l fr = l f + l r wheelbase PARAMETER DEFINITIONS a 22 = 2C αf + 2C αr mv x, a 23 = a 22 V x, a 24 = 2C αf l f 2C αr l r mvx 2, a 24 = (a 24 )V x, a 42 = 2C αf l f 2C αr l r I z, a 42 = a 42 V x, a 43 = a 42, a 44 = 2C αf l 2 f + 2C αrl 2 r I z V x, Trajectory Command b 2 = 2C αf mv x, b 2 = b 2 V x, b 4 = 2C αf l f I z. 2. PROBLEM DESCRIPTION Arbitration Speed Lateral _x d ± d Multi-sensor Data fusion G cc clp _x_x ± G sc clp Vehicle Motion Fig.. Autonomous Driing Control Framework Lidar Radar Camera GPS IMU. We are interested in deeloping a new paradigm for autonomous driing design and implemenation as shown in Fig.. The framework dissects a complex automotie system into some accessible cyber-physical subsystems (consisting of physical systems and softwares, with communications between them). The proposed paradigm has a significant adantage of allowing cyberphysical systems approach: one can independently determine each sub-system or software while just considering possible high-leel communication between them. One can thus easily apply well deeloped ariety of and estimation theories. Seamless integration into ehicles is quite natural because the communication is already well defined. We are thus interested in deeloping some essential techniques to realize autonomous driing in the proposed autonomous driing framework. Specifically, we are interested in deeloping cyber-physical sub-system modelings, deeloping ehicle localization and enironment perception, designing the trajectory command and the arbitration, the speed, and the lateral. For reliable ehicle localization and enironment perception, we are interested in deeloping a multirate decentralized state estimator based multi sensor-data fusion. In regard to a trajectory command, we are interested in deeloping an innoatie method that can efficiently describe the condition of ehicle s enironment in pursue of safest autonomous maneuering. 3. SUB-SYSTEM MODELING In order to deal with the autonomous driing framework shown in Fig., let us deelop a unique set of cyber-physical sub-system modelings. The figure dissects the automotie system into some sub-systems to be modeled. By the cyber-physical sub-system modeling we mean that we model the sub-systems that are either physical system or cyber-physical: real physical system motion, () softwares, or approximations of concepts/phenomena. We are to deelop a high-leel ehicle motion model transfer function from [ ẋ d δ d] T, the desired longitudinal elocity and steering angle, to the ehicle pose in terms of road lane cure tracking error at a look-ahead distance error. We also deelop the cruise closedloop G cc clp to describe the high-leel longitudinal motion and the steering closed-loop G sc clp. By combining them we are to build a high-leel ehicle motion model. 77

3 9th IFAC World Congress Cape Town, South Africa. August 24-29, Lateral Motion Model In highway driing, it is quite practical to assume steady state tire deformation, small tire slip angle, and (almost) constant µf z. In this case, the lateral tire force modeling becomes simple: the tire lateral force F y can be approximately represented by tire slip angle α and a constant cornering stiffness C αf such that F y = C αf α. For large tire slip angles, we need to introduce more sophisticated nonlinear tire model such as Pacejka s magic formula cure (Pacejka et al. (987)). The lateral motion model is described in terms of road lane cure tracking error in {xyz}. Considering expert driers behaior to obsere the road at a look-ahead distance while driing, we describe the lateral motion model in terms of error at a look-ahead distance error (Fig. 2). fyg fyg Reference trajectory e ÃL eã e à à des;l e yl 3.2 Longitudinal Motion Model Some part of longitudinal motion model are softwares: The electronic stability (ESC) software and the cruise software. It is usual to design the ESC closed-loop system such that G esc clp = ẍ ẍ d = τs + where τ is typically.5 (see e.g. Rajamani (26)). Moreoer, the cruise ler G cc is in a form of proportionalintegral. Then, it is immediate to find the closedloop cruise system transfer function G cc clp = ẋ ẋ d = G esc clpg cc s + G esc clp G cc that describes high-leel longitudinal ehicle motion. The ehicle s front fixed longitudinal position x in {xyz} is simply an integration: x/ẋ = /s. Remark. The longitudinal motion model x/ẋ = /s is independent of the lateral motion model. The lateral motion model requires ẋ from the longitudinal model. V y e y _e y = V x(e à ) V V x à V x(e ÃL ) L_e à L fxg fxg 3.3 Steering System Model Some part of steering system are also softwares: The AFDR and the steering in Fig. 3. Fig. 2. Lateral position and elocity errors at the lookahead distance point Considering possible state measurements that may be conducted ia the use of multiple sensors with different principles, the ehicle lateral motion is described in terms of the state ector x = [ ] x T x T T m with x = [e yl ė y e ψ ] T and x m = [ ψ ], u = δ ẋ = Ax + Bu + B ϕ ϕ + B φ sin φ [ ] [ ] A A = m B x + u + A m A m B m [ Bϕ ] ϕ + [ ] Bφ sin φ () where ϕ = [ ] T ψ des e ψl e ψ, [ ] A = a 22 a 23, A m = [a 44 ], A m = L a 24, A m = [ a ] 42 a 43, B = b 2, B m = [b 4 ], [ ] [ ] L Vx B ϕ = V x, B φ = g. A detailed analytical deriation of the model is explained in (Lee et al. (submitted)). For the ECU sampling period T c, one can obtain the ZOH discrete-time equialent quadruplet, to (A, B, B ϕ, B φ ), ([ ] [ ] [ ] [ ]) Φ Φ (Φ, Γ, Γ ϕ, Γ φ ) = m Γ Γϕ Γφ,,,. Φ m Φ m Γ m T d μ s V x AFDR T AF DR T s =N ± d Steering T ± T EPS Steering system Fig. 3. Closed loop steering system with T δ The AFDR torque can be expressed as T AF DR = T A + T F + T D + T R, where T A is the assistant torque (for drier s easy steering with steering torque T d + T A ), T F is the friction (to compensate for mechanical friction increase due to T d direction change), T D is the damping (to attain comfortable damped steering return with T s + T D ), T R is the return (to attain neutral steering position θ s = Nδ = when T d = ). We describe the steering mechanism as a second order system. If the drier s torque T d =, then the transfer function from T δ to δ can be expressed as G str = δ T δ N(I swe s 2 + C sw s). Once we design a steering sero ler G sc (e.g. feedforward and PID ). Then, the closed-loop steering system transfer function G sc clp = δ/δ d can be readily computed. Further, it can be approximately described by G sc clp = δ δ d τ s s + where τ s is typically..2 sec (our experimental obseration). ± 78

4 9th IFAC World Congress Cape Town, South Africa. August 24-29, VEHICLE LOCALIZATION 4. Multirate to Synchronous Sampling Sensing in autonomous ehicle is inherently multirate. Let T c be the update period (that is equal to the sampling period of the ehicle s ECU, T ecu ), T cam be the camera-ision processing system s update period, and T rad be the radar update period. Without loss of generality, we assume (can let) T cam = R m T ecu and T rad = R mr T ecu for some integers R m and R mr. The ehicle s yaw rate ψ and longitudinal elocity V x are measurable and aailable from the ehicle ECU at a sampling rate of /T c. Let k, k and k r denote the ECU, the camera, and the radar update indices, respectiely. Then the synchronous time is represented by t = kt c = (k + i/r m )T cam = (k r + j/r mr )T rad (2) for k, k, k r Z = {,, 2,... } and i Z = {,,..., R m } and j Z r = {,,..., R mr }. By (2), we mean that there exist some time index sets (k), (k, i), (k r, j) satisfying the time synchronous condition: e.g. u(k) = u(k, i) = u(k r, j). In the next subsections, utilizing the synchronous time, we are to perform ehicle localization and enironment perception through multi sensor-data fusion at a fast rate of the ehicle s ECU using decentralized multirate state estimation using multirate sensing from the camera-ision sensor (lane cure and obstacle ehicles at T cam ), the radar sensor (obstacle ehicles detection at T rad ), and the inertia sensor (yaw rate, speed, etc.). 4.2 Multirate Decentralized State Estimation Using the model (), we design a multirate decentralized state estimator: A state estimator to estimate x m is { xm (k + ) = Φ mˆx m (k) + Γ m u(k) + Φ m ˆx (k, i) (3a) ˆx m (k) = x m (k) + L lm (y m (k) C m x m (k)) where L lm is the state estimator gain that stabilizes Φ m Φ m L lm C m. In this case, ˆx are all assumed to be aailable from the multirate state estimator for ˆx we are to design. In order to estimate the state x, we are to use a multirate state estimator x (k, i + ) = Φ ˆx (k, i) + Γ δ(k, i) + Φ mˆx m (k, i) + Γ ϕ ψ des (k, i) + Γ φ sin φ ˆx (k, i) = x (k, i) + L l (y (k, ) C x (k, )) (3b) where L l is the state estimator gain to be determined. Definition. A multirate state estimator is referred to as conergent if it is conergent at some sampling periods. Admitting that the output measurement y ( ) is aailable at each sampling instant k T cam, we are to make the multirate state estimator (3b) conergent at the sampling period T cam. Now, applying discrete-time lifting (see e.g. Kranc (957); Meyer (992)) leads to x(k +, ) = ( Φ Rm R m + ) Φ Rm L l C x(k, ) Φ n y(k, ). with a definition of Φ Rm L l = R m Φ n L l. Utilizing a gain L l that stabilizes Φ Rm Φ Rm L l C, we immediately compute L l = ( Rm Φ n ) Φ Rm L l that guarantees the conergence of the state estimator (3b) at each camera-ision processing update time. Proposition. The decentralized multirate state estimators gien in (3) are conergent, if their dynamics show conergence at some respectie sampling periods. Proof: Skipped due to space limitation. 4.3 Vehicle Localization Vehicle localization on road is achieed by detecting road lane marks as a cloithoidal cubic polynomial. The ehicle motion model in terms of the road tracking error describes ehicle location on road: Vehicle localization. The camera and ision processing system can proide a lane cure equation (see e.g., Dickmanns (22)) f(x) = c o + c x + c 2 x 2 + c 3 x 3 (4) on the ehicle coordinate system, at a slow sampling rate of /T cam. Here, c i s denote the lateral offset, heading angle error, curature/2, curature rate/6, respectiely. For robust road lane detection, we apply multirate multisensor data fusion using the multirate decentralized state estimation C ˆx in (3b) and the nonholonomic constraint on the clothoidal road model - slowly arying curature κ = 6c 3 V x T c + 2c 2. By fusing these informations, we obtain an optimal road lane cure estimation in the case of intermittent faulty lane detection. We first use x (k, i) in (3b) to obtain a lane cure prediction at time (k, i): c = ē ψ (k, i), the heading angle error prediction, c 3 = c 3, c 2 = κ/2 with a curature prediction κ = 6 c 3 V x T c + 2c 2, and c = ē yl (k, i) c L c 2 L 2 c 3 L 3. These coefficients can be used to build a lane cure prediction f(x). It is our obseration that the cubic polynomial lane cure f(x) in (4) is ery sensitie to the errors in the coefficients c 2 and c 3. By this we mean that erroneous detections of c 2 and c 3 by the camera-ision sensors may cause a fishtail cure to occur. In this regard, we need to ealuate reliability of a detection of lane cure using the Mahalanobis distance (see e.g. Thrun et al. (26)) ] [ ]) T ] [ ]) ([ c2 d 2 M f ( f, c2 ([ c2 f) = R c 3 c c2 f (5) 3 c 3 c 3 where R f denotes an error coariance matrix associated with the lane curature and its rate. A lane cure detection is reliable and can thus be used, proided d Mf ( f, f) in (5) is less than a pre-specified threshold alue. Otherwise, it is considered as a faulty lane cure detection that cannot be used. Now, we can use ˆx (k, i) in (3b) to estimate the lane cure at time (k, i): ĉ = ê ψ (k, i), the heading angle error estimation, ĉ 3 = c 3, ĉ 2 = ˆκ/2 with ˆκ = 6ĉ 3 V x T c + 2c 2, and ĉ = ê yl (k, i) ĉ L ĉ 2 L 2 ĉ 3 L 3. These coefficients can be used to build a lane cure estimation ˆf(x). 79

5 9th IFAC World Congress Cape Town, South Africa. August 24-29, ENVIRONMENT PERCEPTION For autonomous driing, perception of enironment (other ehicles around), in addition to on-road ehicle localization, must be used in producing a trajectory command. This section is dedicated to describing an innoatie way to describe the results of enironment perception and to determine a trajectory command utilizing it. 5. Control Block for Block-Wise Enironment Perception As far as we are concerned with safest driing, we are interested in determining risk-free enironment rather than acceptable risk through a complex risk assessment to determine quantitatie or qualitatie alue of risk related to lane keeping/changing. In order to describe the results of enironment perception in a block-wise manner, just determining risk-free or not, we propose a simple block-wise enironment perception method referred to as Control Block (Fig. 4). Assumption. Perception of enironment in such a blockwise manner is aailable so as to determine the condition of each sub-block. It should be noted that Assumption just requires a simplest risk assessment. If an obstacle ehicle is already in, just entering, or expected to moe into a sub-block (in the ery short future), then the sub-block becomes red. Such a simple block-wise condition determination ia enironment perception is a ery simple yet efficient risk assessment to determine admissibility of lane keeping/changing. In reality, as far as we are concerned about safest driing, quantitatie or qualitatie alue of risk related to lane changing appears to be useless. By this we mean that we are simply interested in risk-free situation that leads to safest driing. fyg x d x (;) fxg (;) ( ;) (;) (;) ( ;) (; ) (; ) ( ; ) Fig. 4. Control block consists of 3 3 sub-blocks. The block, consists of 3 3 sub-blocks in {xyz} is simply a block-wise description of the enironment of the ehicle: The origin sub-block B(, ) is taken by the ehicle, and the other sub-blocks are either acant or (possibly) taken by surrounding ehicles. The (red-colored) occupied sub-blocks are taken by arounded ehicles. The (green-colored) admissible sub-blocks, among the acant sub-blocks, are candidate targets the ehicle can moe into. Some admissible sub-blocks (yellow-colored) can only be reached ia detour sub-blocks. Each sub-block has a width of a lane and a height of minimum safe platoon driing distance (described by the tip-to-tail headway position x). Let x in {xyz} be a minimum tip-to-tail headway position representing a distance from the tip of the ehicle to the tail of leading block added to the longitudinal distance from the center of graity to the tip (Fig. 4). With a longitudinal elocity of ẋ, the position x in {XY Z} can be reached in a tipto-tail headway time τ x. The headway time is time taken by the ehicle to coer the headway distance. By keeping a constant headway position x, the elocity set point ẋ d can be kept constant. Increasng/descreasing the headway position x, with a fixed headway time τ x, leads to a corresponding elocity set point adjustment. 5.2 Control Block Topology for Trajectory Command In order to determine if a candidate target sub-block is admissible, we propose a method referred to as Control Block Topology. Definition 2. In a case of moing from B(, ) to a target sub-block B(i t, j t ) (simply noted as B(, ) B(i t, j t )), we define a maneuering sub-block set B([ : i t ], [ : j t ]) where [ : i t ] ([ : j t ]) denotes ascending/descending integers to i t (j t ) and ([ : i t ], [ : j t ]) denotes a set of finite combinations of such ascending/descending integers. Further, in a case of moing B(, ) B(i d, j d ) B(i t, j t ), we define a maneuering sub-block set B([ : i d ], [ : j d ]) B([i d : i t ], [j d : j t ]). Remark 2. The maneuering sub-block set B([ : i t ], [ : j t ]) consists of finite combination of ascending/descending integers to i t (j t ). Definition 3. In terms of the block, a maneuering in which the (edges and ertices of) origin sub-block B(, ) neer inade red sub-blocks in its maneuering subblock set is defined as risk-free maneuering. The following proposition addresses risk-free (neer inading red sub-blocks) maneuering (lane keeping/changing). Proposition 2. A sub-block B(i t, j t ) is admissible, if the set B([ : i t ], [ : j t ]) includes no red sub-block. Further, if the set B([ : i d ], [ : j d ]) B([i d : i t ], [j d : j t ]) includes no red sub-block, the sub-block B(i t, j t ) becomes admissible ia an admissible detour sub-block B(i d, j d ). Proof: Skipped due to space limitation. Now, a target sub-block, B(i t, j t ), for possible lane change is determined through the block topology in Proposition 2. We then need to design a trajectory command for the ler we are to design. For longitudinal maneuering, a headway position x d is gien to moe into B(, j t ). For lateral maneuering, we introduce a Virtual Lane Cure (VLC) that passes through the center of the target sub-block B(i t, j t ): f lc (x) = f(x) + e lc y where e lc y is the lane cure offset to the lane change direction from the lane cure at B(, ). Remark 3. The irtual lane cure at the target sub-block B(i t, i t ) introduced for lane change from the origin sub- 7

6 9th IFAC World Congress Cape Town, South Africa. August 24-29, 24 block B(, ) naturally becomes the real lane cure as the target lane is taken by the ehicle. The trajectory command is gien in terms of the state reference described by x d = [ e lc yl ė r y e lc ψ ] T (6) where ė r y denotes a desired decay rate of error associated with the VLC. By determining ė r y, one can adjust the lateral position error decay rate, Assigning a target sub-block B(i t, j t ) is equialent to giing (x d, x d ), a set of desired headway position and desired lateral pose error, that leads the ehicle to the target subblock. By assigning a target/detour sub-block, a ariety of autonomous driing scenarios can be realized: lane keeping with cruising, lane changing with cruising, lane changing with passing/being-passed-by other ehicles. 6. CONTROL DESIGN The Trajectory Command in Fig. computes a reference set for ehicle maneuering: a set of desired headway position and desired lateral pose error. Gien a trajectory command (x d, x d ), the Speed and the Lateral determine (ẋ d, δ d ): The Speed generates a desired longitudinal elocity ẋ d that is to be applied to the cruise closed-loop G cc clp, whilst the Lateral generates a desired steering angle δ d that is to be applied to the steering closed-loop G sc clp. The role of the Arbitration in Fig. includes determination of possible lateral mode change. 6. Longitudinal Speed Control The Speed in Fig. generates a desired longitudinal elocity ẋ d that is to be applied to the cruise closed-loop G cc clp. For longitudinal speed design, we propose a map to generate a elocity set point trajectory ( ẋ d fx (x d ) x) = ẋ + sat γ x T c (7) γ x T c where γ x > is a design constant to limit the rate of change in longitudinal elocity such that ẋd ẋ < γx T c. A simple form of f x ( ) is surely (x d x)/τ x. The elocity command ẋ d becomes an input to the cruise closed-loop G cc clp. The desired longitudinal elocity ẋ d is expressed in terms of the desired and current headway positions. 6.2 Lateral Control The Lateral in Fig. generates a desired steering angle δ d that is to be applied to the steering closedloop G sc clp. For lateral, we apply model predictie (MPC) to generate a desired steering angle δ d which becomes an input to the steering closed-loop. The reference trajectory for MPC is determined as r(k + i) = e ηi Cx d (k), i =,..., N p (8) where N p is the prediction horizon and η > is a design constant. For real-time optimality of the lateral ler, we are to apply the multileel approximate model prediction for real-time optimality (see Lee and Chung (23)). The predictie scheme attains optimality the adantage of the predictie while significantly saing computing time. Details are not gien here due to space limitation. The interested readers are referred to the reference. 7. IMPLEMENTATION AND TESTS The autonomous driing system is implemented for in-ehicle tests on a test ehicle (Hyundai Tucson). The high-leel commands ẋ d, the elocity set point, and δ d, the desired steering angle, generated from the speed and lateral, respectiely, in Fig. are injected into the in-ehicle cruise ler as a elocity set point and the in-ehicle EPS system as a alue aided function torque input, both thru the CAN communication. By this, the proposed autonomous driing system is seamlessly integrated into the test ehicle with modification for implementation being minimized. Look down distance [m] Look down distance [m] c3= 5e 6 c2=.4 c=.68 c=.68 estimated true erroneous meas Lateral position error [m] c3= 3.8e 6 c2=.42 c=.59 c=.59 estimated true erroneous meas. (a) Lateral position error [m] (b) Fig. 5. Frame sequence in road lane cure estimation simulation: a fishtail cure by the camera-ision measurement error is corrected. First, road lane cure estimation scheme is tested. A frame sequence in Fig. 5 demonstrates that the cubic polynomial 7

7 9th IFAC World Congress Cape Town, South Africa. August 24-29, 24 eyl [m] ey [m] ėy [m/s] eψ [rad] ψ [rad/s] δ d [deg] Time [s] Fig. 6. Lane change experiment with a scenario of B(, ) B(, ) cure is ery sensitie to the errors in the coefficients c 2 and c 3 : een ±% random errors cause such a problematic fish tail cure. We find that some intermittent cameraision measurement errors/failures can be corrected by considering the ehicle motion and the clothoidal road model constraint. We then conducted an autonomous lane changing experiment on a ehicle performance test track. As a safest lane change scenario, we tried a lane change at a ehicle speed of 3m/s on straight road lane with obstacle ehicles taking their sub-blocks B(, ), B(, ), and B(, ) in the block (Fig. 4). By applying the block topology, an admissible target sub-block B(, ) is determined for lane change. The predictie lateral ler with a reference trajectory (8) and the longitudinal speed ler in (7) are applied. The result of lane change experiment with a scenario of B(, ) B(, ) is shown in Fig. 6. The VLC is introduced at about 4.3s. Lane crossing occurs at about 7s. Lane change completes in 5.5s. 8. CONCLUSIONS A systems approach has been proposed for autonomous driing system deelopment and implementation. The proposed autonomous driing system framework dissected an automotie system into some subsystems with communications between them being considerred such that systematic system designs can be accomplished. The proposed block and block topology used block-wise perception of enironment and ehicle localization to produce a trajectory command ia a irtual lane cure for longitudinal/lateral ehicle. As shown through an application, the proposed autonomous driing system and its design methods allow a systematic autonomous driing design to be accomplished in a systems approach, well deeloped ariety of and estimation theories can be easily applied with readiness for seamless implementation. REFERENCES Dickmanns, E. (22). The deelopment of machine ision for road ehicles in the last decade. In IEEE Intelligent Vehicles Symposium, olume. IEEE. Falcone, P., Borrelli, F., Asgari, J., Tseng, H., and Hroat, D. (27). Predictie actie steering for autonomous ehicle systems. IEEE Trans. Control Syst. Technol., 5(3), Guldner, J., Sienel, W., Tan, H., Ackermann, J., Patwardhan, S., and Bunte, T. (999). Robust automatic steering for look-down reference systems with front and rear sensors. IEEE Trans. Control Syst. Technol., 7(), 2. Hatipoglu, C., Özgüner, Ü., and Redmill, K. (23). Automated lane change ler design. IEEE Trans. Intelligent Transportation Systems, 4(), Hedrick, J., McMahon, D., Narendran, V., and Swaroop, D. (99). Longitudinal ehicle ler design for IVHS systems. In Amer. Contr. Conf., IEEE. Ioannou, P., Xu, Z., Eckert, S., Clemons, D., and Sieja, T. (993). Intelligent cruise : theory and experiment. In Conf. Decision Contr., IEEE. Kranc, G.M. (957). Input-output analysis of multirate feedback systems. IRE Trans. Automatic Control, Lee, S.H. and Chung, C.C. (23). Multileel approximate model predictie and its application to autonomous ehicle actie steering. In Conf. Decision Contr., Lee, S.H., Son, Y., and Chung, C. (submitted). Autonomous driing ehicle : A systems approach to deelopment and implementation. IEEE Trans. Control Syst. Technol. Li, S., Li, K., Rajamani, R., and Wang, J. (2). Model predictie multi-objectie ehicular adaptie cruise. IEEE Trans. Control Syst. Technol., (99),. Meyer, D.G. (992). Cost translation and a lifting approach to the multirate LQG problem. IEEE Trans. Autom. Control, 37, Möbus, R., Baotic, M., and Morari, M. (23). Multiobject adaptie cruise. Hybrid Systems: Computation and Control, Pacejka, H.B., Bakker, E., and Nyborg, L. (987). Tyre modelling for use in ehicle dynamics studies. SAE paper. Pham, H., Hedrick, K., and Tomizuka, M. (994). Combined lateral and longitudinal of ehicles for IVHS. In Amer. Contr. Conf., olume 2, IEEE, Baltimore, MD, USA. Rajamani, R. (26). Vehicle dynamics and. Springer. Rajamani, R., Tan, H., Law, B., and Zhang, W. (2). Demonstration of integrated longitudinal and lateral for the operation of automated ehicles in platoons. IEEE Trans. Control Syst. Technol., 8(4), Thrun, S., Burgard, W., and Fox, D. (26). Probabilistic Robotics. The MIT Press. 72