- Email: [email protected]
Development of Autonomous Platooning System for Heavy-duty Trucks
7th IFAC Symposium on Advances in Automotive Control The International Federation of Automatic Control September 4-7, 2013. Tokyo, Japan
Development of Autonomous Platooning System for Heavy-duty Trucks ? Toshiyuki Sugimachi ∗ Takanori Fukao ∗∗ Yoshitada Suzuki ∗∗∗ Hiroki Kawashima ∗∗∗∗ ∗
Assistant Professor, Department of Mechanical Engineering, Kobe University (Tel: 078-803-6115; e-mail: sugimachi@ tiger.kobe-u.ac.jp) ∗∗ Associate Professor, Department of Mechanical Engineering, Kobe University (e-mail: [email protected]) ∗∗∗ Researcher, Japan Automobile Research Institute, (e-mail: [email protected]) ∗∗∗∗ Researcher, Japan Automobile Research Institute, (e-mail: [email protected]) Abstract: In Japan, the New Energy and Industrial Technology Development Organization established the gEnergy ITS projecth in 2008 for reducing CO2 emissions. This project aims to develop techniques for autonomous platooning of heavy-duty trucks and reduce their air resistance in expressway driving. In platooning, the inter-truck distance should remain small and constant. This study proposes a novel control method for platooning of heavy-duty trucks. The proposed method uses information acquired from the front and rear trucks by inter-vehicle communication. String stability is guaranteed on the basis of the Lyapunov stability theory. The experimental results of autonomous platooning are provided to ascertain the effectiveness of the proposed method. Keywords: Autonomous control, Autonomous vehicles, Space vehicles, Velocity control, Lyapunov stability 1. INTRODUCTION
Longitudinal control of a platoon of vehicles is divided into two types of control frameworks on the basis of the target distance between two vehicles [11]: (a) maintaining a constant inter-truck distance [12] [13], and (b) maintaining a constant-time headway [14]. In the second control method, the distance is controlled on the basis of velocity. The target distance is represented by sv + h, where v is velocity, and s and h are constant.
Energy consumption and CO2 emissions are worldwide issues. In a report [1] of the Japanese Ministry of Economy, Trade and Industry, the realization of a low-carbon society using intelligent transport systems (ITS) is advocated. Approximately 20% of CO2 emissions in Japan are from the transportation industry, and exhaust from vehicles constitutes approximately 90% of these emissions. The New Energy and Industrial Technology Development Organization established the gEnergy ITS projecth in 2008. This project involves the development of an autonomous platooning system for heavy-duty trucks to reduce CO2 emissions and considers an expected increase in traffic volume [2]. This project is based on the concept that an autonomous platooning system does not essentially depend on road infrastructure. Platooning can improve the driving efficiency and reduce CO2 emissions [3]. As the air resistance of trucks is decreased by maintaining a small and constant inter-truck distance, the energy consumption efficiency increases. Many studies have been conducted on autonomous driving and platooning [4] [5] [6]. Although most methods require specialized road infrastructure, techniques developed in recent years have used the existing infrastructure in Japan, Europe, [7] [8] and the United States [9].
In longitudinal control, the inter-truck distance is adjusted to the target distance, and the platoon is stabilized [9]. Concretely, longitudinal control prevents the propagation and amplification of the spacing error between subsequent vehicles. This concept is called string stability. If the string stability is poor, even a minor error that occurs near the head of a platoon can be propagated and amplified. The subsequent vehicles would require to stop in order to ensure safety [15]. To maintain a constant inter-truck distance, the subsequent vehicles require information on velocity, acceleration, and other parameters of the leading vehicle to maintain string stability [16]. Inter-vehicle communication is required to acquire this information from the leading vehicle. To maintain a constant-time headway between subsequent vehicles, string stability can be established without obtaining information from the leading vehicle [11]. However, a high-gain controller is needed owing to a short time headway, and it is difficult to determine the optimal gain. When acceleration performance is poor (e.g., in a heavy-duty truck) a long inter-truck distance is
? This study was supported by New Energy and Industrial Technology Development Organization.
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needed. Therefore, increasing road capacity and reducing air resistance is difficult [17]. The above-described controller utilizes the distance from the front vehicle. This control method is referred as the F model in this study. Another existing study [18] proposed a method of longitudinal control using information from both front and rear vehicles. This control method is referred as the FR model in this study. In [18], the subsequent vehicles (i.e., all vehicles except the leading vehicle) in a platoon are controlled. The controller guarantees string stability without using preview information about the leading vehicle. The control performance is evaluated by simulation.
Fig. 1. Heavy-duty truck used in this study controlled vehicles and in their velocity are represented as follows:
In this study, the controller is designed assuming that all vehicles in the platoon are controlled. The proposed controller uses a common target velocity and information from both front and rear vehicles. In the present study, the inter-truck distance for longitudinal control is maintained at a small and constant value to improve fuel consumption. String stability is guaranteed on the basis of the Lyapunov stability theory. The effectiveness of the proposed method is experimentally evaluated. In this experiment, the platoon is composed of three trucks. The operation of acceleration is controlled, and the inter truck distance is maintained at 10 m.
v˙ i = −
1 Ki vi + ui , Ti Ti
(3)
w i = vi − vr ,
(4)
where xi is position, vi is velocity, d is desired constant spacing, vr is desired constant velocity, and Li is length of the vehicle. This longitudinal control model maintains a constant distance between the vehicles controlled in the platoon and prompts the velocity of each truck to follow the desired constant velocity, i. e., ei and wi converge to 0.
Each controlled object is a heavy-duty truck as shown in Fig. 1. The inputs to the truck are throttle position and pressure on the brake (the pressure of the master cylinder). The output is position of the truck. The truck is modeled as follows: x˙ i = vi ,
ei = xi − xi+1 − d − Li ,
2.1 Controller of the F model In this study, the F model is compared with the FR model by simulation. The controller of the F model is described by the following equations. The controller of the lead vehicle is represented by The controller of the lead vehicle is represented by µ ¶ Ti 1 u1 = vi + v˙ r − c0 w1 , (5) Ki Ti
(1) (2)
where xi is position, vi is velocity, and ui is input to the truck, Ki is gain in acceleration or braking, and Ti is time constant. The subscript i, 1 ≤ i ≤ n, represents the number of vehicles. i = 1 represents the leading vehicle and i = n the last vehicle.
and the controllers of the interior vehicles and the last vehicle are represented by µ ¶ Ti 1 vi + v˙ r − c0 wi + k1 ei−1 + c1 (vi−1 − vi ) , (6) ui = Ki Ti
Though Ki and Ti vary with velocity or gear ratio, we assume these variables to be constant. If ui ≥ 0, ui is throttle position, Ti is Tai , and Ki is Kai . The input is 100ui (%). If ui < 0, ui is pressure on the brake, Ti is Tbi , and Ki is Kbi . The input in the case is |ui | (MPa). This model is represented by simple expressions. A more detailed model that considers mechanical resistance and air resistance can be considered. However, for a detailed model, the control law is complex and number of parameters to be identified increases. If an appropriate identification cannot be performed, the performance of the controller may decline when compared to the simple model. Therefore, in this study, we use the simple model as shown in (1) and (2), to decrease the number of parameters to be identified and enable concise expression of the controller.
where c0 , c1 , and k1 are positive constants (c0 = c1 ). 2.2 Controller of the FR model The controller of leading vehicle in the FR model is represented by µ ¶ Ti 1 u1 = vi + v˙ r − c0 w1 − k1 ei − c1 (v1 − v2 ) , (7) Ki Ti that of the interior vehicles is represented by µ Ti 1 ui = vi + v˙ r − c0 wi + k1 ei−1 − k2 ei Ki T i ¶ +c1 (vi−1 − vi ) − c1 (vi − vi+1 ) ,
2. LONGITUDINAL CONTROL
(8)
and that of the last vehicle is represented by µ ¶ Ti 1 un = vi + v˙ r − c0 wn + k1 en−1 + c1 (vn−1 − vn ) ,(9) Ki Ti
This section presents the purpose of longitudinal control and controller design. Errors in the distance between the 53
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
Fig. 2. Platoon where c0 , c1 , k1 , and k2 are positive constants (c0 = c1 and k1 = k2 ). Proof of the model’s stability is given in Appendix A.
platoon, is propagated and amplified, as shown in Fig. 3. The maximum value of the backward error of each vehicle is larger than that of the forward error. The platoon is unstable in the F model.
3. STRING STABILITY
On the other hand, in the FR model,|ei | is not propagatedand amplified, as shown in Fig. 4. The maximum value of the backward error is less than that of the forward error. The platoon is stable in the FR model. Therefore, we confirm that the optimal range of gain of the FR model is larger than that of the F model.
String stability is required to prevent propagation and amplification of any spacing error. The maximum gain of a controller is often limited for string stability [16]. The configurable gain of the FR model is compared with that of the F model. 3.1 Condition for string stability The Laplace transform of an error represented by (3) is defined as Ei . The transfer function between successive spacing, errors is represented by Ei+1 (s) Gi (s) = (1 ≤ i ≤ n − 2). (10) Ei (s) In the F model, Gi (s) is represented by c1 s + k1 Gi (s) = 2 . s + (c0 + c1 )s + k1
(11)
In the FR model, Gi (s)(1 ≤ i ≤ n − 3) is represented by c1 s + k1 Gn−2 Gn−2 = 2 , Gi (s) = .(12) s + (c0 + 2c1 )s + 2k1 1 − Gn−2 Gi+1 The condition for string stability is represented by Z∞ |gi (t)| dt ≤ 1 (i = 1, . . . , n − 2),
Fig. 3. Spacing errors of the F model (13)
0
where gi (t) is the inverse Laplace transform of Gi (s). 3.2 Comparison of configurable gain A platoon consisting of 32 ideal vehicles that constitutes a first-order lag system is considered. The configurable gain of the FR model is compared with that of the F model by simulation. The gains of the F and FR models are set to the same values: c0 = 0.41, c1 = 0.41, k1 = 0.33, and k2 = 0.33. A disturbance is added to generate a spacing error. The velocity of the leading vehicle of the platoon was varied at −5.9 m/s2 for 1 s. The result pertaining to the F model is shown in Fig. 3 and that pertaining to the FR model is shown in Fig. 4. the order of the vehicle is represented byi in Veh.i, where 1 ≤ i ≤ 32. ei after e4 each show two errors, and the legend is omitted. In the F model, |ei |, which occurs near the head of the
Fig. 4. Spacing errors of the FR model
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IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
4. EXPERIMENT In this experiment, a private expressway shown in Fig. 5 is used.
Fig. 5. Test course The operation of acceleration is controlled. The platoon is composed of three trucks as shown in Fig. 6. Fig. 7. System architecture 4.2 System parameters and variables The system parameters of a truck used in this study are shown in Table 1, and the control gains are shown in Table 2. Table 1. Parameters of a truck used in this study Parameter M [kg] Length [m] Width [m] Height [m]
Fig. 6. Autonomous platooning
Value 13045 11.87 2.48 2.5
Table 2. Control gains
The target velocity of trucks is controlled from 60 km/h to 80 km/h. The target distance is varied from 10 m to 15 m.
Acceleration Brake
T 50 9
K 50 16
c0 0.54 5.2
c1 0.25 0.18
c2 0.25 0.18
k1 0.13 0.13
k2 0.13 0.13
4.3 Experimental results 4.1 System architecture The results of longitudinal control are shown in Figs. 8, 9, and 10. In these experiments, all trucks are controlled by the FR model, and the target velocity and distance are varied. The target velocity is varied from 60 km/h to 80 km/h. The target distance is varied from 10 to 15 m. The error of the inter-truck distances was maintained at less than ± 0.2 m in a steady state. The error of the velocity of the controlled trucks was maintained at less than ± 0.3 m/s. When the target velocity and distance were varied, there was no instability in the platoon. We also confirmed that the platoon was controlled accurately during a lane change.
One of the experimental trucks and its system architecture are shown in Fig. 1 and Fig. 7, respectively. The truck has three tire axles. The second and third tire axles have double tires. The driving wheels are on the second axle. The truck has the following on-board sensors: a wheel speed sensor and yaw rate sensor. The truck’s velocity is obtained by the wheel speed sensor. The information from the sensors is processed and sent to a dSPACE Autobox. Autobox is a device that can provide codes for the Engine Control Unit (ECU). In addition, it can display the data from the sensors and tune the parameters in real time. In this study, a block diagram of the control model is made using MATLAB/Simulink, and it is compiled for Autobox. The control input is calculated from the information measured by the sensors. Autobox sends the control input to the engine ECU and Electronic Broking System (EBS) through Controller Area Network (CAN). The control cycle of the truck is 20 ms.
5. CONCLUSION In this study, we proposed a method of autonomous platooning that uses information acquired from the front and rear trucks by inter-vehicle communication. The effectiveness of the proposed method was experimentally 55
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
Fig. 10. Experimental results (Third truck) Fig. 8. Experimental results (First truck)
evaluated. The error of the inter-truck distances was maintained at less than ± 0.2 m, and the error of the velocity of the controlled trucks was maintained at less than ± 0.3 m/s. As a result, the proposed method has a precise performance required for autonomous platooning. REFERENCES [1] [2]
[3]
[4] [5]
[6]
[7]
Fig. 9. Experimental results (Second truck)
56
http://www.meti.go.jp/english/, 2009. Y. Suzuki, T. Hori, T. Kitazumi, K. Aoki, T. Fukao, and T. Sugimachi, ”Development of Automated Platooning System Based on Heavy Duty Trucks,” 17th ITS World Congress, TP058-1, 2010. D. Mitra and A. Mazumdar, ”Pollution control by reduction of drag on cars and buses through platooning,” International Journal of Environment and Pollution, pp. 90-96, 2007. S. Sheikholeslam and C. A. Desoer, ”Longitudinal control of a platoon of vehicles,” American Control Conference, pp. 291-296, 1980. S. E. Shladover, X. Yun, B. Song, S. Dickey, C. Nowakowski, A. Howell, F. Bu, D. Marco, H. Sue, and D. Nelson, ”Demonstration of automated heavyduty vehicles,” Institute of Transportation Studies University of California, Berkeley, 2005. Y. Zhang, B. Kosmatopoulos and P.Ioannou, ”Using front and back information for tight vehicle following maneuvers,” IEEE Transactions on Vehicular Technology, Vol. 48, No. 1, pp. 319-328, 1999. R. Hoeger, A. Amditis, M. Kunert, A. Hoess, F. Flemisch, H. P. Krueger, A. Bartels, A. Beutner, and K. Pagle, ”Highly automated vehicles for intelligent transport:HAVEit approach,” 15th World Congress on Intelligent Transport Systems and ITS America’s, 2008.
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
[8] C. Bergenhem, Q. Hung, A. Benmimoun, and T. Robinson, ”Challenges of platooning on public motorways,” 17th World Congress on Intelligent Transport Systems, 2010. [9] R. Kunze, R. Ramekers, K. Henning, and S. Jeschke, ”Organization and operation of electronically couples truck platoons on German motorways,” ICIRA Lecture Notes in Artificial Intelligence 5928, 2009. [10] C. Y. Liang and H. Peng, ”String stability analysis of adaptive cruise controlled vehicles,” JSME International Journal, 2000. [11] T. Kawabata, ”Automatic Driving Control for Intelligent Transportation Systems - Spacing Control and String Stability,” Transactions of the Japan Society of Mechanical Engineers, 104(989), pp. 228-231, 2001. [12] T. S. No and K. T. Chong, ”Longitudinal spacing control of vehicles in a platoon,” The Institute of Control, Automation and Systems Engineers, KOREA, Vol. 2, No. 2, pp. 92-97, 2000. [13] J. Zhang, Y. Suda, T. Iwasa, and H. Komine, ”Vector Liapunov Function Approach to Longitudinal Control of Vehicles in a Platoon,” JSME International Journal, Vol. 47, No. 2, pp. 653-658, 2004. [14] D. Yanakiev and I. Kanellakopoulos, ”Nonlinear spacing policies for automated heavy-duty vehicles,” IEEE VT, Vol. 47, pp. 1365-1377, 1998. [15] S. Kato and S. Tsugawa, ”An Examination of Longitudinal Control including Stop & Go for Influence of Traffic Flow,” TECHNICAL REPORT OF IEICE ITS 2002-30, pp. 7-12, 2002.. [16] D. Yanakiev and I. Kanellakopoulos, ”A Simplified Framework For String Stability Analysis In AHS,” Preprints of the 13th IFAC World Congress, San Francisco, 1996. [17] D. Swaroop, J. K. Hedrick, C. C. Chien, and P. A. Ioannou, ”A comparison of spacing and headway control laws for automatically controlled vehicles,” Vehicle System Dynamics, Volume 23, pp. 597-625, 1994. [18] Y. Zhang, E. B. Kosmatopoulos, and P. A. Ioannou, ”Autonomous Intelligent Cruise Control Using Front and Back Information for Tight Vehicle Following Maneuvers,” IEEE Transaction on Vehiclar Thchnology, Vol. 48, No. 1, pp. 319-328, 1999.
w˙ j = −c0 wj + k1 ej−1 − k1 ej + c1 (wj−1 − wj ) −c1 (wj − wj+1 ), 2 ≤ j ≤ n − 1, (A.4) w˙ n = −c0 wn − k1 wn en−1 + c1 (wn−1 − wn ). (A.5) From (A.3), (A.4), and (A.5), and en−1 sequentially converge to 0 sequentially because w˙ i and wi converge to 0. Therefore, the control objective is achieved.
Appendix A. PROOF FOR THE CONTROLLER OF THE FR MODEL The stability of the controller of the FR model is described below on the basis of the Lyapunov direct method. For a platoon that consists of n vehicles, a Lyapunov function candidate V is defined by n−1 n k1 X 2 1 X 2 V = ei + w . (A.1) 2 i=1 2 i=1 i The derivative of V is given by n n−1 X X V˙ = −c0 wi2 − c1 (vi − vi−1 )2 ≤ 0. i=1
(A.2)
i=1
Therefore, wi converges to 0 and di is bounded. From (2), (7), (8) and (9), w˙ i is represented as follows: w˙ 1 = −c0 w1 − k1 e1 − c1 (w1 − w2 ), (A.3) 57
Development of Autonomous Platooning System for Heavy-duty Trucks ? Toshiyuki Sugimachi ∗ Takanori Fukao ∗∗ Yoshitada Suzuki ∗∗∗ Hiroki Kawashima ∗∗∗∗ ∗
Assistant Professor, Department of Mechanical Engineering, Kobe University (Tel: 078-803-6115; e-mail: sugimachi@ tiger.kobe-u.ac.jp) ∗∗ Associate Professor, Department of Mechanical Engineering, Kobe University (e-mail: [email protected]) ∗∗∗ Researcher, Japan Automobile Research Institute, (e-mail: [email protected]) ∗∗∗∗ Researcher, Japan Automobile Research Institute, (e-mail: [email protected]) Abstract: In Japan, the New Energy and Industrial Technology Development Organization established the gEnergy ITS projecth in 2008 for reducing CO2 emissions. This project aims to develop techniques for autonomous platooning of heavy-duty trucks and reduce their air resistance in expressway driving. In platooning, the inter-truck distance should remain small and constant. This study proposes a novel control method for platooning of heavy-duty trucks. The proposed method uses information acquired from the front and rear trucks by inter-vehicle communication. String stability is guaranteed on the basis of the Lyapunov stability theory. The experimental results of autonomous platooning are provided to ascertain the effectiveness of the proposed method. Keywords: Autonomous control, Autonomous vehicles, Space vehicles, Velocity control, Lyapunov stability 1. INTRODUCTION
Longitudinal control of a platoon of vehicles is divided into two types of control frameworks on the basis of the target distance between two vehicles [11]: (a) maintaining a constant inter-truck distance [12] [13], and (b) maintaining a constant-time headway [14]. In the second control method, the distance is controlled on the basis of velocity. The target distance is represented by sv + h, where v is velocity, and s and h are constant.
Energy consumption and CO2 emissions are worldwide issues. In a report [1] of the Japanese Ministry of Economy, Trade and Industry, the realization of a low-carbon society using intelligent transport systems (ITS) is advocated. Approximately 20% of CO2 emissions in Japan are from the transportation industry, and exhaust from vehicles constitutes approximately 90% of these emissions. The New Energy and Industrial Technology Development Organization established the gEnergy ITS projecth in 2008. This project involves the development of an autonomous platooning system for heavy-duty trucks to reduce CO2 emissions and considers an expected increase in traffic volume [2]. This project is based on the concept that an autonomous platooning system does not essentially depend on road infrastructure. Platooning can improve the driving efficiency and reduce CO2 emissions [3]. As the air resistance of trucks is decreased by maintaining a small and constant inter-truck distance, the energy consumption efficiency increases. Many studies have been conducted on autonomous driving and platooning [4] [5] [6]. Although most methods require specialized road infrastructure, techniques developed in recent years have used the existing infrastructure in Japan, Europe, [7] [8] and the United States [9].
In longitudinal control, the inter-truck distance is adjusted to the target distance, and the platoon is stabilized [9]. Concretely, longitudinal control prevents the propagation and amplification of the spacing error between subsequent vehicles. This concept is called string stability. If the string stability is poor, even a minor error that occurs near the head of a platoon can be propagated and amplified. The subsequent vehicles would require to stop in order to ensure safety [15]. To maintain a constant inter-truck distance, the subsequent vehicles require information on velocity, acceleration, and other parameters of the leading vehicle to maintain string stability [16]. Inter-vehicle communication is required to acquire this information from the leading vehicle. To maintain a constant-time headway between subsequent vehicles, string stability can be established without obtaining information from the leading vehicle [11]. However, a high-gain controller is needed owing to a short time headway, and it is difficult to determine the optimal gain. When acceleration performance is poor (e.g., in a heavy-duty truck) a long inter-truck distance is
? This study was supported by New Energy and Industrial Technology Development Organization.
978-3-902823-48-9/2013 © IFAC
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10.3182/20130904-4-JP-2042.00127
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
needed. Therefore, increasing road capacity and reducing air resistance is difficult [17]. The above-described controller utilizes the distance from the front vehicle. This control method is referred as the F model in this study. Another existing study [18] proposed a method of longitudinal control using information from both front and rear vehicles. This control method is referred as the FR model in this study. In [18], the subsequent vehicles (i.e., all vehicles except the leading vehicle) in a platoon are controlled. The controller guarantees string stability without using preview information about the leading vehicle. The control performance is evaluated by simulation.
Fig. 1. Heavy-duty truck used in this study controlled vehicles and in their velocity are represented as follows:
In this study, the controller is designed assuming that all vehicles in the platoon are controlled. The proposed controller uses a common target velocity and information from both front and rear vehicles. In the present study, the inter-truck distance for longitudinal control is maintained at a small and constant value to improve fuel consumption. String stability is guaranteed on the basis of the Lyapunov stability theory. The effectiveness of the proposed method is experimentally evaluated. In this experiment, the platoon is composed of three trucks. The operation of acceleration is controlled, and the inter truck distance is maintained at 10 m.
v˙ i = −
1 Ki vi + ui , Ti Ti
(3)
w i = vi − vr ,
(4)
where xi is position, vi is velocity, d is desired constant spacing, vr is desired constant velocity, and Li is length of the vehicle. This longitudinal control model maintains a constant distance between the vehicles controlled in the platoon and prompts the velocity of each truck to follow the desired constant velocity, i. e., ei and wi converge to 0.
Each controlled object is a heavy-duty truck as shown in Fig. 1. The inputs to the truck are throttle position and pressure on the brake (the pressure of the master cylinder). The output is position of the truck. The truck is modeled as follows: x˙ i = vi ,
ei = xi − xi+1 − d − Li ,
2.1 Controller of the F model In this study, the F model is compared with the FR model by simulation. The controller of the F model is described by the following equations. The controller of the lead vehicle is represented by The controller of the lead vehicle is represented by µ ¶ Ti 1 u1 = vi + v˙ r − c0 w1 , (5) Ki Ti
(1) (2)
where xi is position, vi is velocity, and ui is input to the truck, Ki is gain in acceleration or braking, and Ti is time constant. The subscript i, 1 ≤ i ≤ n, represents the number of vehicles. i = 1 represents the leading vehicle and i = n the last vehicle.
and the controllers of the interior vehicles and the last vehicle are represented by µ ¶ Ti 1 vi + v˙ r − c0 wi + k1 ei−1 + c1 (vi−1 − vi ) , (6) ui = Ki Ti
Though Ki and Ti vary with velocity or gear ratio, we assume these variables to be constant. If ui ≥ 0, ui is throttle position, Ti is Tai , and Ki is Kai . The input is 100ui (%). If ui < 0, ui is pressure on the brake, Ti is Tbi , and Ki is Kbi . The input in the case is |ui | (MPa). This model is represented by simple expressions. A more detailed model that considers mechanical resistance and air resistance can be considered. However, for a detailed model, the control law is complex and number of parameters to be identified increases. If an appropriate identification cannot be performed, the performance of the controller may decline when compared to the simple model. Therefore, in this study, we use the simple model as shown in (1) and (2), to decrease the number of parameters to be identified and enable concise expression of the controller.
where c0 , c1 , and k1 are positive constants (c0 = c1 ). 2.2 Controller of the FR model The controller of leading vehicle in the FR model is represented by µ ¶ Ti 1 u1 = vi + v˙ r − c0 w1 − k1 ei − c1 (v1 − v2 ) , (7) Ki Ti that of the interior vehicles is represented by µ Ti 1 ui = vi + v˙ r − c0 wi + k1 ei−1 − k2 ei Ki T i ¶ +c1 (vi−1 − vi ) − c1 (vi − vi+1 ) ,
2. LONGITUDINAL CONTROL
(8)
and that of the last vehicle is represented by µ ¶ Ti 1 un = vi + v˙ r − c0 wn + k1 en−1 + c1 (vn−1 − vn ) ,(9) Ki Ti
This section presents the purpose of longitudinal control and controller design. Errors in the distance between the 53
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
Fig. 2. Platoon where c0 , c1 , k1 , and k2 are positive constants (c0 = c1 and k1 = k2 ). Proof of the model’s stability is given in Appendix A.
platoon, is propagated and amplified, as shown in Fig. 3. The maximum value of the backward error of each vehicle is larger than that of the forward error. The platoon is unstable in the F model.
3. STRING STABILITY
On the other hand, in the FR model,|ei | is not propagatedand amplified, as shown in Fig. 4. The maximum value of the backward error is less than that of the forward error. The platoon is stable in the FR model. Therefore, we confirm that the optimal range of gain of the FR model is larger than that of the F model.
String stability is required to prevent propagation and amplification of any spacing error. The maximum gain of a controller is often limited for string stability [16]. The configurable gain of the FR model is compared with that of the F model. 3.1 Condition for string stability The Laplace transform of an error represented by (3) is defined as Ei . The transfer function between successive spacing, errors is represented by Ei+1 (s) Gi (s) = (1 ≤ i ≤ n − 2). (10) Ei (s) In the F model, Gi (s) is represented by c1 s + k1 Gi (s) = 2 . s + (c0 + c1 )s + k1
(11)
In the FR model, Gi (s)(1 ≤ i ≤ n − 3) is represented by c1 s + k1 Gn−2 Gn−2 = 2 , Gi (s) = .(12) s + (c0 + 2c1 )s + 2k1 1 − Gn−2 Gi+1 The condition for string stability is represented by Z∞ |gi (t)| dt ≤ 1 (i = 1, . . . , n − 2),
Fig. 3. Spacing errors of the F model (13)
0
where gi (t) is the inverse Laplace transform of Gi (s). 3.2 Comparison of configurable gain A platoon consisting of 32 ideal vehicles that constitutes a first-order lag system is considered. The configurable gain of the FR model is compared with that of the F model by simulation. The gains of the F and FR models are set to the same values: c0 = 0.41, c1 = 0.41, k1 = 0.33, and k2 = 0.33. A disturbance is added to generate a spacing error. The velocity of the leading vehicle of the platoon was varied at −5.9 m/s2 for 1 s. The result pertaining to the F model is shown in Fig. 3 and that pertaining to the FR model is shown in Fig. 4. the order of the vehicle is represented byi in Veh.i, where 1 ≤ i ≤ 32. ei after e4 each show two errors, and the legend is omitted. In the F model, |ei |, which occurs near the head of the
Fig. 4. Spacing errors of the FR model
54
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
4. EXPERIMENT In this experiment, a private expressway shown in Fig. 5 is used.
Fig. 5. Test course The operation of acceleration is controlled. The platoon is composed of three trucks as shown in Fig. 6. Fig. 7. System architecture 4.2 System parameters and variables The system parameters of a truck used in this study are shown in Table 1, and the control gains are shown in Table 2. Table 1. Parameters of a truck used in this study Parameter M [kg] Length [m] Width [m] Height [m]
Fig. 6. Autonomous platooning
Value 13045 11.87 2.48 2.5
Table 2. Control gains
The target velocity of trucks is controlled from 60 km/h to 80 km/h. The target distance is varied from 10 m to 15 m.
Acceleration Brake
T 50 9
K 50 16
c0 0.54 5.2
c1 0.25 0.18
c2 0.25 0.18
k1 0.13 0.13
k2 0.13 0.13
4.3 Experimental results 4.1 System architecture The results of longitudinal control are shown in Figs. 8, 9, and 10. In these experiments, all trucks are controlled by the FR model, and the target velocity and distance are varied. The target velocity is varied from 60 km/h to 80 km/h. The target distance is varied from 10 to 15 m. The error of the inter-truck distances was maintained at less than ± 0.2 m in a steady state. The error of the velocity of the controlled trucks was maintained at less than ± 0.3 m/s. When the target velocity and distance were varied, there was no instability in the platoon. We also confirmed that the platoon was controlled accurately during a lane change.
One of the experimental trucks and its system architecture are shown in Fig. 1 and Fig. 7, respectively. The truck has three tire axles. The second and third tire axles have double tires. The driving wheels are on the second axle. The truck has the following on-board sensors: a wheel speed sensor and yaw rate sensor. The truck’s velocity is obtained by the wheel speed sensor. The information from the sensors is processed and sent to a dSPACE Autobox. Autobox is a device that can provide codes for the Engine Control Unit (ECU). In addition, it can display the data from the sensors and tune the parameters in real time. In this study, a block diagram of the control model is made using MATLAB/Simulink, and it is compiled for Autobox. The control input is calculated from the information measured by the sensors. Autobox sends the control input to the engine ECU and Electronic Broking System (EBS) through Controller Area Network (CAN). The control cycle of the truck is 20 ms.
5. CONCLUSION In this study, we proposed a method of autonomous platooning that uses information acquired from the front and rear trucks by inter-vehicle communication. The effectiveness of the proposed method was experimentally 55
IFAC AAC 2013 September 4-7, 2013. Tokyo, Japan
Fig. 10. Experimental results (Third truck) Fig. 8. Experimental results (First truck)
evaluated. The error of the inter-truck distances was maintained at less than ± 0.2 m, and the error of the velocity of the controlled trucks was maintained at less than ± 0.3 m/s. As a result, the proposed method has a precise performance required for autonomous platooning. REFERENCES [1] [2]
[3]
[4] [5]
[6]
[7]
Fig. 9. Experimental results (Second truck)
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http://www.meti.go.jp/english/, 2009. Y. Suzuki, T. Hori, T. Kitazumi, K. Aoki, T. Fukao, and T. Sugimachi, ”Development of Automated Platooning System Based on Heavy Duty Trucks,” 17th ITS World Congress, TP058-1, 2010. D. Mitra and A. Mazumdar, ”Pollution control by reduction of drag on cars and buses through platooning,” International Journal of Environment and Pollution, pp. 90-96, 2007. S. Sheikholeslam and C. A. Desoer, ”Longitudinal control of a platoon of vehicles,” American Control Conference, pp. 291-296, 1980. S. E. Shladover, X. Yun, B. Song, S. Dickey, C. Nowakowski, A. Howell, F. Bu, D. Marco, H. Sue, and D. Nelson, ”Demonstration of automated heavyduty vehicles,” Institute of Transportation Studies University of California, Berkeley, 2005. Y. Zhang, B. Kosmatopoulos and P.Ioannou, ”Using front and back information for tight vehicle following maneuvers,” IEEE Transactions on Vehicular Technology, Vol. 48, No. 1, pp. 319-328, 1999. R. Hoeger, A. Amditis, M. Kunert, A. Hoess, F. Flemisch, H. P. Krueger, A. Bartels, A. Beutner, and K. Pagle, ”Highly automated vehicles for intelligent transport:HAVEit approach,” 15th World Congress on Intelligent Transport Systems and ITS America’s, 2008.
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[8] C. Bergenhem, Q. Hung, A. Benmimoun, and T. Robinson, ”Challenges of platooning on public motorways,” 17th World Congress on Intelligent Transport Systems, 2010. [9] R. Kunze, R. Ramekers, K. Henning, and S. Jeschke, ”Organization and operation of electronically couples truck platoons on German motorways,” ICIRA Lecture Notes in Artificial Intelligence 5928, 2009. [10] C. Y. Liang and H. Peng, ”String stability analysis of adaptive cruise controlled vehicles,” JSME International Journal, 2000. [11] T. Kawabata, ”Automatic Driving Control for Intelligent Transportation Systems - Spacing Control and String Stability,” Transactions of the Japan Society of Mechanical Engineers, 104(989), pp. 228-231, 2001. [12] T. S. No and K. T. Chong, ”Longitudinal spacing control of vehicles in a platoon,” The Institute of Control, Automation and Systems Engineers, KOREA, Vol. 2, No. 2, pp. 92-97, 2000. [13] J. Zhang, Y. Suda, T. Iwasa, and H. Komine, ”Vector Liapunov Function Approach to Longitudinal Control of Vehicles in a Platoon,” JSME International Journal, Vol. 47, No. 2, pp. 653-658, 2004. [14] D. Yanakiev and I. Kanellakopoulos, ”Nonlinear spacing policies for automated heavy-duty vehicles,” IEEE VT, Vol. 47, pp. 1365-1377, 1998. [15] S. Kato and S. Tsugawa, ”An Examination of Longitudinal Control including Stop & Go for Influence of Traffic Flow,” TECHNICAL REPORT OF IEICE ITS 2002-30, pp. 7-12, 2002.. [16] D. Yanakiev and I. Kanellakopoulos, ”A Simplified Framework For String Stability Analysis In AHS,” Preprints of the 13th IFAC World Congress, San Francisco, 1996. [17] D. Swaroop, J. K. Hedrick, C. C. Chien, and P. A. Ioannou, ”A comparison of spacing and headway control laws for automatically controlled vehicles,” Vehicle System Dynamics, Volume 23, pp. 597-625, 1994. [18] Y. Zhang, E. B. Kosmatopoulos, and P. A. Ioannou, ”Autonomous Intelligent Cruise Control Using Front and Back Information for Tight Vehicle Following Maneuvers,” IEEE Transaction on Vehiclar Thchnology, Vol. 48, No. 1, pp. 319-328, 1999.
w˙ j = −c0 wj + k1 ej−1 − k1 ej + c1 (wj−1 − wj ) −c1 (wj − wj+1 ), 2 ≤ j ≤ n − 1, (A.4) w˙ n = −c0 wn − k1 wn en−1 + c1 (wn−1 − wn ). (A.5) From (A.3), (A.4), and (A.5), and en−1 sequentially converge to 0 sequentially because w˙ i and wi converge to 0. Therefore, the control objective is achieved.
Appendix A. PROOF FOR THE CONTROLLER OF THE FR MODEL The stability of the controller of the FR model is described below on the basis of the Lyapunov direct method. For a platoon that consists of n vehicles, a Lyapunov function candidate V is defined by n−1 n k1 X 2 1 X 2 V = ei + w . (A.1) 2 i=1 2 i=1 i The derivative of V is given by n n−1 X X V˙ = −c0 wi2 − c1 (vi − vi−1 )2 ≤ 0. i=1
(A.2)
i=1
Therefore, wi converges to 0 and di is bounded. From (2), (7), (8) and (9), w˙ i is represented as follows: w˙ 1 = −c0 w1 − k1 e1 − c1 (w1 − w2 ), (A.3) 57