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An adaptive model predictive approach for automated vehicle control in fallback procedure based on virtual vehicle scheme

An adaptive model predictive approach for automated vehicle control in fallback procedure based... Purpose – Automated driving systems (ADSs) are being developed to avoid human error and improve driving safety. However, limited focus has been given to the fallback behavior of automated vehicles, which act as a fail-safe mechanism to deal with safety issues resulting from sensor failure. Therefore, this study aims to establish a fallback control approach aimed at driving an automated vehicle to a safe parking lane under perceptive sensor malfunction. Design/methodology/approach – Owing to an undetected area resulting from a front sensor malfunction, the proposed ADS first creates virtual vehicles to replace existing vehicles in the undetected area. Afterward, the virtual vehicles are assumed to perform the most hazardous driving behavior toward the host vehicle; an adaptive model predictive control algorithm is then presented to optimize the control task during the fallback procedure, avoiding potential collisions with surrounding vehicles. This fallback approach was tested in typical cases related to car-following and lane changes. Findings – It is confirmed that the host vehicle avoid collision with the surrounding vehicles during the fallback procedure, revealing that the proposed method is effective for the test scenarios. Originality/value – This study presents a model for the path-planning problem regarding an automated vehicle under perceptive sensor failure, and it proposes an original path-planning approach based on virtual vehicle scheme to improve the safety of an automated vehicle during a fallback procedure. This proposal gives a different view on the fallback safety problem from the normal strategy, in which the mode is switched to manual if a driver is available or the vehicle is instantly stopped. Keywords Model predictive control, Automated vehicles, Fallback, Sensor failure, Virtual vehicle scheme Paper type Research paper fallback procedure of an automated vehicle under front 1. Introduction sensor failure without human intervention. The development of automated driving technologies is Currently available automated vehicles require a receptive rapidly advancing. However, safety issues resulting from human driver to a takeover request. Therefore, work has been perceptive sensor failure are still crucial to automated conducted that explores the time and quality of driver driving safety (Harris, 2016). When perceptive sensor intervention after the ADS issues a takeover request to reduce failure occurs during the automated driving procedure, it is the risk during the shift from autopilot to manual driving mode necessary for human drivers or the automated driving (Braunagel et al., 2017; Zeeb et al., 2015). However, it is system (ADS) to perform fallback behavior, which is to difficult to guarantee that the driver will always be available to operate the automated vehicle as well as achieve a minimal take over the vehicle. Therefore, when an abrupt sensor failure risk condition (SAE On-Road Automated Vehicle Standards event occurs, an advanced ADS not only has the ability to Committee, 2016). For the ADS at Levels 1-3, the human driver is assumed to perform the fallback maneuver, while at Level 4 or 5, the ADS can execute fallback behavior without © Wei Xue, Rencheng Zheng, Bo Yang, Zheng Wang, Tsutomu Kaizuka and Kimihiko Nakano. Published in Journal of Intelligent and Connected human intervention. Therefore, this study focuses on the Vehicles. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to The current issue and full text archive of this journal is available on full attribution to the original publication and authors. The full terms of this Emerald Insight at: www.emeraldinsight.com/2399-9802.htm licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode This study was supported in part by the State Key Laboratory of Automotive Safety and Energy under Project No. KF1815. Journal of Intelligent and Connected Vehicles Received 8 June 2019 2/2 (2019) 67–77 Revised 24 September 2019 Emerald Publishing Limited [ISSN 2399-9802] [DOI 10.1108/JICV-06-2019-0007] Accepted 24 October 2019 67 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 instruct the driver to take over the vehicle but can also perform scheme was developed to assist the ADS to complete the the fallback task without human assistance. perception model of the driving environment. Based on the There has been research on safe fallback behavior performed completed perception model, predictions of the subsequent by ADS. Emzivat et al. (2017) proposed a fallback strategy variations in the surrounding driving environment as well as aimed at Level 4 ADS features designed to operate a vehicle on constraints on collision avoidance were made. Furthermore, a road, whose ability to monitor the environment has been a controller was developed from the adaptive MPC compromised. They considered a specific scenario where the algorithm. The present paper is an improved version of our visibility range of a driver is limited. Owing to the limited conference paper (Xue et al., 2018). We present an visibility range, a low-speed strategy was proved to be safer than improved method including real-time consideration as well an emergency stop. Svensson et al. (2018) proposed a trajectory as a numerical analysis on additional fallback scenarios. planning method to safely stop a vehicle on a road shoulder, in The rest of the paper is organized as follows. A fallback which the safe stop problem was formulated as an optimal problem for an automated vehicle is described in Section 2. control problem. However, their method lacks consideration of The vehicle model is presented in Section 3. Details of the moving obstacles; thus, it is not applicable to scenarios proposed vehicle control approach are introduced in Section 4. involving multiple vehicles. Little attention has been given to The numerical analysis on the test scenarios is shown in Section 5. safe control of an automated vehicle for the fallback procedure Finally, the conclusions drawn from the research are presented in a dynamic driving environment. in Section 6. Normally, a proper control algorithm for the fallback procedure is supposed to perform optimal vehicle control 2. Problem description tasks under multiple constraints on road boundaries, traffic As illustrated in Figure 1, the host vehicle is assumed to lose regulations, and collision avoidance. Research has shown its ability to collect environmental information ahead owing that model predictive control (MPC) could be applied to to front sensor malfunction while traveling in automated build a theoretical framework of the constrained vehicle driving mode. As a result, an undetected area appears in control problem (Mayne et al., 2000). MPC is designed to front of the host vehicle. The host vehicle fails to read road predict future responses based on a dynamic model of the signs or perceive obstacles in the undetected area. In control process, thereby anticipating future events and response, the ADS immediately terminates the current calculating optimal control actions. With the development driving task and executes the fallback maneuver. The of research on vehicle issues, MPC has exhibited great performance on vehicle control (Erlien et al., 2016; Falcone detection delay of the sensor failure is neglected in this study et al., 2007; Lima et al.,2017; Yang et al., 2018; Yoshida because algorithms to reduce the fault detection delay have et al., 2008), trajectory planning (Howard, 2009; Li et al., already been proposed, which can reduce the delay to a fairly 2014; Ji et al., 2017) and collision avoidance (Anderson low level for sensors with high sampling frequencies (Jeong et al., 2010; Liu et al., 2017). et al., 2015; Kim, 1994). Thecompletefallbackprocedure In this study, a vehicle control problem was modeled with comprises three phases under the problem setting: lane- regard to the fallback event of an automated vehicle under keeping, lane change and pulling over. First, in the lane- sensor failure. Moreover, adaptive MPC is applied to the keeping phase, the ADS adjusts the vehicle speed and keeps vehicle control in the fallback procedure. Normally, a vehicle thehostvehicle in theoriginallanewhile issuingatakeover control task requires explicit environmental information. request to the driver. Then, if no response is received, it may Nevertheless, the environmental information is usually be necessary for the vehicle to change to the emergency uncertain to the automated vehicle as a result of perceptive parking lane and slow to a minimum cruise velocity. Finally, sensor failure in the fallback procedure. To maintain operation the host vehicle must be pulled over to the road shoulder. In of the ADS, a prior prediction of the behavior of surrounding this study, it is assumed that the driver is unable to respond vehicles in the undetected area is necessary when perceptive to the takeover request. In addition, the pulling-over phase sensor failure occurs. Therefore, this study applied a virtual was not considered. Therefore, the problem focuses on the vehicle scheme (Kim et al.,2009) to perform predictions of lane-keeping and lane-changing phases in the fallback undetectable vehicles. The method has been applied in the procedure. longitudinal control of car-following (Kim, 2012; Liu et al., Theproblem is modeledonastraight road sectionofatwo- 2017) to smooth the vehicle motion control in lane-keeping lane, one-direction and left-hand expressway with a speed limit of scenarios. This study expands upon the implementation of the virtual vehicle scheme in dealing with abrupt sensor Figure 1 Illustration of the driving environment in a fallback event malfunction, using virtual vehicles to give a transitory prediction of the behavior of undetectable vehicles. The virtual vehicles fill the detection gap caused by sensor failure, thus, further enabling the ADS to predict the behavior of surrounding vehicles during the fallback process. Furthermore, in this study, the vehicle control problem was modeled from highway traffic, including manually driven vehicles and an automated vehicle with abrupt perceptive sensor failure. Considering an undetectable area resulting from perceptive sensor failure, the virtual vehicle 68 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 50-100 km/h. An emergency parking lane was the designated Y ¼ v cosu 1 u sinu (6) destination of the fallback procedure as soon as it was executed. The parking lane was marked in the embedded digital map of the where M is the total mass of the vehicle; u, v, and g denote the host vehicle in advance, and it was assumed to be unoccupied longitudinal velocity, lateral velocity, and yaw rate of the vehicle during the fallback procedure. The surrounding vehicles are at its center of gravity, respectively; F is the total longitudinal manually driven when sensor failure occurs and have no direct force on the tires; F and F represent the lateral forces on the Yf Yr communication with the host vehicle. Normally, it is considered front and rear tires, respectively; I is the yaw moment of that potential collisions only occur between vehicles. inertia; l and l represent the distances from the vehicle’s center f r Despite front sensor failure, the side and rear perceptive of gravity to the front and rear axles, respectively; X and Y sensors of the host vehicle are assumed to function well, denote the longitudinal position and lateral position of the guaranteeing the detection of road boundaries and rear center of gravity of the vehicle; and u is the heading angle with vehicles. The ADS can collect the real-time positions and respect to the X-axis. velocities of detected vehicles from the well-functioning According to the tire model proposed by Fiala (1954), the sensors. Meanwhile, the localization module, for example, lateral forces on tires are approximately described as follows: global positioning system, is assumed to be unaffected by the v1 l g sensor failure during the fallback procedure. Moreover, the F ¼ C d  (7) Yf f ADS is assumed to be equipped with high-precision digital map. Therefore, the host vehicle still retains the ability to v  l g perform lane-keeping and lane-changing behavior under sensor F ¼ C  (8) Yr r failure. where C and C represent the cornering stiffness values of front f r 3. Vehicle model and rear tires, respectively, and d is the front steering angle. This section presents a model of the host vehicle as a nonlinear The nonlinear vehicle model can be compactly defined from dynamic system, while a linear and discrete model is derived equations (1)- (8) as follows: from the nonlinear vehicle model for use of the MPC x _ ¼ Fx; u (9) optimization process. ðÞ c T T 3.1 Vehicle modeling where x ¼ Xu Y v ug and u ¼ F d c X As illustrated in Figure 2, the X-Y coordinates were fixed on the road and represent the longitudinal and transverse 3.2 Model linearization and discretization directions on the road, respectively. A 2-DOF bicycle model The nonlinear model, given in equation (9), can be linearized (Abe, 2015) was used to describe the vehicle dynamics, whose by a one-order Taylor series around the operating point (x , u ) s c,s dynamic equations were established as follows: as follows: MðÞ u _  vg ¼ F (1) x  x x _  Fx ; u 1 rFx ; u (10) ðÞ s c;s ðÞ s c;s M v _ 1 ug ¼ F 1 F (2) u  u ðÞ c c;s Yf Yr where r represents the gradient. I g _ ¼ l F  l F (3) z f Yf r Yr Rewriting equation (10) into state-space representation, we obtained the following continuous-time model: u ¼ g (4) x _ ¼ Ax x1 Bu 1Nx (11) ðÞ s c ðÞ s X ¼ u cosu  v sinu (5) where: 2 3 Figure 2 Illustration of vehicle model   1 0 000 0 @F @F M 4 5 Ax ¼ ; B ¼ ¼ ðÞ C l C f f f @x @u x c s u 000 0 c;s M I Nx ¼ Fx ; u Ax x  Bu : ðÞ ðÞ s ðÞ s c;s s s c;s By discretizing the continuous-time model over a sample time T , equation (11) was transformed into a discrete state-space representation as follows: x ¼ A x x 1 B x u 1 N x (12) ðÞ ðÞ ðÞ k1 1 d s k d s c;k d s Ax T Ax t ðÞ s s ðÞ s where A x ¼ e ; B x ¼ e Bdt and N x ¼ ðÞ ðÞ ðÞ d s d s d s AxðÞt e Nx dt. ðÞ s 69 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 4. Control algorithm Figure 4 Velocity prediction of the virtual vehicle This section presents the development of the adaptive model predictive controller for the fallback procedure. The virtual vehicle scheme was implemented to complete the perception model of the surrounding driving environment, introduced in Section 4.1. Predictions of the behavior of surrounding vehicles were developed for the construction of safe driving constraints, as in Section 4.2. The desired control outputs are defined in Section 4.3, including the desired longitudinal velocity and lateral trajectory in the fallback procedure. Finally, a model predictive controller was formulated as in Section 4.4. 4.1 Virtual vehicle scheme Front vehicles become undetectable to the host vehicle owing to front sensor malfunction. Therefore, the virtual vehicle scheme was implemented to give a prediction of the movement of the undetected front vehicles. As illustrated in Figure 3, when the ADS fails to detect front vehicles owing to sensor failure, the same number of virtual vehicles is created to replace each undetected vehicle. The virtual vehicle inherits the position and velocity from the history data of its corresponding undetected vehicle. To reduce the collision risk during the fallback procedure, the control algorithm should anticipate the most dangerous driving behavior that the undetected vehicles would take and further manage to avoid accidents under these conditions. Therefore, virtual vehicles are assumed to approach the host vehicle in hazardous ways. The prediction of the velocity of a virtual vehicle is illustrated in Figure 4. The virtual vehicle is vehicle before decelerating at maximum deceleration until it assumed to decelerate at a maximum deceleration until a stop if reaches a stop. The velocity profile is defined as follows: it is in the same lane as the host vehicle, which is the most dangerous manner to approach the host vehicle. The velocity v ðÞ t ; t < t  t f 0 0 d profile of a virtual vehicle, v ,isdefined as follows: v ðÞ t ¼ max v ðÞ t  aðÞ t  t ; 0 ; t > t f 0 m d d v ðÞ t ¼ max v t  a t  t ; 0 ; t > t (13) f ðÞ fðÞ 0 mðÞ 0 0 (14) where t denotes the time when sensor failure occurs and a is 0 m the maximum deceleration of the virtual vehicle. where t is the time delay assumed for the lane change. The If the virtual vehicle is in another lane, it is assumed to delay is considered for two reasons. First, a driver rarely maintain its initial speed and change to the lane of the host decelerates significantly while changing lane; second, vehicles in different lanes may not have enough longitudinal space, the delay gives the host vehicle time to make space for the sudden Figure 3 Explanations of virtual vehicle schemes cutting-in behavior of the virtual vehicle. Although a short-term traffic prediction method, for example, long short-term memory network (Zhao et al., 2017) may match the driving behavior of the front vehicle in most of the cases that method can hardly predict an abrupt dangerous behavior of the front vehicle. In this work, the most dangerous condition is taken into consideration, to make the host vehicle avoid all the potential collisions with undetectable vehicles. 4.2 Safe driving constraints The safe driving constraints were built upon the predictions of the surrounding vehicles. The constraints were considered up to a maximum prediction step, n . Here, n is named the p p prediction horizon. The prediction of the velocity of the front vehicle up to the prediction horizon was determined based on the velocity profile in equation (13) as follows: 70 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 v ^ ¼ vðÞ t ; i ¼ 1; ... ; n (15) f ;k1 i f k1 i p y ¼ uY ¼ Cx; "# (21) 01 00 00 where k denotes the current timestep and i is the prediction C ¼ step. The notation “^” represents that the marked variable is a 00 10 00 prediction. T y ¼ u Y ; (22) des des des The rear vehicle was assumed to keep following the host vehicle, while responding to the velocity variation of the host where y is the vector of the output variables; y is the vector of des vehicle after a short delay. Therefore, the prediction of the rear the desired outputs; and u and Y are the desired des des vehicle follows the car-following model proposed by Chandler longitudinal velocity and lateral position, respectively. et al. (1958), as shown below: The lane-keeping and lane-changing phases were considered. During the lane-keeping phase, the host vehicle v _ ¼ l u  v ; i ¼ 1; ... ; n (16) r;k1 iðÞ k1 in r;k1 in p p p decelerates along the active lane, waiting for a possible takeover from the driver. After this, the vehicle enters the lane-changing where v represents the velocity of the rear vehicle; v _ is the phase, changing to the emergency parking lane and slowing, prediction of the acceleration of the rear vehicle; and l is a ready to be pulled over to the road shoulder. constant parameter. The time to switch from the lane-keeping phase to the lane- The safe driving constraints were defined based on the time- changing phase is denoted as t . When t < t < t , the desired l 0 l to-collision (TTC) values between the host vehicle and outputs are defined as follows: surrounding vehicles as follows: TTC  T  i  T ; a 2fg f ; r ; a;k1 i safe s u ðÞ t ¼ maxðÞ utðÞ1 a ðÞ t  t ; v ; des 0 des 0 c;min (17) (23) i ¼ 1; .. . ; n ; p Y ðÞ t ¼ Yt des ðÞ 0 ^ ^ where u (t )and Y (t ) are the longitudinal velocity and the X  X  L 0 0 f ;k1 i k1 i f TTC ¼ (18) f ;k1 i lateral position of the host vehicle when sensor failure occurs, u ^  v ^ k1 i f ;k1 i respectively; v is the minimum cruising speed; and a is c,min des the desired acceleration. ^ ^ X  X  L k1 i r;k1 i r When t  t , the desired outputs in the lane-changing phase TTC ¼ (19) r;k1 i ^ ^ v  u are defined as follows: r;k1 i k1 i u ðÞ t ¼ max ut 1 a t  t ; v ; ðÞ ðÞ ðÞ des 0 ref 0 c;min where TTC ,for a [ {f, r}, denotes the TTC value between the host vehicle and the front vehicle or the rear vehicle; X PtðÞ; t  t < t 1 T l l lc Y ðÞ t ¼ ; and X are the longitudinal positions of the front vehicle’s r des L 1Yt ; t  t 1 T w ðÞ 0 l lc ^ ^ back and the rear vehicle’s front, respectively; X and X f r "# were derived from the predictions of the velocities of the 5 4 3 t  t t  t t  t l l l front and rear vehicles, respectively; L and L denote the f r PtðÞ ¼ L 6  15 1 10 1Yt ðÞ w 0 T T T lc lc lc distances from the center of gravity of the host vehicle to its front and back, respectively; and T represents the safe (24) safe TTC value. The safe driving constraints take effect until the host vehicle where Y was designed based on a quintic polynomial on time des completely leaves the active lane. Consequently, the safe P (t); L represents the lane width; and T is the desired time w lc driving constraints can be defined in a discrete representation cost of the lane change. The quintic polynomial is implemented during the prediction horizon interval as follows: to generate a smooth lateral position target, satisfying the position, lateral velocity and lateral acceleration constraints at E ^x  h1 D w ^ ; i ¼ 1; .. . ; n (20) i k1 i i k1 i p both ends of the lateral position trajectory. where hi T 4.4 Adaptive model predictive control ^ ^ h ¼ L L , w ^ ¼ X v ^ X v ^ ; f r f f r r The model predictive controller predicts the response of the "# vehicle up to a prediction horizon, and it optimizes a predefined 1 T  i  T 00 00 safe s E ¼ ; and i objective function with constrained control inputs and outputs 1 T 1 i  T 00 00 safe s up to that horizon based on the predicted values. For a nonlinear "# 1 T  i  T 00 safe s system, the adaptive MPC (Giselsson, 2010) and nonlinear D ¼ . MPC (Borrelli et al.,2005; Du et al.,2016) are two major 00 1 T 1 i  T safe s methods that resolve the nonlinear optimization problem. The 4.3 Determination of desired outputs adaptive MPC updates the embedded model with an It is assumed that the desired velocity and lane were approximate linear model in each optimization iteration, which predefinedinan optimizationproblem fortracking. has a lower computation cost than nonlinear MPC. Therefore, the longitudinal velocity and lateral position of A diagram of the adaptive MPC is illustrated in Figure 5. the host vehicle’s center of gravity are the outputs to be Based on the measured state, an approximate linear model tracked: was generated to update the embedded model in the 71 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Discretizing the desired outputs predefined in equations (22)- Figure 5 Diagram of adaptive MPC scheme (24), the vehicle control problem can be transformed into the following optimization problem: min ^y  y Q ^y  y ðÞðÞ k1 i des; k1 i k1 i ref ;k1 i i¼1 n 1 n 1 c c X X T T 2 1 u Ru 1 D u S D u 1 r « c;k1 i c;k1 i c;k1 i c;k1 i « i¼0 i¼0 (29a) s:t: E ^x  h1 D w ^ 1 «V (29b) i1 1 k1 i1 1 i1 1 k1 i1 1 y  ^y  y (29c) min max controller. By means of the embedded model, the MPC k1 i1 1 predicts future behaviors of the host vehicle. This prediction determines the future states within a specified prediction u  u  u (29d) c;min c;k1 i c;max horizon, and based on these future states, control inputs are optimized to force the constrained output variables to track Du  Du  Du (29e) c;min c;k1 i c;max the predefined references. The model update in each optimization iteration is based on «  0 (29f) the state variables of the vehicle as follows: x ¼ A x 1 B u 1 N (25) k1 1 d;k k d;k c;k d;k i ¼ 0; 1; ... ; n  1 (29g) where A = A (x ), B = B (x ), and N = N (x ). d,k d k d,k d k d,k d k where ^y ¼ C^x , which is the vector of the predictive output Using the model in equation (25),the MPCwas designed kþi kþi variables; Q, R and S represent the weight matrices on the outputs, to predict the future state variables during the prediction inputs, and input increments, respectively; and Du represents horizon interval, [1, n ], through the current state variables p c,k1i the discrete input increment. The constraint of equation (29b) is a and the control inputs. Note that the control inputs only soft constraint extended from equation (20),implyingthatthe change during the control horizon interval and remain constraint violation is allowed but that violation is penalized in the constant after that, that is, u ¼ u for n  i  n – c;k1 i c;k1 n 1 c p objective function. « is a slack variable to allow the constraint 1, in which n denotes the control horizon. The vectors of the violation, and r is the weight on the penalty for constraint predictive state variables x (k) and control inputs u (k)are p c « represented by: violation. The vector V is the band for constraint softening, which is used to adjust the strictness of each constraint. A larger band ðÞ ^ ^ ^ x k ¼ x x  x (26) p k1 1 k1 2 k1 n represents less penalty on the constraint violation, while a zero band does not allow any constraint violation. The constraint of ðÞ u u  u u k ¼ (27) c c;k c;k1 1 c;k1 n 1 equation (29c) was determined owing to the trafficregulations on The predictive state variables during the prediction horizon speed limits and road boundaries in specific scenarios. interval can be formulated as follows: The MPC optimization problem in equation (29) can be ðÞ ðÞ transformed into a quadratic programming problem. The x k ¼ W x 1 H u k 1 K N (28) p k k k c k d;k hi sequence of the optimal input can be obtained through a 2 p where W ¼ A A  A , k d;k d;k d;k quadratic programming solver as follows: ðÞ u u  u u k ¼ (30) c;k c;k1 1 c;k1 n 1 c c 2 3 B 0  0 d;k where u is transferred to the vehicle plant as the optimal 6 7 c;k 6 A B B  0 7 d;k d;k d;k control input at the current timestep. 6 7 6 7 . . . . 6 7 . . . . 6 7 . . . . 6 7 5. Case studies H ¼ ; and k 6 7 n 1 n 2 c c 6 A B A B  B 7 d;k d;k d;k d;k d;k 6 7 5.1 Test scenarios 6 7 6 . . . . 7 In this study, four test scenarios were defined to test the . . . . 6 7 . . . . 4 5 performance of the proposed approach. The test scenarios n 1 n 2 n n p p p c A B A B  A B represent only some of the many cases that could occur when d;k d;k d;k d;k d;k d;k 2 3 the automated vehicle encounters front sensor failure. Nevertheless, these scenarios can evaluate the performance of 6 7 6 7 d;k the proposed approach in avoiding rear-end collisions with 6 7 6 7 K ¼ k surrounding vehicles during the lane-keeping and lane- 6 7 6 7 changing phases in the fallback procedure. 4 5 n 1 In each scenario, the surrounding vehicles were modeled as d;k double integrators whose input is acceleration and outputs are 72 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 position and velocity. A virtual vehicle was created upon the The initial parameters of the test scenarios are listed in Table I, initial position and velocity of the front vehicle, and it was set to including the initial positions and velocities of the rear, host and behave in a hazardous way, as described in Section 4.1. The rear front vehicles as well as the deceleration of the host vehicle. The numerical results are obtained by a simulation vehicle in each scenario was set to maintain its original speed within the first 2.4 s, and decelerate to 50 km/h at a constant procedure conducted in a Simulink and CarSim environment. deceleration a . This driver reaction time was chosen according to The MPC controller is programmed with Simulink tools, and the study result that over 95 per cent of drivers take less than 2.4 s the plant of host vehicle is a Mercedes-Benz B-class hatchback to react with an unalert deceleration of the front vehicle (Taoka, model, whose parameters were extracted from CarSim 1989). The ADS adopted a fixed fallback strategy that the host database. The controller parameters are listed in Table II. vehicle keeps in the initial lane within the first 3 s waiting for the driver to take over and then moves to the emergency parking lane 5.2 Numerical analysis for a low-speed cruise. The analysis results of Scenario 1 are illustrated in Figure 7.The Scenarios 1 and 2 were developed from a car-following case, path of the host vehicle is illustrated in Figure 7(a).Inthis figure, as illustrated in Figure 6(a). In Scenario 1, there is a short car- the colored markers describe the positions of the host vehicle, following distance between the host vehicle and the rear rear vehicle and virtual front vehicle at four sample times. vehicle. The host vehicle should follow the desired longitudinal Different vehicles are represented by different shapes, and each velocity to decelerate during the lane-keeping phase, while the color represents a sample time. As it is shown, the host vehicle rear vehicle does not react sufficiently to the sudden maintains its position in the original lane within the first3sand deceleration of the host vehicle and decelerates slower than then changes to the parking lane after. The host vehicle maintains expected. Therefore, the host vehicle may need to decrease the a short distance with the rear vehicle until it leaves the lane at brake pedal force to avoid a collision with the rear vehicle. In 5.8 s. As illustrated in Figure 7(d), the host vehicle decelerates Scenario 2, there is a short car-following distance between the along the desired velocity at the beginning of the fallback host vehicle and the front vehicle. A virtual vehicle was created procedure but later maintains its speed for a short while to avoid a on the initial position of the front vehicle, and it was supposed close separation with the rear vehicle, until leaving the active lane. to decelerate at the maximum deceleration. The host vehicle As illustrated in Figure 7(e), before the host vehicle leaves the may need to follow a velocity profile lower than the desired active lane, the minimum TTC value with the rear vehicle is velocity profile before leaving the active lane. 2.74 s. Because the safe driving constraint is a soft constraint, the Scenarios 3 and 4 test the performances of the proposed constraint violation will not result in an infeasible solution to the method in an overtaken and overtake case, respectively, as illustrated in Figure 6(b). In Scenario 3, the host vehicle is overtaken by the front vehicle in the right lane. In Scenario Table I Test scenario parameters 4, the host vehicle overtakes the front vehicle in the right X (m) X (m) u (km/h) v (km/h) v (km/h) a (m/s ) lane at a velocity 20 km/h higher than that of the front f r f r r vehicle, just before executing a fallback behavior. The host Scenario 1 90 45 90 90 90 2.0 vehicle may need to avoid a potential collision brought by Scenario 2 50 60 90 90 90 2.5 the sudden cut-in behavior of the front vehicle. In both Scenario 3 20 60 90 70 90 2.5 scenarios, the host vehicle may need to keep a safe distance Scenario 4 5 70 90 95 90 2.5 with the rear vehicle, as well. Figure 6 Illustration of test scenarios Table II Parameters of the path-planning controller Symbol Value (unit) Symbol Value (unit) M 1230 (kg) I 1343.1 (kgm ) C 100800 (N) C 70800 (N) f r l 1.04 (m) l 1.56 (m) f r L 1.70 (m) L 2.26 (m) f r a 5 (m/s ) t 3 (s) m d 1 2 k 0.4 (s ) a 2.5 (m/s ) \ibie\ L 3.5 (m) t 3 (s) w l T 4 (s) v 18 (km/h) lc c,min T 4 (s) t 0 (s) safe 0 T 0.05 (s) r 10 s \ill\ n 40 n 5 p c Q diag (6, 100) R diag (7e7,10) S diag (4e7,8e5) V [10,10,0] T T y [0, 5] y [27.8, 4.25] min max T T u [6150, 0.2] u [6150, 0.2] c,min c,max T T Du [308, 0.02] Du [308, 0.02] c,min c,max 73 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Figure 7 Numerical analysis results of scenario 1 Figure 8 Numerical analysis results of scenario 2 quadratic programming problem. Therefore, the controller still lower velocity than its following vehicle in the first 3 s and then works even if the safe driving constraint is violated. decelerates to a full stop. Owing to the dangerous cut-in Scenario 2 describes a dense car-following case, whose behavior, the host vehicle sharply decelerates, as illustrated in numerical analysis results are illustrated in Figure 8. As can be Figure 9(d). The velocity of the host vehicle is mostly lower seen in Figure 8(a), the host vehicle starts the lane-changing than the desired velocity before the host vehicle leaves the active phase at 3 s and leaves the left lane completely at 7.45 s. lane, indicating that the host vehicle takes a hard brake to avoid Figure 8(d) illustrates the velocity profiles of the three vehicles the potential collision with the virtual vehicle. The host vehicle in this scenario. The host vehicle makes a sharp deceleration to leaves the lane at 7.9 s, and the TTC value between the host avoid a potential collision with the virtual front vehicle. Before vehicle and the front vehicle remains above 1.41 s. the host vehicle leaves the active lane, the TTC values with the In general, encounters of vehicles with a minimum TTC, of front and rear vehicle remain above 2.03 s, as illustrated in less than 1.5 s, are considered critical (Horst and Hogema, Figure 8(e). 1993). The numerical analysis shows that in the four test Scenario 3 is an overtaken case, whose numerical analysis scenarios, the proposed method avoid collisions with the results are illustrated in Figure 10. The host vehicle completely surrounding vehicles during fallback procedures. In Scenarios 1, leaves the middle lane until 7.55 s. From the velocity graph 2 and 3, the host vehicle maintains relative safe separations to the illustrated in Figure 10(d) and the TTC values illustrated in surrounding vehicles, with minimum TTCs larger than the Figure 10(e), it is implied that the fast front vehicle has little critical value. The TTC in Scenario 4 indicates that the host influence on the control of the host vehicle. When the host vehicle encounters a critical situation before leaving the active vehicle travels into the middle lane, the TTC value with the lane, as a result of the 3-second waiting time for driver response, front vehicle is higher than the safe TTC value in the safe which is too long in that situation. It is necessary to adjust the driving constraint, while the minimum TTC value with the rear fallback strategy according to different fallback situations, and vehicle is slightly lower than the safe TTC value. furthermore, the proposed approach can be applied to evaluate Scenario 4 was developed from an overtaking case. The fallback strategies during the fallback procedure. positions of the host vehicle and surrounding vehicles are The average calculation time of an optimization iteration was illustrated in Figure 9(a). In this figure, the virtual front vehicle 0.0131 s over all the test scenarios and therefore the control cuts into the left lane within the first 3 s, before braking to a stop problem can be solved in real time, because the sample time is after. As illustrated in Figure 9(d), the front vehicle maintains a 0.05 s. 74 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Figure 9 Numerical analysis results of scenario 3 Figure 10 Numerical analysis results of scenario 4 2003). Moreover, several traffic accident reports already showed that human drivers can easily make mistakes after 6. Conclusions taking over the vehicle under critical conditions (Favarò et al., This paper proposes an adaptive model predictive approach 2017). Therefore, it is still necessary for ADS to require a based on virtual vehicle scheme, to realize a fallback procedure performing capability of fallback behavior. Anyway, to ensure of an automated vehicle while encountering a front perceptive driving safety of automated vehicles, different fallback sensor failure during highway transportation. To design the strategies should be preserved in ADS for a variety of traffic fallback procedure, the automated vehicle is normally required conditions. to perform lane-keeping and lane-changing behaviors, until On the other hand, a hard brake to stop is commonly used as safely reaching a low cruise speed in the emergency parking the fallback strategy in low-speed scenarios or when the ego lane. Therefore, it was assumed that the undetectable vehicles vehicle encounters inevitable collision (Jain et al.,2019). In continually perform hazardous driving behaviors, which may high-speed traffic environment, an abrupt stop in an active lane oblige the host vehicle to actively avoid incoming collisions. probably results in rear-end collisions. Therefore, Emzivat et al. In the beginning, virtual vehicles can be established from the (2017) verified that a low-speed cruise strategy is safer than an history data to replace the surrounding vehicles in undetectable emergency stop, when the speed limit is up to 70 km/h. For the areas, then, an adaptive MPC controller is implemented to highway case that emergency parking areas are normally set up, optimize the velocity and steering control for the fallback an alternative solution may be necessary to drive the automated procedure. Furthermore, to reduce the computation cost vehicles to the emergency parking area. brought by the nonlinear vehicle model, the embedded model Thereby, the proposed method takes an emergency parking in MPC is updated by a linearized discrete vehicle model at area as the objective, while focuses on the steering and velocity each optimization iteration. In this manner, the MPC control during the fallback process. This study further indicates optimization process can be solved as a real-time quadratic that the proposed approach is effective for the driving safety of programming problem. automated vehicles, even only regarding the front perceptive As a common sense, it is considered to be a safe fallback sensors. Compared with the emergency stop strategy and the strategy that a human driver takes over the vehicle. However, low-speed cruise strategy, the strategy proposed in this study driving automation causes drowsiness, which may lead to a late can reduce the subsequent impact on highway traffic. take-over response from the driver (Thiffault and Bergeron, Additionally, it may be an interesting topic to evaluate the 75 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. 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(2008), “Lane Corresponding author change steering manoeuvre using model predictive control Wei Xue can be contacted at: xue-w@iis.u-tokyo.ac.jp For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Intelligent and Connected Vehicles Emerald Publishing

An adaptive model predictive approach for automated vehicle control in fallback procedure based on virtual vehicle scheme

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Emerald Publishing
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© Wei Xue, Rencheng Zheng, Bo Yang, Zheng Wang, Tsutomu Kaizuka and Kimihiko Nakano.
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2399-9802
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10.1108/jicv-06-2019-0007
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Abstract

Purpose – Automated driving systems (ADSs) are being developed to avoid human error and improve driving safety. However, limited focus has been given to the fallback behavior of automated vehicles, which act as a fail-safe mechanism to deal with safety issues resulting from sensor failure. Therefore, this study aims to establish a fallback control approach aimed at driving an automated vehicle to a safe parking lane under perceptive sensor malfunction. Design/methodology/approach – Owing to an undetected area resulting from a front sensor malfunction, the proposed ADS first creates virtual vehicles to replace existing vehicles in the undetected area. Afterward, the virtual vehicles are assumed to perform the most hazardous driving behavior toward the host vehicle; an adaptive model predictive control algorithm is then presented to optimize the control task during the fallback procedure, avoiding potential collisions with surrounding vehicles. This fallback approach was tested in typical cases related to car-following and lane changes. Findings – It is confirmed that the host vehicle avoid collision with the surrounding vehicles during the fallback procedure, revealing that the proposed method is effective for the test scenarios. Originality/value – This study presents a model for the path-planning problem regarding an automated vehicle under perceptive sensor failure, and it proposes an original path-planning approach based on virtual vehicle scheme to improve the safety of an automated vehicle during a fallback procedure. This proposal gives a different view on the fallback safety problem from the normal strategy, in which the mode is switched to manual if a driver is available or the vehicle is instantly stopped. Keywords Model predictive control, Automated vehicles, Fallback, Sensor failure, Virtual vehicle scheme Paper type Research paper fallback procedure of an automated vehicle under front 1. Introduction sensor failure without human intervention. The development of automated driving technologies is Currently available automated vehicles require a receptive rapidly advancing. However, safety issues resulting from human driver to a takeover request. Therefore, work has been perceptive sensor failure are still crucial to automated conducted that explores the time and quality of driver driving safety (Harris, 2016). When perceptive sensor intervention after the ADS issues a takeover request to reduce failure occurs during the automated driving procedure, it is the risk during the shift from autopilot to manual driving mode necessary for human drivers or the automated driving (Braunagel et al., 2017; Zeeb et al., 2015). However, it is system (ADS) to perform fallback behavior, which is to difficult to guarantee that the driver will always be available to operate the automated vehicle as well as achieve a minimal take over the vehicle. Therefore, when an abrupt sensor failure risk condition (SAE On-Road Automated Vehicle Standards event occurs, an advanced ADS not only has the ability to Committee, 2016). For the ADS at Levels 1-3, the human driver is assumed to perform the fallback maneuver, while at Level 4 or 5, the ADS can execute fallback behavior without © Wei Xue, Rencheng Zheng, Bo Yang, Zheng Wang, Tsutomu Kaizuka and Kimihiko Nakano. Published in Journal of Intelligent and Connected human intervention. Therefore, this study focuses on the Vehicles. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to The current issue and full text archive of this journal is available on full attribution to the original publication and authors. The full terms of this Emerald Insight at: www.emeraldinsight.com/2399-9802.htm licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode This study was supported in part by the State Key Laboratory of Automotive Safety and Energy under Project No. KF1815. Journal of Intelligent and Connected Vehicles Received 8 June 2019 2/2 (2019) 67–77 Revised 24 September 2019 Emerald Publishing Limited [ISSN 2399-9802] [DOI 10.1108/JICV-06-2019-0007] Accepted 24 October 2019 67 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 instruct the driver to take over the vehicle but can also perform scheme was developed to assist the ADS to complete the the fallback task without human assistance. perception model of the driving environment. Based on the There has been research on safe fallback behavior performed completed perception model, predictions of the subsequent by ADS. Emzivat et al. (2017) proposed a fallback strategy variations in the surrounding driving environment as well as aimed at Level 4 ADS features designed to operate a vehicle on constraints on collision avoidance were made. Furthermore, a road, whose ability to monitor the environment has been a controller was developed from the adaptive MPC compromised. They considered a specific scenario where the algorithm. The present paper is an improved version of our visibility range of a driver is limited. Owing to the limited conference paper (Xue et al., 2018). We present an visibility range, a low-speed strategy was proved to be safer than improved method including real-time consideration as well an emergency stop. Svensson et al. (2018) proposed a trajectory as a numerical analysis on additional fallback scenarios. planning method to safely stop a vehicle on a road shoulder, in The rest of the paper is organized as follows. A fallback which the safe stop problem was formulated as an optimal problem for an automated vehicle is described in Section 2. control problem. However, their method lacks consideration of The vehicle model is presented in Section 3. Details of the moving obstacles; thus, it is not applicable to scenarios proposed vehicle control approach are introduced in Section 4. involving multiple vehicles. Little attention has been given to The numerical analysis on the test scenarios is shown in Section 5. safe control of an automated vehicle for the fallback procedure Finally, the conclusions drawn from the research are presented in a dynamic driving environment. in Section 6. Normally, a proper control algorithm for the fallback procedure is supposed to perform optimal vehicle control 2. Problem description tasks under multiple constraints on road boundaries, traffic As illustrated in Figure 1, the host vehicle is assumed to lose regulations, and collision avoidance. Research has shown its ability to collect environmental information ahead owing that model predictive control (MPC) could be applied to to front sensor malfunction while traveling in automated build a theoretical framework of the constrained vehicle driving mode. As a result, an undetected area appears in control problem (Mayne et al., 2000). MPC is designed to front of the host vehicle. The host vehicle fails to read road predict future responses based on a dynamic model of the signs or perceive obstacles in the undetected area. In control process, thereby anticipating future events and response, the ADS immediately terminates the current calculating optimal control actions. With the development driving task and executes the fallback maneuver. The of research on vehicle issues, MPC has exhibited great performance on vehicle control (Erlien et al., 2016; Falcone detection delay of the sensor failure is neglected in this study et al., 2007; Lima et al.,2017; Yang et al., 2018; Yoshida because algorithms to reduce the fault detection delay have et al., 2008), trajectory planning (Howard, 2009; Li et al., already been proposed, which can reduce the delay to a fairly 2014; Ji et al., 2017) and collision avoidance (Anderson low level for sensors with high sampling frequencies (Jeong et al., 2010; Liu et al., 2017). et al., 2015; Kim, 1994). Thecompletefallbackprocedure In this study, a vehicle control problem was modeled with comprises three phases under the problem setting: lane- regard to the fallback event of an automated vehicle under keeping, lane change and pulling over. First, in the lane- sensor failure. Moreover, adaptive MPC is applied to the keeping phase, the ADS adjusts the vehicle speed and keeps vehicle control in the fallback procedure. Normally, a vehicle thehostvehicle in theoriginallanewhile issuingatakeover control task requires explicit environmental information. request to the driver. Then, if no response is received, it may Nevertheless, the environmental information is usually be necessary for the vehicle to change to the emergency uncertain to the automated vehicle as a result of perceptive parking lane and slow to a minimum cruise velocity. Finally, sensor failure in the fallback procedure. To maintain operation the host vehicle must be pulled over to the road shoulder. In of the ADS, a prior prediction of the behavior of surrounding this study, it is assumed that the driver is unable to respond vehicles in the undetected area is necessary when perceptive to the takeover request. In addition, the pulling-over phase sensor failure occurs. Therefore, this study applied a virtual was not considered. Therefore, the problem focuses on the vehicle scheme (Kim et al.,2009) to perform predictions of lane-keeping and lane-changing phases in the fallback undetectable vehicles. The method has been applied in the procedure. longitudinal control of car-following (Kim, 2012; Liu et al., Theproblem is modeledonastraight road sectionofatwo- 2017) to smooth the vehicle motion control in lane-keeping lane, one-direction and left-hand expressway with a speed limit of scenarios. This study expands upon the implementation of the virtual vehicle scheme in dealing with abrupt sensor Figure 1 Illustration of the driving environment in a fallback event malfunction, using virtual vehicles to give a transitory prediction of the behavior of undetectable vehicles. The virtual vehicles fill the detection gap caused by sensor failure, thus, further enabling the ADS to predict the behavior of surrounding vehicles during the fallback process. Furthermore, in this study, the vehicle control problem was modeled from highway traffic, including manually driven vehicles and an automated vehicle with abrupt perceptive sensor failure. Considering an undetectable area resulting from perceptive sensor failure, the virtual vehicle 68 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 50-100 km/h. An emergency parking lane was the designated Y ¼ v cosu 1 u sinu (6) destination of the fallback procedure as soon as it was executed. The parking lane was marked in the embedded digital map of the where M is the total mass of the vehicle; u, v, and g denote the host vehicle in advance, and it was assumed to be unoccupied longitudinal velocity, lateral velocity, and yaw rate of the vehicle during the fallback procedure. The surrounding vehicles are at its center of gravity, respectively; F is the total longitudinal manually driven when sensor failure occurs and have no direct force on the tires; F and F represent the lateral forces on the Yf Yr communication with the host vehicle. Normally, it is considered front and rear tires, respectively; I is the yaw moment of that potential collisions only occur between vehicles. inertia; l and l represent the distances from the vehicle’s center f r Despite front sensor failure, the side and rear perceptive of gravity to the front and rear axles, respectively; X and Y sensors of the host vehicle are assumed to function well, denote the longitudinal position and lateral position of the guaranteeing the detection of road boundaries and rear center of gravity of the vehicle; and u is the heading angle with vehicles. The ADS can collect the real-time positions and respect to the X-axis. velocities of detected vehicles from the well-functioning According to the tire model proposed by Fiala (1954), the sensors. Meanwhile, the localization module, for example, lateral forces on tires are approximately described as follows: global positioning system, is assumed to be unaffected by the v1 l g sensor failure during the fallback procedure. Moreover, the F ¼ C d  (7) Yf f ADS is assumed to be equipped with high-precision digital map. Therefore, the host vehicle still retains the ability to v  l g perform lane-keeping and lane-changing behavior under sensor F ¼ C  (8) Yr r failure. where C and C represent the cornering stiffness values of front f r 3. Vehicle model and rear tires, respectively, and d is the front steering angle. This section presents a model of the host vehicle as a nonlinear The nonlinear vehicle model can be compactly defined from dynamic system, while a linear and discrete model is derived equations (1)- (8) as follows: from the nonlinear vehicle model for use of the MPC x _ ¼ Fx; u (9) optimization process. ðÞ c T T 3.1 Vehicle modeling where x ¼ Xu Y v ug and u ¼ F d c X As illustrated in Figure 2, the X-Y coordinates were fixed on the road and represent the longitudinal and transverse 3.2 Model linearization and discretization directions on the road, respectively. A 2-DOF bicycle model The nonlinear model, given in equation (9), can be linearized (Abe, 2015) was used to describe the vehicle dynamics, whose by a one-order Taylor series around the operating point (x , u ) s c,s dynamic equations were established as follows: as follows: MðÞ u _  vg ¼ F (1) x  x x _  Fx ; u 1 rFx ; u (10) ðÞ s c;s ðÞ s c;s M v _ 1 ug ¼ F 1 F (2) u  u ðÞ c c;s Yf Yr where r represents the gradient. I g _ ¼ l F  l F (3) z f Yf r Yr Rewriting equation (10) into state-space representation, we obtained the following continuous-time model: u ¼ g (4) x _ ¼ Ax x1 Bu 1Nx (11) ðÞ s c ðÞ s X ¼ u cosu  v sinu (5) where: 2 3 Figure 2 Illustration of vehicle model   1 0 000 0 @F @F M 4 5 Ax ¼ ; B ¼ ¼ ðÞ C l C f f f @x @u x c s u 000 0 c;s M I Nx ¼ Fx ; u Ax x  Bu : ðÞ ðÞ s ðÞ s c;s s s c;s By discretizing the continuous-time model over a sample time T , equation (11) was transformed into a discrete state-space representation as follows: x ¼ A x x 1 B x u 1 N x (12) ðÞ ðÞ ðÞ k1 1 d s k d s c;k d s Ax T Ax t ðÞ s s ðÞ s where A x ¼ e ; B x ¼ e Bdt and N x ¼ ðÞ ðÞ ðÞ d s d s d s AxðÞt e Nx dt. ðÞ s 69 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 4. Control algorithm Figure 4 Velocity prediction of the virtual vehicle This section presents the development of the adaptive model predictive controller for the fallback procedure. The virtual vehicle scheme was implemented to complete the perception model of the surrounding driving environment, introduced in Section 4.1. Predictions of the behavior of surrounding vehicles were developed for the construction of safe driving constraints, as in Section 4.2. The desired control outputs are defined in Section 4.3, including the desired longitudinal velocity and lateral trajectory in the fallback procedure. Finally, a model predictive controller was formulated as in Section 4.4. 4.1 Virtual vehicle scheme Front vehicles become undetectable to the host vehicle owing to front sensor malfunction. Therefore, the virtual vehicle scheme was implemented to give a prediction of the movement of the undetected front vehicles. As illustrated in Figure 3, when the ADS fails to detect front vehicles owing to sensor failure, the same number of virtual vehicles is created to replace each undetected vehicle. The virtual vehicle inherits the position and velocity from the history data of its corresponding undetected vehicle. To reduce the collision risk during the fallback procedure, the control algorithm should anticipate the most dangerous driving behavior that the undetected vehicles would take and further manage to avoid accidents under these conditions. Therefore, virtual vehicles are assumed to approach the host vehicle in hazardous ways. The prediction of the velocity of a virtual vehicle is illustrated in Figure 4. The virtual vehicle is vehicle before decelerating at maximum deceleration until it assumed to decelerate at a maximum deceleration until a stop if reaches a stop. The velocity profile is defined as follows: it is in the same lane as the host vehicle, which is the most dangerous manner to approach the host vehicle. The velocity v ðÞ t ; t < t  t f 0 0 d profile of a virtual vehicle, v ,isdefined as follows: v ðÞ t ¼ max v ðÞ t  aðÞ t  t ; 0 ; t > t f 0 m d d v ðÞ t ¼ max v t  a t  t ; 0 ; t > t (13) f ðÞ fðÞ 0 mðÞ 0 0 (14) where t denotes the time when sensor failure occurs and a is 0 m the maximum deceleration of the virtual vehicle. where t is the time delay assumed for the lane change. The If the virtual vehicle is in another lane, it is assumed to delay is considered for two reasons. First, a driver rarely maintain its initial speed and change to the lane of the host decelerates significantly while changing lane; second, vehicles in different lanes may not have enough longitudinal space, the delay gives the host vehicle time to make space for the sudden Figure 3 Explanations of virtual vehicle schemes cutting-in behavior of the virtual vehicle. Although a short-term traffic prediction method, for example, long short-term memory network (Zhao et al., 2017) may match the driving behavior of the front vehicle in most of the cases that method can hardly predict an abrupt dangerous behavior of the front vehicle. In this work, the most dangerous condition is taken into consideration, to make the host vehicle avoid all the potential collisions with undetectable vehicles. 4.2 Safe driving constraints The safe driving constraints were built upon the predictions of the surrounding vehicles. The constraints were considered up to a maximum prediction step, n . Here, n is named the p p prediction horizon. The prediction of the velocity of the front vehicle up to the prediction horizon was determined based on the velocity profile in equation (13) as follows: 70 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 v ^ ¼ vðÞ t ; i ¼ 1; ... ; n (15) f ;k1 i f k1 i p y ¼ uY ¼ Cx; "# (21) 01 00 00 where k denotes the current timestep and i is the prediction C ¼ step. The notation “^” represents that the marked variable is a 00 10 00 prediction. T y ¼ u Y ; (22) des des des The rear vehicle was assumed to keep following the host vehicle, while responding to the velocity variation of the host where y is the vector of the output variables; y is the vector of des vehicle after a short delay. Therefore, the prediction of the rear the desired outputs; and u and Y are the desired des des vehicle follows the car-following model proposed by Chandler longitudinal velocity and lateral position, respectively. et al. (1958), as shown below: The lane-keeping and lane-changing phases were considered. During the lane-keeping phase, the host vehicle v _ ¼ l u  v ; i ¼ 1; ... ; n (16) r;k1 iðÞ k1 in r;k1 in p p p decelerates along the active lane, waiting for a possible takeover from the driver. After this, the vehicle enters the lane-changing where v represents the velocity of the rear vehicle; v _ is the phase, changing to the emergency parking lane and slowing, prediction of the acceleration of the rear vehicle; and l is a ready to be pulled over to the road shoulder. constant parameter. The time to switch from the lane-keeping phase to the lane- The safe driving constraints were defined based on the time- changing phase is denoted as t . When t < t < t , the desired l 0 l to-collision (TTC) values between the host vehicle and outputs are defined as follows: surrounding vehicles as follows: TTC  T  i  T ; a 2fg f ; r ; a;k1 i safe s u ðÞ t ¼ maxðÞ utðÞ1 a ðÞ t  t ; v ; des 0 des 0 c;min (17) (23) i ¼ 1; .. . ; n ; p Y ðÞ t ¼ Yt des ðÞ 0 ^ ^ where u (t )and Y (t ) are the longitudinal velocity and the X  X  L 0 0 f ;k1 i k1 i f TTC ¼ (18) f ;k1 i lateral position of the host vehicle when sensor failure occurs, u ^  v ^ k1 i f ;k1 i respectively; v is the minimum cruising speed; and a is c,min des the desired acceleration. ^ ^ X  X  L k1 i r;k1 i r When t  t , the desired outputs in the lane-changing phase TTC ¼ (19) r;k1 i ^ ^ v  u are defined as follows: r;k1 i k1 i u ðÞ t ¼ max ut 1 a t  t ; v ; ðÞ ðÞ ðÞ des 0 ref 0 c;min where TTC ,for a [ {f, r}, denotes the TTC value between the host vehicle and the front vehicle or the rear vehicle; X PtðÞ; t  t < t 1 T l l lc Y ðÞ t ¼ ; and X are the longitudinal positions of the front vehicle’s r des L 1Yt ; t  t 1 T w ðÞ 0 l lc ^ ^ back and the rear vehicle’s front, respectively; X and X f r "# were derived from the predictions of the velocities of the 5 4 3 t  t t  t t  t l l l front and rear vehicles, respectively; L and L denote the f r PtðÞ ¼ L 6  15 1 10 1Yt ðÞ w 0 T T T lc lc lc distances from the center of gravity of the host vehicle to its front and back, respectively; and T represents the safe (24) safe TTC value. The safe driving constraints take effect until the host vehicle where Y was designed based on a quintic polynomial on time des completely leaves the active lane. Consequently, the safe P (t); L represents the lane width; and T is the desired time w lc driving constraints can be defined in a discrete representation cost of the lane change. The quintic polynomial is implemented during the prediction horizon interval as follows: to generate a smooth lateral position target, satisfying the position, lateral velocity and lateral acceleration constraints at E ^x  h1 D w ^ ; i ¼ 1; .. . ; n (20) i k1 i i k1 i p both ends of the lateral position trajectory. where hi T 4.4 Adaptive model predictive control ^ ^ h ¼ L L , w ^ ¼ X v ^ X v ^ ; f r f f r r The model predictive controller predicts the response of the "# vehicle up to a prediction horizon, and it optimizes a predefined 1 T  i  T 00 00 safe s E ¼ ; and i objective function with constrained control inputs and outputs 1 T 1 i  T 00 00 safe s up to that horizon based on the predicted values. For a nonlinear "# 1 T  i  T 00 safe s system, the adaptive MPC (Giselsson, 2010) and nonlinear D ¼ . MPC (Borrelli et al.,2005; Du et al.,2016) are two major 00 1 T 1 i  T safe s methods that resolve the nonlinear optimization problem. The 4.3 Determination of desired outputs adaptive MPC updates the embedded model with an It is assumed that the desired velocity and lane were approximate linear model in each optimization iteration, which predefinedinan optimizationproblem fortracking. has a lower computation cost than nonlinear MPC. Therefore, the longitudinal velocity and lateral position of A diagram of the adaptive MPC is illustrated in Figure 5. the host vehicle’s center of gravity are the outputs to be Based on the measured state, an approximate linear model tracked: was generated to update the embedded model in the 71 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Discretizing the desired outputs predefined in equations (22)- Figure 5 Diagram of adaptive MPC scheme (24), the vehicle control problem can be transformed into the following optimization problem: min ^y  y Q ^y  y ðÞðÞ k1 i des; k1 i k1 i ref ;k1 i i¼1 n 1 n 1 c c X X T T 2 1 u Ru 1 D u S D u 1 r « c;k1 i c;k1 i c;k1 i c;k1 i « i¼0 i¼0 (29a) s:t: E ^x  h1 D w ^ 1 «V (29b) i1 1 k1 i1 1 i1 1 k1 i1 1 y  ^y  y (29c) min max controller. By means of the embedded model, the MPC k1 i1 1 predicts future behaviors of the host vehicle. This prediction determines the future states within a specified prediction u  u  u (29d) c;min c;k1 i c;max horizon, and based on these future states, control inputs are optimized to force the constrained output variables to track Du  Du  Du (29e) c;min c;k1 i c;max the predefined references. The model update in each optimization iteration is based on «  0 (29f) the state variables of the vehicle as follows: x ¼ A x 1 B u 1 N (25) k1 1 d;k k d;k c;k d;k i ¼ 0; 1; ... ; n  1 (29g) where A = A (x ), B = B (x ), and N = N (x ). d,k d k d,k d k d,k d k where ^y ¼ C^x , which is the vector of the predictive output Using the model in equation (25),the MPCwas designed kþi kþi variables; Q, R and S represent the weight matrices on the outputs, to predict the future state variables during the prediction inputs, and input increments, respectively; and Du represents horizon interval, [1, n ], through the current state variables p c,k1i the discrete input increment. The constraint of equation (29b) is a and the control inputs. Note that the control inputs only soft constraint extended from equation (20),implyingthatthe change during the control horizon interval and remain constraint violation is allowed but that violation is penalized in the constant after that, that is, u ¼ u for n  i  n – c;k1 i c;k1 n 1 c p objective function. « is a slack variable to allow the constraint 1, in which n denotes the control horizon. The vectors of the violation, and r is the weight on the penalty for constraint predictive state variables x (k) and control inputs u (k)are p c « represented by: violation. The vector V is the band for constraint softening, which is used to adjust the strictness of each constraint. A larger band ðÞ ^ ^ ^ x k ¼ x x  x (26) p k1 1 k1 2 k1 n represents less penalty on the constraint violation, while a zero band does not allow any constraint violation. The constraint of ðÞ u u  u u k ¼ (27) c c;k c;k1 1 c;k1 n 1 equation (29c) was determined owing to the trafficregulations on The predictive state variables during the prediction horizon speed limits and road boundaries in specific scenarios. interval can be formulated as follows: The MPC optimization problem in equation (29) can be ðÞ ðÞ transformed into a quadratic programming problem. The x k ¼ W x 1 H u k 1 K N (28) p k k k c k d;k hi sequence of the optimal input can be obtained through a 2 p where W ¼ A A  A , k d;k d;k d;k quadratic programming solver as follows: ðÞ u u  u u k ¼ (30) c;k c;k1 1 c;k1 n 1 c c 2 3 B 0  0 d;k where u is transferred to the vehicle plant as the optimal 6 7 c;k 6 A B B  0 7 d;k d;k d;k control input at the current timestep. 6 7 6 7 . . . . 6 7 . . . . 6 7 . . . . 6 7 5. Case studies H ¼ ; and k 6 7 n 1 n 2 c c 6 A B A B  B 7 d;k d;k d;k d;k d;k 6 7 5.1 Test scenarios 6 7 6 . . . . 7 In this study, four test scenarios were defined to test the . . . . 6 7 . . . . 4 5 performance of the proposed approach. The test scenarios n 1 n 2 n n p p p c A B A B  A B represent only some of the many cases that could occur when d;k d;k d;k d;k d;k d;k 2 3 the automated vehicle encounters front sensor failure. Nevertheless, these scenarios can evaluate the performance of 6 7 6 7 d;k the proposed approach in avoiding rear-end collisions with 6 7 6 7 K ¼ k surrounding vehicles during the lane-keeping and lane- 6 7 6 7 changing phases in the fallback procedure. 4 5 n 1 In each scenario, the surrounding vehicles were modeled as d;k double integrators whose input is acceleration and outputs are 72 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 position and velocity. A virtual vehicle was created upon the The initial parameters of the test scenarios are listed in Table I, initial position and velocity of the front vehicle, and it was set to including the initial positions and velocities of the rear, host and behave in a hazardous way, as described in Section 4.1. The rear front vehicles as well as the deceleration of the host vehicle. The numerical results are obtained by a simulation vehicle in each scenario was set to maintain its original speed within the first 2.4 s, and decelerate to 50 km/h at a constant procedure conducted in a Simulink and CarSim environment. deceleration a . This driver reaction time was chosen according to The MPC controller is programmed with Simulink tools, and the study result that over 95 per cent of drivers take less than 2.4 s the plant of host vehicle is a Mercedes-Benz B-class hatchback to react with an unalert deceleration of the front vehicle (Taoka, model, whose parameters were extracted from CarSim 1989). The ADS adopted a fixed fallback strategy that the host database. The controller parameters are listed in Table II. vehicle keeps in the initial lane within the first 3 s waiting for the driver to take over and then moves to the emergency parking lane 5.2 Numerical analysis for a low-speed cruise. The analysis results of Scenario 1 are illustrated in Figure 7.The Scenarios 1 and 2 were developed from a car-following case, path of the host vehicle is illustrated in Figure 7(a).Inthis figure, as illustrated in Figure 6(a). In Scenario 1, there is a short car- the colored markers describe the positions of the host vehicle, following distance between the host vehicle and the rear rear vehicle and virtual front vehicle at four sample times. vehicle. The host vehicle should follow the desired longitudinal Different vehicles are represented by different shapes, and each velocity to decelerate during the lane-keeping phase, while the color represents a sample time. As it is shown, the host vehicle rear vehicle does not react sufficiently to the sudden maintains its position in the original lane within the first3sand deceleration of the host vehicle and decelerates slower than then changes to the parking lane after. The host vehicle maintains expected. Therefore, the host vehicle may need to decrease the a short distance with the rear vehicle until it leaves the lane at brake pedal force to avoid a collision with the rear vehicle. In 5.8 s. As illustrated in Figure 7(d), the host vehicle decelerates Scenario 2, there is a short car-following distance between the along the desired velocity at the beginning of the fallback host vehicle and the front vehicle. A virtual vehicle was created procedure but later maintains its speed for a short while to avoid a on the initial position of the front vehicle, and it was supposed close separation with the rear vehicle, until leaving the active lane. to decelerate at the maximum deceleration. The host vehicle As illustrated in Figure 7(e), before the host vehicle leaves the may need to follow a velocity profile lower than the desired active lane, the minimum TTC value with the rear vehicle is velocity profile before leaving the active lane. 2.74 s. Because the safe driving constraint is a soft constraint, the Scenarios 3 and 4 test the performances of the proposed constraint violation will not result in an infeasible solution to the method in an overtaken and overtake case, respectively, as illustrated in Figure 6(b). In Scenario 3, the host vehicle is overtaken by the front vehicle in the right lane. In Scenario Table I Test scenario parameters 4, the host vehicle overtakes the front vehicle in the right X (m) X (m) u (km/h) v (km/h) v (km/h) a (m/s ) lane at a velocity 20 km/h higher than that of the front f r f r r vehicle, just before executing a fallback behavior. The host Scenario 1 90 45 90 90 90 2.0 vehicle may need to avoid a potential collision brought by Scenario 2 50 60 90 90 90 2.5 the sudden cut-in behavior of the front vehicle. In both Scenario 3 20 60 90 70 90 2.5 scenarios, the host vehicle may need to keep a safe distance Scenario 4 5 70 90 95 90 2.5 with the rear vehicle, as well. Figure 6 Illustration of test scenarios Table II Parameters of the path-planning controller Symbol Value (unit) Symbol Value (unit) M 1230 (kg) I 1343.1 (kgm ) C 100800 (N) C 70800 (N) f r l 1.04 (m) l 1.56 (m) f r L 1.70 (m) L 2.26 (m) f r a 5 (m/s ) t 3 (s) m d 1 2 k 0.4 (s ) a 2.5 (m/s ) \ibie\ L 3.5 (m) t 3 (s) w l T 4 (s) v 18 (km/h) lc c,min T 4 (s) t 0 (s) safe 0 T 0.05 (s) r 10 s \ill\ n 40 n 5 p c Q diag (6, 100) R diag (7e7,10) S diag (4e7,8e5) V [10,10,0] T T y [0, 5] y [27.8, 4.25] min max T T u [6150, 0.2] u [6150, 0.2] c,min c,max T T Du [308, 0.02] Du [308, 0.02] c,min c,max 73 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Figure 7 Numerical analysis results of scenario 1 Figure 8 Numerical analysis results of scenario 2 quadratic programming problem. Therefore, the controller still lower velocity than its following vehicle in the first 3 s and then works even if the safe driving constraint is violated. decelerates to a full stop. Owing to the dangerous cut-in Scenario 2 describes a dense car-following case, whose behavior, the host vehicle sharply decelerates, as illustrated in numerical analysis results are illustrated in Figure 8. As can be Figure 9(d). The velocity of the host vehicle is mostly lower seen in Figure 8(a), the host vehicle starts the lane-changing than the desired velocity before the host vehicle leaves the active phase at 3 s and leaves the left lane completely at 7.45 s. lane, indicating that the host vehicle takes a hard brake to avoid Figure 8(d) illustrates the velocity profiles of the three vehicles the potential collision with the virtual vehicle. The host vehicle in this scenario. The host vehicle makes a sharp deceleration to leaves the lane at 7.9 s, and the TTC value between the host avoid a potential collision with the virtual front vehicle. Before vehicle and the front vehicle remains above 1.41 s. the host vehicle leaves the active lane, the TTC values with the In general, encounters of vehicles with a minimum TTC, of front and rear vehicle remain above 2.03 s, as illustrated in less than 1.5 s, are considered critical (Horst and Hogema, Figure 8(e). 1993). The numerical analysis shows that in the four test Scenario 3 is an overtaken case, whose numerical analysis scenarios, the proposed method avoid collisions with the results are illustrated in Figure 10. The host vehicle completely surrounding vehicles during fallback procedures. In Scenarios 1, leaves the middle lane until 7.55 s. From the velocity graph 2 and 3, the host vehicle maintains relative safe separations to the illustrated in Figure 10(d) and the TTC values illustrated in surrounding vehicles, with minimum TTCs larger than the Figure 10(e), it is implied that the fast front vehicle has little critical value. The TTC in Scenario 4 indicates that the host influence on the control of the host vehicle. When the host vehicle encounters a critical situation before leaving the active vehicle travels into the middle lane, the TTC value with the lane, as a result of the 3-second waiting time for driver response, front vehicle is higher than the safe TTC value in the safe which is too long in that situation. It is necessary to adjust the driving constraint, while the minimum TTC value with the rear fallback strategy according to different fallback situations, and vehicle is slightly lower than the safe TTC value. furthermore, the proposed approach can be applied to evaluate Scenario 4 was developed from an overtaking case. The fallback strategies during the fallback procedure. positions of the host vehicle and surrounding vehicles are The average calculation time of an optimization iteration was illustrated in Figure 9(a). In this figure, the virtual front vehicle 0.0131 s over all the test scenarios and therefore the control cuts into the left lane within the first 3 s, before braking to a stop problem can be solved in real time, because the sample time is after. As illustrated in Figure 9(d), the front vehicle maintains a 0.05 s. 74 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. Volume 2 · Number 2 · 2019 · 67–77 Figure 9 Numerical analysis results of scenario 3 Figure 10 Numerical analysis results of scenario 4 2003). Moreover, several traffic accident reports already showed that human drivers can easily make mistakes after 6. Conclusions taking over the vehicle under critical conditions (Favarò et al., This paper proposes an adaptive model predictive approach 2017). Therefore, it is still necessary for ADS to require a based on virtual vehicle scheme, to realize a fallback procedure performing capability of fallback behavior. Anyway, to ensure of an automated vehicle while encountering a front perceptive driving safety of automated vehicles, different fallback sensor failure during highway transportation. To design the strategies should be preserved in ADS for a variety of traffic fallback procedure, the automated vehicle is normally required conditions. to perform lane-keeping and lane-changing behaviors, until On the other hand, a hard brake to stop is commonly used as safely reaching a low cruise speed in the emergency parking the fallback strategy in low-speed scenarios or when the ego lane. Therefore, it was assumed that the undetectable vehicles vehicle encounters inevitable collision (Jain et al.,2019). In continually perform hazardous driving behaviors, which may high-speed traffic environment, an abrupt stop in an active lane oblige the host vehicle to actively avoid incoming collisions. probably results in rear-end collisions. Therefore, Emzivat et al. In the beginning, virtual vehicles can be established from the (2017) verified that a low-speed cruise strategy is safer than an history data to replace the surrounding vehicles in undetectable emergency stop, when the speed limit is up to 70 km/h. For the areas, then, an adaptive MPC controller is implemented to highway case that emergency parking areas are normally set up, optimize the velocity and steering control for the fallback an alternative solution may be necessary to drive the automated procedure. Furthermore, to reduce the computation cost vehicles to the emergency parking area. brought by the nonlinear vehicle model, the embedded model Thereby, the proposed method takes an emergency parking in MPC is updated by a linearized discrete vehicle model at area as the objective, while focuses on the steering and velocity each optimization iteration. In this manner, the MPC control during the fallback process. This study further indicates optimization process can be solved as a real-time quadratic that the proposed approach is effective for the driving safety of programming problem. automated vehicles, even only regarding the front perceptive As a common sense, it is considered to be a safe fallback sensors. Compared with the emergency stop strategy and the strategy that a human driver takes over the vehicle. However, low-speed cruise strategy, the strategy proposed in this study driving automation causes drowsiness, which may lead to a late can reduce the subsequent impact on highway traffic. take-over response from the driver (Thiffault and Bergeron, Additionally, it may be an interesting topic to evaluate the 75 Adaptive model predictive approach Journal of Intelligent and Connected Vehicles Wei Xue et al. 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(2008), “Lane Corresponding author change steering manoeuvre using model predictive control Wei Xue can be contacted at: xue-w@iis.u-tokyo.ac.jp For instructions on how to order reprints of this article, please visit our website: www.emeraldgrouppublishing.com/licensing/reprints.htm Or contact us for further details: permissions@emeraldinsight.com

Journal

Journal of Intelligent and Connected Vehicles – Emerald Publishing

Published: Dec 17, 2019

Keywords: Model predictive control; Automated vehicles; Fallback; Sensor failure; Virtual vehicle scheme

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