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A simple yet efficient Path Tracking Controller for Autonomous Trucks⁎
10th IFAC Symposium on Intelligent Autonomous Vehicles 10th IFAC Symposium on Autonomous 10th IFACPoland, Symposium on Intelligent Intelligent Autonomous Vehicles Vehicles Gdansk, July 3-5, 2019 10th IFAC Symposium on Intelligent Autonomous Vehicles Gdansk, Available online at www.sciencedirect.com Gdansk, Poland, Poland, July July 3-5, 3-5, 2019 2019 Gdansk, July 3-5, 2019 10th IFACPoland, Symposium on Intelligent Autonomous Vehicles Gdansk, Poland, July 3-5, 2019
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IFAC PapersOnLine 52-8 (2019) 307–312
A simple yet efficient Path Tracking A simple yet efficient Path Tracking A simple yet efficient Path Tracking Controller for Autonomous Trucks A simple yet efficient Path Tracking Controller for Autonomous Trucks Controller for Autonomous Trucks ∗ Controller∗ for Autonomous Trucks ∗
Julius K. Julius K. Kolb Kolb ∗∗∗ Gunter Gunter Nitzsche Nitzsche ∗∗∗ Sebastian Sebastian Wagner Wagner ∗∗∗ Julius Julius K. K. Kolb Kolb Gunter Gunter Nitzsche Nitzsche Sebastian Sebastian Wagner Wagner ∗ ∗ Julius K. Kolb Gunter Nitzsche ∗ Sebastian Wagner ∗ Fraunhofer Institute for Transportation and Infrastructure ∗ ∗ Fraunhofer Institute for Transportation and Infrastructure for Transportation and Infrastructure ∗ Fraunhofer Institute Systems IVI, Dresden, Germany Fraunhofer Institute for Transportation and Infrastructure Systems IVI, Dresden, Germany ∗ Systems IVI, Dresden, Germany (e-mail: [email protected]). Fraunhofer Institute for Transportation and Infrastructure Systems IVI, Dresden, Germany (e-mail: [email protected]). [email protected]). (e-mail: Systems IVI, Dresden, Germany (e-mail: [email protected]). (e-mail: [email protected]). Abstract: This paper presents path tracking controller implemented for the Robot Operating Abstract: This This paper paper presents presents aa a path path tracking tracking controller controller implemented implemented for for the the Robot Robot Operating Operating Abstract: System (ROS). It is developed for the funded project AutoTruck in which a 18 t truck will be Abstract: This paper presents a path tracking controller implemented for the Robot Operating System (ROS). (ROS). It It is is developed developed for for the the funded funded project project AutoTruck AutoTruck in in which which aa 18 18 tt truck truck will will be be System automated for yard applications. The goal was to design a simple yet sufficient controller, which Abstract: This paper presents a path tracking controller implemented for the Robot Operating System (ROS). It is developed for the funded project AutoTruck in which a 18 t truck will be automated for yard applications. The goal was to design a simple yet sufficient controller, which automated for yard goal was to aa simple yet controller, which could also be on a standard in vehicle unit. Therefore, no advanced non linear System (ROS). It isapplications. developed forThe the funded project AutoTruck in sufficient which a 18 t truck be automated for used yard applications. The wascontrol to design design simple yet sufficient controller, which could also also be used on a standard standard in goal vehicle control unit. Therefore, no advanced advanced nonwill linear could be used on a in vehicle control unit. Therefore, no non linear controller was designed. The controller is a combination of a PID controller and a point follow automated for yard applications. The goal was to design a simple yet sufficient controller, which could also be used on a standard in vehicle control unit. Therefore, no advanced non linear controller was was designed. designed. The The controller controller is is aa combination combination of of a PID PID controller controller and and a point follow follow controller controller. Both controllers individually their drawbacks the application. However, could also was be used on aThe standard in vehicle control unit. advanced non linear controller designed. controller is have a combination of aaTherefore, PIDfor controller and aa point point follow controller. Both controllers individually have their drawbacks drawbacks for thenoapplication. application. However, controller. Both controllers individually have their for the However, the combination proves to provide a good tracking performance. The controllers are tested in controller was designed. The controller is a combination of a PID controller and a point follow controller. Both controllers individually have their drawbacks for the application. However, the combination combination proves proves to to provide provide aa good good tracking tracking performance. performance. The The controllers controllers are are tested tested in in the simulation and with 1:32 scale trucks in the test environment called DriveLab. controller. Both controllers individually have their drawbacks for the application. However, the combination proves to provide a good tracking performance. The controllers are tested in simulation and with 1:32 scale trucks in the test environment called DriveLab. simulation and 1:32 trucks in test called DriveLab. the combination proves provide a good performance. The controllers are tested in simulation and with with 1:32toscale scale trucks in the thetracking test environment environment called DriveLab. © 2019, IFAC (International Federation of in Automatic Control) Hosting by Elsevier Ltd. All rights reserved. simulation and with 1:32Vehicles, scale trucks the test environment called DriveLab. Keywords: Autonomous Closed Loop Control, ROS, PID control Keywords: Autonomous Autonomous Vehicles, Vehicles, Closed Closed Loop Loop Control, Control, ROS, ROS, PID PID control control Keywords: Keywords: Autonomous Vehicles, Closed Loop Control, ROS, PID control Keywords: Autonomous Vehicles, Closed Loop Control, ROS, driving PID control 1. INTRODUCTION autonomous of trucks on fenced areas like distri1. INTRODUCTION INTRODUCTION autonomous driving of trucks on fenced areas like distri1. autonomous driving of trucks on fenced areas like distribution centres. An overview is provided on the project 1. INTRODUCTION autonomous driving of trucks on fenced areas like distribution centres. centres. An overview overview is is provided provided on on the the project project 1 bution An 1. INTRODUCTION website also in a short video. autonomous driving of trucks on fenced areas like distribution centres. An overview is provided on the project Autonomous vehicles are a field of research for several 1 1 website also in a short video. Autonomous vehicles vehicles are are aa field field of of research research for for several several website aa short video. 1 also inAn Autonomous bution centres. overview is provided on the project website also in short video. decades now. In the recent years more and more appliAutonomous vehicles are a field of research for several idea decades now. now. In In the the recent recent years years more more and and more more appliappli- The 1 is, that the truck driver stops and leaves the truck decades The idea is, that truck driver stops and leaves the truck also in the a short video. cations are shown and the number of test drives on public Autonomous vehicles are a years field of research for several decades now. In the recent more and more appli- website The idea is, the truck stops leaves the truck when entering The truck is then cations are shown and the number of test drives on public The idea is, that thatthe thedistribution truck driver driver centre. stops and and leaves the truck cations are shown andrecent the number number of testet drives on public public when entering the distribution centre. The truck is then roads increases. According to van Vliet al. (2018) and decades now. In the years more and more applications are shown and the of test drives on when entering the distribution centre. The truck is then switched to automatic mode and registers itself wireless The idea is, that the truck driver stops and leaves the truck roads increases. According to van Vliet et al. (2018) and when entering the distribution centre. The truck is then roads increases. According to van Vliet et al. (2018) and switched to automatic mode and registers itself wireless Kusumakar et al. (2018) automated driving – including cations are shown and the number of test drives on public roads increases. According to van Vliet et al. (2018) and switched to automatic mode and registers itself wireless with the infrastructure of the distribution centre. Now an entering the distribution centre. The truck is then Kusumakar et et al. al. (2018) (2018) automated automated driving driving –– including including when switched to automatic mode and registers itself wireless Kusumakar with the infrastructure of the distribution centre. Now an truck platooning – is going to change on road logistics in roads increases. According to Vliet al. –(2018) and Kusumakar et al. driving including with the infrastructure of the distribution centre. Now an operator can select the truck in the management software to automatic mode and registers itself wireless truck platooning platooning – (2018) is going goingautomated to van change onetroad road logistics in switched with the infrastructure of the distribution centre. Now an truck – is to change on logistics in operator can select the truck in the management software the future. Therefore, many researchers from academics Kusumakar et al. (2018) automated driving – including truck platooning – is going to change on road logistics in operator can select the truck in the management software HelyOS (Highly Efficient Online Yard Operating System) with the infrastructure of the distribution centre. Now an the future. Therefore, many researchers from academics operator can select the truck in the management software the future. Therefore, many researchers from academics HelyOS (Highly Efficient Online Yard Operating System) and industry are different aspects of autruck platooning – investigating is going change on road logistics in HelyOS the future. Therefore, manytoresearchers from academics (Highly Efficient Online Yard Operating System) and can assign missions to the truck. Missions consist of operator can select the truck in the management software and industry are investigating different aspects of auHelyOS (Highly Efficient Online Yard Operating System) and industry are investigating investigating different aspects ofetauauand can assign missions to the truck. Missions consist of tonomous vehicles, starting perception, Kuhnt al. the future. Therefore, manyfrom researchers from academics and industry are different aspects of can assign missions to the truck. Missions consist of single tasks like ”drive to loading dock 42” or ”drive to HelyOS (Highly Efficient Online Yard Operating System) tonomous vehicles, starting from perception, Kuhnt et al. al. and and can assign missions to the truck. Missions consist of tonomous vehicles, starting from perception, Kuhnt et single tasks tasks like like ”drive ”drive to to loading loading dock dock 42” 42” or or ”drive ”drive to to (2016), over motion planning, Magdici and Althoff (2016), and industry are investigating different aspects of autonomous vehicles, starting from perception, Kuhnt et al. single charger”. Once the vehicle is ready to leave the distribution and can assign missions to the truck. Missions consist of (2016), over motion planning, Magdici and Althoff (2016), single tasks like ”drive to loading dock 42” or ”drive to (2016), over motion planning, Magdici and Althoff (2016), charger”. Once Once the the vehicle vehicle is is ready ready to to leave leave the the distribution distribution to the control of autonomous vehicles, Nilsson et al. (2015). tonomous vehicles, starting from perception, Kuhnt et al. charger”. (2016), over motion planning, Magdici and Althoff (2016), centre, it drives to the hand over point, checks out of the single tasks like ”drive to loading dock 42” or ”drive to to the control of autonomous vehicles, Nilsson et al. (2015). charger”. Once the vehicle is ready to leave the distribution to the the control control of autonomous autonomous vehicles, Nilsson et al. al. (2015). (2015). it drives to the hand over point, checks out of the (2016), over motion planning,vehicles, MagdiciNilsson and Althoff (2016), centre, to of et centre, it drives to the over checks out of the infrastructure, off mode taken charger”. the isautonomous ready to leave the and distribution centre, it Once drivesswitches to vehicle the hand hand over point, point, checks outis of the Nevertheless, the authors think, that it is still a long way infrastructure, switches off autonomous mode and is taken Nevertheless, the authors think, that it is still a long way to the control of autonomous vehicles, Nilsson et al. (2015). infrastructure, switches off autonomous mode and is taken Nevertheless, the authors think, that it is still a long way over by the driver. centre, it drives to the hand over point, checks out of the infrastructure, switches off autonomous mode and is taken until we see serial autonomous vehicles on public roads. Nevertheless, the authors think, that it is still a long way over by by the the driver. driver. until we we see see serial serial autonomous autonomous vehicles vehicles on on public public roads. roads. over until infrastructure, switches off autonomous mode and is taken over by the driver. The main reason legislative technical chalNevertheless, the are authors think,hurdles that itand ison still a long way The paths between the different stops of a mission are until we see serial autonomous vehicles public roads. The main main reason are legislative hurdles and technical chalThe reason are legislative hurdles and technical chalThe paths different stops of a mission are over by the between driver. the lenges to ensure the functional safety of such vehicles in all until we see serial autonomous vehicles on public roads. The main reason are legislative hurdles and technical chalThe paths between the different stops of are with aa path planner, which is based on Beyerslenges to to ensure ensure the the functional functional safety safety of of such such vehicles vehicles in in all all planned The paths between the different stops of aa mission mission are lenges planned with path planner, which is based on Beyersdriving situations over the whole vehicle lifetime. The most The main reason are legislative hurdles and technical challenges to ensure the functional safety of such vehicles in all planned with a path planner, which is based on Beyersdorfer and Wagner (2013). These paths avoid stationary The paths between the different stops of a mission are driving situations over the whole vehicle lifetime. The most planned with a path planner, which is based on Beyersdriving situations over the whole vehicle lifetime. The most dorfer and Wagner (2013). These paths avoid stationary likely next commercial step towards autonomous driving lenges tosituations ensure the functional safety of such vehicles in all dorfer driving over the whole vehicle lifetime. The most and Wagner (2013). These paths avoid stationary objects geometrically. The paths are enhanced to trajectoplanned with a path planner, which is based on Beyerslikely next commercial step towards autonomous driving dorfer and Wagner (2013). These paths avoid stationary likely next commercial step towards autonomous driving geometrically. The paths are enhanced to trajectowill be an increased use of such vehicles in controlled driving situations over the whole vehicle lifetime. The most objects likely step autonomous driving objects geometrically. The are enhanced to trajectories by prescribing profile, which avoids collisions dorfer and Wagneraa velocity (2013). These avoid will be benext an commercial increased use oftowards such vehicles in controlled controlled objects geometrically. The paths paths arepaths enhanced tostationary trajectowill an increased use of such vehicles in ries by prescribing velocity profile, which avoids collisions environments within fenced areas, like harbours or distrilikely next commercial step towards autonomous driving will be an increased use ofareas, such like vehicles in controlled ries by prescribing a velocity profile, which avoids collisions with other autonomous trucks managed by HelyOS. It is objects geometrically. The paths are enhanced to trajectoenvironments within fenced harbours or distriries by prescribing a velocity profile, which avoids collisions environments within fenced areas, like harbours or distriwith other autonomous trucks managed by HelyOS. It is bution Based on the experience gained such will be centres. an increased use ofareas, such vehicles in controlled environments within fenced like harbours orin distriwith other autonomous trucks managed by HelyOS. It is the task of the path tracking controller, which is described ries by prescribing a velocity profile, which avoids collisions bution centres. Based on the experience gained in such with other autonomous trucks managed by HelyOS. It is bution centres. Based on the the experience gained indistrisuch the task of the path tracking controller, which is described applications the development can go on, to enable safe environments within fenced areas, like harbours or bution centres. Based on experience gained in such the task of the path tracking controller, which is described in section 4, to follow this trajectory. To avoid collisions with other autonomous trucks managed by HelyOS. It is applications the development can go on, to enable safe the task of the path tracking controller, which is described applications the development can go The on, gained to enable safe in section 4, to follow this trajectory. To avoid collisions autonomous driving on public roads. path tracking bution centres. Based the can experience in such applications the development go on, to enable safe in section 4, to follow this trajectory. To avoid collisions with humans or objects unknown to HelyOS, the vehicle the task of the path tracking controller, which is described autonomous driving ononpublic public roads. The path tracking in section 4, to follow this trajectory. To avoid collisions autonomous driving on roads. The path tracking with humans or objects unknown to the vehicle controller, which is going to be presented section 4, is applications the development go The on, in to enable safe autonomous driving on public roads. path tracking with humans or objects unknown to HelyOS, HelyOS, the vehicle needs to its For this it equipped section to follow this trajectory. To avoid collisions controller, which which is going going to be becan presented in section 4, is in with humans or on objects unknown HelyOS, the vehicle controller, is to presented in section 4, is needs to be be4,safe safe on its own. own. For thistopurpose purpose it is is equipped part of a funded project called AutoTruck, which aims at autonomous driving on public roads. The path tracking controller, which is going to be presented in section 4, is needs to be safe on its own. For this purpose it is equipped safety measures such as laser scanners, which can dewith humans or objects unknown to HelyOS, the vehicle part of a funded project called AutoTruck, which aims at needs to be safe on its own. For this purpose it is equipped part of a funded project called AutoTruck, which aims at with safety measures such as laser scanners, which can deautomated driving dedicated automation zones. Before controller, which isin going to beAutoTruck, presented inwhich section 4, at is with part of a funded project called aims safety measures such as laser scanners, which can detect surrounding objects and stop the vehicle if necessary. needs to be safe on its own. For this purpose it is equipped automated driving in dedicated automation zones. Before with safety measures such as laser scanners, which can deautomated driving in dedicated automation zones. Before tect surrounding objects and stop the vehicle if necessary. going into the controller details, the project is desribed part of a funded project called AutoTruck, which aims at automated driving in dedicated automation zones. Before tect surrounding objects and stop the vehicle if necessary. safety measures suchand as laser scanners, which can degoing into into the the controller controller details, details, the the project project is is desribed desribed with tect surrounding objects stop the vehicle if necessary. going project aa real truck is built up with the necessary briefly in the following section. automated driving in dedicated zones. Before In going the controller details,automation the project is desribed In the the project real truck is built up with the necessary tect surrounding objects and stop the vehicle if necessary. briefly into in the the following section. the project aa includes real truck is built up with the necessary briefly in following section. technology. This an electronic steering system and going into thefollowing controller details, the project is desribed In In the project real truck is built up with the necessary briefly in the section. technology. This includes an electronic steering system and technology. This includes an electronic steering system and the laser scanners, which are not only used for safety, but In the project a real truck is built up with the necessary briefly in the following section. technology. This includes an electronic steering system and 2. AUTOTRUCK the laser scanners, which are not only used for safety, but the laser scanners, which are not only used for safety, but 2. AUTOTRUCK AUTOTRUCK also for the localization together with GPS and odomtechnology. This includes an electronic steering system and 2. the laser scanners, which are not only used for safety, but 2. AUTOTRUCK also for the localization together with GPS and odomalso for the localization together with GPS and odometry. The underlying localization algorithm is provided the laser scanners, which are not only used for safety, but also for the localization together with GPS and odom2. AUTOTRUCK AutoTruck is a project funded by the Federal Ministry etry. The underlying localization algorithm is provided The underlying localization algorithm is provided AutoTruck is is aa project project funded funded by by the the Federal Federal Ministry Ministry etry. by Goetting KG. Wabco supports the development with also for the localization together with GPS and odometry. The underlying localization algorithm is provided AutoTruck for Economic and Energy of Germany. The project Goetting KG. Wabco supports the development with AutoTruck is Affairs a project the Federal by Goetting KG. Wabco supports the development with for Economic Economic Affairs and funded Energy by of Germany. Germany. TheMinistry project by control of the braking system and aaalgorithm V2X communication etry. The underlying localization is provided by Goetting KG. Wabco supports the development with for Affairs and Energy of The project partners from industry and research develop solutions for AutoTruck is a project funded by the Federal Ministry control of the braking system and V2X communication for Economic Affairs and Energy of Germany. The project control of the braking system and a V2X communication partners from industry and research develop solutions for device. Orten fitted the truck with an electric driveline, by Goetting KG. Wabco supports the development with control of the braking system and a V2X communication partners from industry and research develop solutions for for Economic Affairs and Energy of Germany. The project device. Orten Orten fitted fitted the the truck truck with with an an electric electric driveline, driveline, partners from industry and research develop solutions for device. This work control of the braking system and a V2X communication is funded by the Federal Ministry for Economic Affairs device. Orten fitted the truck with an electric driveline, partners from industry and research develop solutions for 1 work is by Federal Ministry for Affairs This This work is funded funded by the the Federal Ministry for Economic Economic Affairs http://www.autotruck-projekt.de/ and Energy device. Orten fitted the truck with an electric driveline, 1 This workGermany. is funded by the Federal Ministry for Economic Affairs and Energy Germany. 1 http://www.autotruck-projekt.de/
and Energy Germany. 1 http://www.autotruck-projekt.de/ http://www.autotruck-projekt.de/ and Energy This workGermany. is funded by the Federal Ministry for Economic Affairs 1 http://www.autotruck-projekt.de/ and Energy Germany. 2405-8963 © © 2019 2019, IFAC IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright Copyright © 2019 Copyright © under 2019 IFAC IFAC Peer review responsibility of International Federation of Automatic Control. Copyright © 2019 IFAC 10.1016/j.ifacol.2019.08.088 Copyright © 2019 IFAC
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which allows for easier automation. The logistics company Emons provides the distribution centre for testing. Fraunhofer IVI is responsible for the overall system integration on the truck and the control algorithms. Furthermore, Fraunhofer IVI develops the management web application HelyOS. 3. DRIVELAB In order to test parts of the technology and algorithms, a test environment called DriveLab was built up before the actual truck is ready. This test environment uses 1:32 scale trucks, which can perform various manoeuvres autonomously, see Fig. 1. Even though, the real truck and the control algorithm assume a single two axle truck, a semi-trailer truck is used in the DriveLab. The trailer has a minor influence on the controller, but is needed to carry the RaspberryPi and the Lithium-Ion battery.
With the help of the DriveLab test environment the following aspects of AutoTruck could already be successfully tested: (1) The main top level concept of sending several vehicles from A to B from a simple user interface on a stationary computer. (2) The ROS system and communication including multi master synchronization between the main computer and the trucks (3) The path tracking controller This shows the feasibility of the AutoTruck concept and technological components. However, adaptations are expected to be necessary for the real vehicle. 4. PATH TRACKING CONTROLLER Parting from an optimal path, tracking steering controllers were designed. While other studies solve the path tracking problem with sophisticated control laws or using nonlinear control theory, Rouchon et al. (1993); Sampei et al. (1995); Divelbiss and Wen (1997); Werling et al. (2014); Riesmeier et al. (2016), this project looked into the achievable performance of simple and easy to implement solutions. Due to the low computation cost, this methods could be incorporated on electronic control units of real vehicles.
Fig. 1. The scale truck used in DriveLab
Table 1. Symbols
Fig. 2 shows a schematic of the DriveLab. The control software and communication is based on the Robot Operating System (ROS). The main control software runs on a stationary computer with one ROS master. The trucks use a RaspberryPi to receive the information from the main computer via WIFI. A beamer projects a map from the top to the ground to visualize different driving scenarios. A camera mounted above the scene detects QR-markers on the truck in order to calculate their current pose.
Symbol u2 δ l2 θi dk dOff KPFC KCTEC
Variable name Velocity of rear axle Steering angle Vehicle wheelbase Orientation w.r.t. fixed coordinate system Euclidean distance from front axle to next path point Cross track error distance Weight for point follow controller Weight for cross track error controller
4.1 Vehicle Model The kinematic model of the truck is shown in Fig. 3. It is based on a car-like model. While the circle represents the steerable front axle, the rectangle shows the rear axle and defines the orientation of the vehicle. ξ2 Fig. 2. Scheme of the development environment DriveLab. The usage of the DriveLab is similar to the planned functionality of HelyOS in AutoTruck. The operator completely controls the vehicles from the main computer. He can select a vehicle, define its start and desired end position, drivable areas and stationary obstacles, which need to be avoided. Then a path is planned from start to end, which is afterwards sent to the scale truck. The truck uses the path tracking controller described in the following section to follow this path. While in AutoTruck the vehicle will be able to localize itself, in DriveLab the scale truck receives its current position from the main computer, which determines it using the camera. 308
δ θ1 x1,2 l2 x2,2
x1
θ2 x2
e2 e1 x2,1 Fig. 3. Kinematic car-like model.
x1,1
ξ1
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T
By setting the input as u = (u1 u2 ) corresponding kinematic equations read x˙ 2,1 = u1 cos θ2 x˙ 2,2 = u1 sin θ2 u1 tan u2 , θ˙2 = l2
T
= (v2 δ) , the
(1)
T
with the state X = (x2,1 x2,2 θ2 ) . In the following methods, a constant velocity is applied and the remaining control variable is the steering angle. The velocity profile for the trajectory tracking is not discussed. The dimensions of the development truck is at a scale of 1:32, resulting a wheelbase of l2 = 115 mm. 4.2 Point Follow Controller (PFC) The idea behind the algorithm is to steer directly to the next path point in order to follow a given discrete path. The geometric approach is shown in Fig. 4. ξ2 xk+1 xk
rth
δ θ1
Path
309
Fig. 5. Scheme of the point follow controller. An extension of this algorithm considers various path points at the same time and computes the weighted steering angle δ = k1 δk + k2 δk+1 + k3 δk+2 + · · · . (7) This could reduce the discontinuities in the commanded steering angle but lead to higher differences w.r.t. the path. 4.3 Cross Track Error Controller (CTEC) A second approach was followed by using merely the cross track error dOff of the vehicle w.r.t. the path as input, defined as shown in Fig. 6. To converge the value of dOff to zero, a PID controller structure was used t de(t) , (8) e(τ ) dτ + Kd u(t) = Kp e(t) + Ki dt 0 which was intergrated in the overall structure, Fig. 7. ξ2
x1
l2 θ2 x2
e2
Path e1
dOff
ξ1
x1
l2
Fig. 4. Point follow controller, geometric principle
θ1
θ2
To head with the front axle to the next point xk , the condition for the orientation follows (2) ∆x1 = xk,1 − x1,1 (3) ∆x2 = xk,2 − x1,2 ∆x2 θ1,k = arctan , (4) ∆x1 and the resulting angle for the steering angle controller is (5) δ = θ1,k − θ2,k . In addition, the point xk is considered as reached when the condition dk ≤ rth holds, being dk = ∆x21 + ∆x22 (6)
the euclidean distance between the points. This relation is used in the path point controller. The complete control system has been illustrated by the scheme in Fig. 5.
Clearly, this method imposes discontinuities in δ which have to be analysed. The resulting tracking performance will highly depend on the path point density and the selected threshold rth , as well as the vehicle velocity. Intuition and measurements show that by increasing rth the path is followed more smoothly but at a bigger distance, which implies a greater cross track error. 309
x2
e2 e1
ξ1
Fig. 6. Cross track error visualisation
Fig. 7. Scheme of the cross track error controller. For the practical implementation, the PID controller is improved with an anti-windup for the integral and an input filter for the differential term, Fig. 8. The signals are: error e, reference r, controller output v, system input u, measured system output y and saturation error es . A possible tuning for the filter time constant Tf and the anti-windup gain Kt is described in Astroem and Murray (2008).
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1.2 1
y/m
0.8 Ref. path Front axle Rear axle
0.6 0.4 0.2
Fig. 8. Practical implementation of PID controller. There exist empirical and model based methods for tuning PID controllers, Lunze (2010); Zacher and Reuter (2011). As a starting point, the empirical method by ZieglerNichols was used to obtain first controller gains. After further optimisation w.r.t to the tracking performance, the best values read Kp = 10.4 rad m−1 Ki = 9.4 rad m−1 s−1 Kd = 3.8 rad m−1 s.
0
0.5
1
1.5
2
x/m Fig. 9. Paths with PFC for rth = 80 mm in xy-plane ·10−3
15
4.4 Performance comparison 10 dOff/m
A test path was used to evaluate and compare the controllers’ behaviour with the scale trucks in the DriveLab test environment. The performance of the PFC is depicted in Tab. 2. Note that the CTE is measured w.r.t. the front axle, as it follows the reference. Its value is positive for the vehicle being at the left of the path and negative otherwise.
5
0 Table 2. Performance PFC Threshold rth / mm 50 80 100
Cross track error (CTE) dOff / mm [-15, 20] [-5, 15] [-5, 20]
Oscillation w.r.t. path strong light light
CTE in curve small small big
−5
To gain greater insight into the performance parameters, Fig. 9 shows the reference for the front axle and the followed paths for the scenario rth = 80 mm, which gives the best result for this controller. It can be seen that the path is followed quite well, except the part of the curve, for which this algorithm gives less accurate tracking.
0
10
20
30 t/s
40
50
60
Fig. 10. CTE with PFC for rth = 80 mm 0.6
0.4
The switching behaviour for the commanded steering angle can be observed in Fig. 11. Although some jump sizes are in the region of ∆δ ≈ 0.20 rad, the dynamics of the steering mechanism handles them satisfactorily. On the other hand, the behaviour of the CTEC is directly shown for the best evaluated controller gains. As can be seen in Fig. 12, initially this controller tracks the path very close. In the curve the truck follows through the outer side of the path, the opposite behaviour of the PFC. The performance degrades significantly after the curve. See Fig. 13 the related cross track error. The computed steering angle for tracking the path is smoother than for the PFC, Fig. 14. 310
δ/rad
The correspondent cross track error is shown in Fig. 10. 0.2
0 −0.2 0
10
20
30 t/s
Fig. 11. δ with PFC for rth = 80 mm
40
50
60
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This quite opposite behaviour of both controllers contributed to the idea of combining them to get the best result of each. The following section introduces the simple combined controller and its resulting performance.
1.2 1 0.8 y/m
311
4.5 Combination of PFC and CTEC
Ref. path Front axle Rear axle
0.6
The resulting controller structure combining the PFC and the CTEC is shown in Fig. 15.
0.4 0.2 0
0.5
1
1.5
2
x/m Fig. 15. Scheme of the combined controller. Fig. 12. Paths with CTEC with best PID gains in xy-plane By using KCTEC = 1 − KPID , the result for different gains is presented in Tab. 3.
·10−3
40
Table 3. Performance combination Gain KPID 0.1 0.5 0.9
dOff/m
20 0
Oscillation w.r.t. path light light light
CTE in curve very small big big
This shows that with a predominant point follow controller the behaviour is significantly improved. For comparison reasons, Fig. 16 shows the reference and the driven paths. The reference is followed very close with this setup.
−20 −40 0
10
20
30 t/s
40
50
1.2
60
1
Fig. 13. CTE with CTEC
0.8 y/m
0.6
δ/rad
CTE dOff / mm [-8, 10] [-30, 19] [-42, 30]
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The resulting cross track error is very small for the full path, Fig. 17. It stays inside a range of [-8,10] mm. Additionally, it shows that the truck remains closer to the reference path.
Fig. 14. δ with CTEC
Finally, the needed steering angle is shown in Fig. 18. 311
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REFERENCES
10
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Fig. 18. δ with PFC + CTEC and KPID = 0.1 5. CONCLUSION It was able to show that a combination of two simple control strategies leads to satisfactory results for a path tracking controller. The controllers were implemented in the ROS framework and were tested with 1:32 scale trucks in the Drivelab test environment. A maximum cross track error of 10 mm was achieved, which should transform to about 30 cm in real world applications – depending on the positioning system. This is considered sufficient for the application in Autotruck-project. In a next step, the control strategy will be integrated in the real world truck. Measurements will reveal the true cross track error.
ACKNOWLEDGEMENTS This work is part of the project Autotruck, funded by the Federal Ministry of Economic Affairs and Energy Germany. 312
Astroem, K.J. and Murray, R.M. (2008). Feedback Systems An Introduction for Scientists and Engineers. Princeton University Press. Beyersdorfer, S. and Wagner, S. (2013). Novel model based path planning for multi-axle steered heavy load vehicles. In 16th International IEEE Conference on Intelligent Transportation Systems (ITSC), S. 424 – 429. IEEE, The Hague, The Netherlands. Divelbiss, A. and Wen, J. (1997). Trajectory tracking control of a car-trailer system. IEEE Transactions on Control Systems Technology, 5(3), 269–278. doi: 10.1109/87.572125. Kuhnt, F., Pfeiffer, M., Zimmer, P., Zimmerer, D., Gomer, J.M., Kaiser, V., Kohlhaas, R., and Zollner, J.M. (2016). Robust environment perception for the audi autonomous driving cup. In 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC). IEEE. doi:10.1109/itsc.2016.7795744. Kusumakar, R., Buning, L., Rieck, F., Schuur, P., and Tillema, F. (2018). INTRALOG – intelligent autonomous truck applications in logistics; single and double articulated autonomous rearward docking on DCs. IET Intelligent Transport Systems, 12(9), 1045–1052. doi:10.1049/iet-its.2018.0083. Lunze, J. (2010). Regelungstechnik 1. Springer Berlin Heidelberg. doi:10.1007/978-3-642-13808-9. Magdici, S. and Althoff, M. (2016). Fail-safe motion planning of autonomous vehicles. In 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC). IEEE. doi:10.1109/itsc.2016.7795594. Nilsson, P., Laine, L., van Duijkeren, N., and Jacobson, B. (2015). Automated highway lane changes of long vehicle combinations: A specific comparison between driver model based control and non-linear model predictive control. In 2015 International Symposium on Innovations in Intelligent SysTems and Applications (INISTA). IEEE. doi:10.1109/inista.2015.7276790. Riesmeier, M., Schnabel, O., Woittennek, F., and Kn¨ uppel, T. (2016). Zur folgeregelung mehrachsiger fahrzeuge. at - Automatisierungstechnik, 64(8). doi: 10.1515/auto-2016-0040. Rouchon, P., Fliess, M., Levine, J., and Martin, P. (1993). Flatness, motion planning and trailer systems. In Proceedings of 32nd IEEE Conference on Decision and Control. IEEE. doi:10.1109/cdc.1993.325686. Sampei, M., Tamura, T., Kobayashi, T., and Shibui, N. (1995). Arbitrary path tracking control of articulated vehicles using nonlinear control theory. IEEE Transactions on Control Systems Technology, 3(1), 125–131. doi:10.1109/87.370718. van Vliet, A., Jansen, R., and Cornelissen, J. (2018). Truck platooning: An update after the european truck platooning challenge. In International Symposium on Heavy Vehicle Transport Technology HVTT15. Rotterdam. Werling, M., Heidingsfeld, M., Reinisch, P., and Gr¨oll, L. (2014). Assistiertes und automatisiertes r¨ uckw¨artsrangieren mit anh¨anger. at – Automatisierungstechnik, 62(1). doi:10.1515/auto-2014-1001. Zacher, S. and Reuter, M. (2011). Regelungstechnik f¨ ur Ingenieure. Vieweg+Teubner. doi:10.1007/978-3-83489837-1.
ScienceDirect
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A simple yet efficient Path Tracking A simple yet efficient Path Tracking A simple yet efficient Path Tracking Controller for Autonomous Trucks A simple yet efficient Path Tracking Controller for Autonomous Trucks Controller for Autonomous Trucks ∗ Controller∗ for Autonomous Trucks ∗
Julius K. Julius K. Kolb Kolb ∗∗∗ Gunter Gunter Nitzsche Nitzsche ∗∗∗ Sebastian Sebastian Wagner Wagner ∗∗∗ Julius Julius K. K. Kolb Kolb Gunter Gunter Nitzsche Nitzsche Sebastian Sebastian Wagner Wagner ∗ ∗ Julius K. Kolb Gunter Nitzsche ∗ Sebastian Wagner ∗ Fraunhofer Institute for Transportation and Infrastructure ∗ ∗ Fraunhofer Institute for Transportation and Infrastructure for Transportation and Infrastructure ∗ Fraunhofer Institute Systems IVI, Dresden, Germany Fraunhofer Institute for Transportation and Infrastructure Systems IVI, Dresden, Germany ∗ Systems IVI, Dresden, Germany (e-mail: [email protected]). Fraunhofer Institute for Transportation and Infrastructure Systems IVI, Dresden, Germany (e-mail: [email protected]). [email protected]). (e-mail: Systems IVI, Dresden, Germany (e-mail: [email protected]). (e-mail: [email protected]). Abstract: This paper presents path tracking controller implemented for the Robot Operating Abstract: This This paper paper presents presents aa a path path tracking tracking controller controller implemented implemented for for the the Robot Robot Operating Operating Abstract: System (ROS). It is developed for the funded project AutoTruck in which a 18 t truck will be Abstract: This paper presents a path tracking controller implemented for the Robot Operating System (ROS). (ROS). It It is is developed developed for for the the funded funded project project AutoTruck AutoTruck in in which which aa 18 18 tt truck truck will will be be System automated for yard applications. The goal was to design a simple yet sufficient controller, which Abstract: This paper presents a path tracking controller implemented for the Robot Operating System (ROS). It is developed for the funded project AutoTruck in which a 18 t truck will be automated for yard applications. The goal was to design a simple yet sufficient controller, which automated for yard goal was to aa simple yet controller, which could also be on a standard in vehicle unit. Therefore, no advanced non linear System (ROS). It isapplications. developed forThe the funded project AutoTruck in sufficient which a 18 t truck be automated for used yard applications. The wascontrol to design design simple yet sufficient controller, which could also also be used on a standard standard in goal vehicle control unit. Therefore, no advanced advanced nonwill linear could be used on a in vehicle control unit. Therefore, no non linear controller was designed. The controller is a combination of a PID controller and a point follow automated for yard applications. The goal was to design a simple yet sufficient controller, which could also be used on a standard in vehicle control unit. Therefore, no advanced non linear controller was was designed. designed. The The controller controller is is aa combination combination of of a PID PID controller controller and and a point follow follow controller controller. Both controllers individually their drawbacks the application. However, could also was be used on aThe standard in vehicle control unit. advanced non linear controller designed. controller is have a combination of aaTherefore, PIDfor controller and aa point point follow controller. Both controllers individually have their drawbacks drawbacks for thenoapplication. application. However, controller. Both controllers individually have their for the However, the combination proves to provide a good tracking performance. The controllers are tested in controller was designed. The controller is a combination of a PID controller and a point follow controller. Both controllers individually have their drawbacks for the application. However, the combination combination proves proves to to provide provide aa good good tracking tracking performance. performance. The The controllers controllers are are tested tested in in the simulation and with 1:32 scale trucks in the test environment called DriveLab. controller. Both controllers individually have their drawbacks for the application. However, the combination proves to provide a good tracking performance. The controllers are tested in simulation and with 1:32 scale trucks in the test environment called DriveLab. simulation and 1:32 trucks in test called DriveLab. the combination proves provide a good performance. The controllers are tested in simulation and with with 1:32toscale scale trucks in the thetracking test environment environment called DriveLab. © 2019, IFAC (International Federation of in Automatic Control) Hosting by Elsevier Ltd. All rights reserved. simulation and with 1:32Vehicles, scale trucks the test environment called DriveLab. Keywords: Autonomous Closed Loop Control, ROS, PID control Keywords: Autonomous Autonomous Vehicles, Vehicles, Closed Closed Loop Loop Control, Control, ROS, ROS, PID PID control control Keywords: Keywords: Autonomous Vehicles, Closed Loop Control, ROS, PID control Keywords: Autonomous Vehicles, Closed Loop Control, ROS, driving PID control 1. INTRODUCTION autonomous of trucks on fenced areas like distri1. INTRODUCTION INTRODUCTION autonomous driving of trucks on fenced areas like distri1. autonomous driving of trucks on fenced areas like distribution centres. An overview is provided on the project 1. INTRODUCTION autonomous driving of trucks on fenced areas like distribution centres. centres. An overview overview is is provided provided on on the the project project 1 bution An 1. INTRODUCTION website also in a short video. autonomous driving of trucks on fenced areas like distribution centres. An overview is provided on the project Autonomous vehicles are a field of research for several 1 1 website also in a short video. Autonomous vehicles vehicles are are aa field field of of research research for for several several website aa short video. 1 also inAn Autonomous bution centres. overview is provided on the project website also in short video. decades now. In the recent years more and more appliAutonomous vehicles are a field of research for several idea decades now. now. In In the the recent recent years years more more and and more more appliappli- The 1 is, that the truck driver stops and leaves the truck decades The idea is, that truck driver stops and leaves the truck also in the a short video. cations are shown and the number of test drives on public Autonomous vehicles are a years field of research for several decades now. In the recent more and more appli- website The idea is, the truck stops leaves the truck when entering The truck is then cations are shown and the number of test drives on public The idea is, that thatthe thedistribution truck driver driver centre. stops and and leaves the truck cations are shown andrecent the number number of testet drives on public public when entering the distribution centre. The truck is then roads increases. According to van Vliet al. (2018) and decades now. In the years more and more applications are shown and the of test drives on when entering the distribution centre. The truck is then switched to automatic mode and registers itself wireless The idea is, that the truck driver stops and leaves the truck roads increases. According to van Vliet et al. (2018) and when entering the distribution centre. The truck is then roads increases. According to van Vliet et al. (2018) and switched to automatic mode and registers itself wireless Kusumakar et al. (2018) automated driving – including cations are shown and the number of test drives on public roads increases. According to van Vliet et al. (2018) and switched to automatic mode and registers itself wireless with the infrastructure of the distribution centre. Now an entering the distribution centre. The truck is then Kusumakar et et al. al. (2018) (2018) automated automated driving driving –– including including when switched to automatic mode and registers itself wireless Kusumakar with the infrastructure of the distribution centre. Now an truck platooning – is going to change on road logistics in roads increases. According to Vliet al. –(2018) and Kusumakar et al. driving including with the infrastructure of the distribution centre. Now an operator can select the truck in the management software to automatic mode and registers itself wireless truck platooning platooning – (2018) is going goingautomated to van change onetroad road logistics in switched with the infrastructure of the distribution centre. Now an truck – is to change on logistics in operator can select the truck in the management software the future. Therefore, many researchers from academics Kusumakar et al. (2018) automated driving – including truck platooning – is going to change on road logistics in operator can select the truck in the management software HelyOS (Highly Efficient Online Yard Operating System) with the infrastructure of the distribution centre. Now an the future. Therefore, many researchers from academics operator can select the truck in the management software the future. Therefore, many researchers from academics HelyOS (Highly Efficient Online Yard Operating System) and industry are different aspects of autruck platooning – investigating is going change on road logistics in HelyOS the future. Therefore, manytoresearchers from academics (Highly Efficient Online Yard Operating System) and can assign missions to the truck. Missions consist of operator can select the truck in the management software and industry are investigating different aspects of auHelyOS (Highly Efficient Online Yard Operating System) and industry are investigating investigating different aspects ofetauauand can assign missions to the truck. Missions consist of tonomous vehicles, starting perception, Kuhnt al. the future. Therefore, manyfrom researchers from academics and industry are different aspects of can assign missions to the truck. Missions consist of single tasks like ”drive to loading dock 42” or ”drive to HelyOS (Highly Efficient Online Yard Operating System) tonomous vehicles, starting from perception, Kuhnt et al. al. and and can assign missions to the truck. Missions consist of tonomous vehicles, starting from perception, Kuhnt et single tasks tasks like like ”drive ”drive to to loading loading dock dock 42” 42” or or ”drive ”drive to to (2016), over motion planning, Magdici and Althoff (2016), and industry are investigating different aspects of autonomous vehicles, starting from perception, Kuhnt et al. single charger”. Once the vehicle is ready to leave the distribution and can assign missions to the truck. Missions consist of (2016), over motion planning, Magdici and Althoff (2016), single tasks like ”drive to loading dock 42” or ”drive to (2016), over motion planning, Magdici and Althoff (2016), charger”. Once Once the the vehicle vehicle is is ready ready to to leave leave the the distribution distribution to the control of autonomous vehicles, Nilsson et al. (2015). tonomous vehicles, starting from perception, Kuhnt et al. charger”. (2016), over motion planning, Magdici and Althoff (2016), centre, it drives to the hand over point, checks out of the single tasks like ”drive to loading dock 42” or ”drive to to the control of autonomous vehicles, Nilsson et al. (2015). charger”. Once the vehicle is ready to leave the distribution to the the control control of autonomous autonomous vehicles, Nilsson et al. al. (2015). (2015). it drives to the hand over point, checks out of the (2016), over motion planning,vehicles, MagdiciNilsson and Althoff (2016), centre, to of et centre, it drives to the over checks out of the infrastructure, off mode taken charger”. the isautonomous ready to leave the and distribution centre, it Once drivesswitches to vehicle the hand hand over point, point, checks outis of the Nevertheless, the authors think, that it is still a long way infrastructure, switches off autonomous mode and is taken Nevertheless, the authors think, that it is still a long way to the control of autonomous vehicles, Nilsson et al. (2015). infrastructure, switches off autonomous mode and is taken Nevertheless, the authors think, that it is still a long way over by the driver. centre, it drives to the hand over point, checks out of the infrastructure, switches off autonomous mode and is taken until we see serial autonomous vehicles on public roads. Nevertheless, the authors think, that it is still a long way over by by the the driver. driver. until we we see see serial serial autonomous autonomous vehicles vehicles on on public public roads. roads. over until infrastructure, switches off autonomous mode and is taken over by the driver. The main reason legislative technical chalNevertheless, the are authors think,hurdles that itand ison still a long way The paths between the different stops of a mission are until we see serial autonomous vehicles public roads. The main main reason are legislative hurdles and technical chalThe reason are legislative hurdles and technical chalThe paths different stops of a mission are over by the between driver. the lenges to ensure the functional safety of such vehicles in all until we see serial autonomous vehicles on public roads. The main reason are legislative hurdles and technical chalThe paths between the different stops of are with aa path planner, which is based on Beyerslenges to to ensure ensure the the functional functional safety safety of of such such vehicles vehicles in in all all planned The paths between the different stops of aa mission mission are lenges planned with path planner, which is based on Beyersdriving situations over the whole vehicle lifetime. The most The main reason are legislative hurdles and technical challenges to ensure the functional safety of such vehicles in all planned with a path planner, which is based on Beyersdorfer and Wagner (2013). These paths avoid stationary The paths between the different stops of a mission are driving situations over the whole vehicle lifetime. The most planned with a path planner, which is based on Beyersdriving situations over the whole vehicle lifetime. The most dorfer and Wagner (2013). These paths avoid stationary likely next commercial step towards autonomous driving lenges tosituations ensure the functional safety of such vehicles in all dorfer driving over the whole vehicle lifetime. The most and Wagner (2013). These paths avoid stationary objects geometrically. The paths are enhanced to trajectoplanned with a path planner, which is based on Beyerslikely next commercial step towards autonomous driving dorfer and Wagner (2013). These paths avoid stationary likely next commercial step towards autonomous driving geometrically. The paths are enhanced to trajectowill be an increased use of such vehicles in controlled driving situations over the whole vehicle lifetime. The most objects likely step autonomous driving objects geometrically. The are enhanced to trajectories by prescribing profile, which avoids collisions dorfer and Wagneraa velocity (2013). These avoid will be benext an commercial increased use oftowards such vehicles in controlled controlled objects geometrically. The paths paths arepaths enhanced tostationary trajectowill an increased use of such vehicles in ries by prescribing velocity profile, which avoids collisions environments within fenced areas, like harbours or distrilikely next commercial step towards autonomous driving will be an increased use ofareas, such like vehicles in controlled ries by prescribing a velocity profile, which avoids collisions with other autonomous trucks managed by HelyOS. It is objects geometrically. The paths are enhanced to trajectoenvironments within fenced harbours or distriries by prescribing a velocity profile, which avoids collisions environments within fenced areas, like harbours or distriwith other autonomous trucks managed by HelyOS. It is bution Based on the experience gained such will be centres. an increased use ofareas, such vehicles in controlled environments within fenced like harbours orin distriwith other autonomous trucks managed by HelyOS. It is the task of the path tracking controller, which is described ries by prescribing a velocity profile, which avoids collisions bution centres. Based on the experience gained in such with other autonomous trucks managed by HelyOS. It is bution centres. Based on the the experience gained indistrisuch the task of the path tracking controller, which is described applications the development can go on, to enable safe environments within fenced areas, like harbours or bution centres. Based on experience gained in such the task of the path tracking controller, which is described in section 4, to follow this trajectory. To avoid collisions with other autonomous trucks managed by HelyOS. It is applications the development can go on, to enable safe the task of the path tracking controller, which is described applications the development can go The on, gained to enable safe in section 4, to follow this trajectory. To avoid collisions autonomous driving on public roads. path tracking bution centres. Based the can experience in such applications the development go on, to enable safe in section 4, to follow this trajectory. To avoid collisions with humans or objects unknown to HelyOS, the vehicle the task of the path tracking controller, which is described autonomous driving ononpublic public roads. The path tracking in section 4, to follow this trajectory. To avoid collisions autonomous driving on roads. The path tracking with humans or objects unknown to the vehicle controller, which is going to be presented section 4, is applications the development go The on, in to enable safe autonomous driving on public roads. path tracking with humans or objects unknown to HelyOS, HelyOS, the vehicle needs to its For this it equipped section to follow this trajectory. To avoid collisions controller, which which is going going to be becan presented in section 4, is in with humans or on objects unknown HelyOS, the vehicle controller, is to presented in section 4, is needs to be be4,safe safe on its own. own. For thistopurpose purpose it is is equipped part of a funded project called AutoTruck, which aims at autonomous driving on public roads. The path tracking controller, which is going to be presented in section 4, is needs to be safe on its own. For this purpose it is equipped safety measures such as laser scanners, which can dewith humans or objects unknown to HelyOS, the vehicle part of a funded project called AutoTruck, which aims at needs to be safe on its own. For this purpose it is equipped part of a funded project called AutoTruck, which aims at with safety measures such as laser scanners, which can deautomated driving dedicated automation zones. Before controller, which isin going to beAutoTruck, presented inwhich section 4, at is with part of a funded project called aims safety measures such as laser scanners, which can detect surrounding objects and stop the vehicle if necessary. needs to be safe on its own. For this purpose it is equipped automated driving in dedicated automation zones. Before with safety measures such as laser scanners, which can deautomated driving in dedicated automation zones. Before tect surrounding objects and stop the vehicle if necessary. going into the controller details, the project is desribed part of a funded project called AutoTruck, which aims at automated driving in dedicated automation zones. Before tect surrounding objects and stop the vehicle if necessary. safety measures suchand as laser scanners, which can degoing into into the the controller controller details, details, the the project project is is desribed desribed with tect surrounding objects stop the vehicle if necessary. going project aa real truck is built up with the necessary briefly in the following section. automated driving in dedicated zones. Before In going the controller details,automation the project is desribed In the the project real truck is built up with the necessary tect surrounding objects and stop the vehicle if necessary. briefly into in the the following section. the project aa includes real truck is built up with the necessary briefly in following section. technology. This an electronic steering system and going into thefollowing controller details, the project is desribed In In the project real truck is built up with the necessary briefly in the section. technology. This includes an electronic steering system and technology. This includes an electronic steering system and the laser scanners, which are not only used for safety, but In the project a real truck is built up with the necessary briefly in the following section. technology. This includes an electronic steering system and 2. AUTOTRUCK the laser scanners, which are not only used for safety, but the laser scanners, which are not only used for safety, but 2. AUTOTRUCK AUTOTRUCK also for the localization together with GPS and odomtechnology. This includes an electronic steering system and 2. the laser scanners, which are not only used for safety, but 2. AUTOTRUCK also for the localization together with GPS and odomalso for the localization together with GPS and odometry. The underlying localization algorithm is provided the laser scanners, which are not only used for safety, but also for the localization together with GPS and odom2. AUTOTRUCK AutoTruck is a project funded by the Federal Ministry etry. The underlying localization algorithm is provided The underlying localization algorithm is provided AutoTruck is is aa project project funded funded by by the the Federal Federal Ministry Ministry etry. by Goetting KG. Wabco supports the development with also for the localization together with GPS and odometry. The underlying localization algorithm is provided AutoTruck for Economic and Energy of Germany. The project Goetting KG. Wabco supports the development with AutoTruck is Affairs a project the Federal by Goetting KG. Wabco supports the development with for Economic Economic Affairs and funded Energy by of Germany. Germany. TheMinistry project by control of the braking system and aaalgorithm V2X communication etry. The underlying localization is provided by Goetting KG. Wabco supports the development with for Affairs and Energy of The project partners from industry and research develop solutions for AutoTruck is a project funded by the Federal Ministry control of the braking system and V2X communication for Economic Affairs and Energy of Germany. The project control of the braking system and a V2X communication partners from industry and research develop solutions for device. Orten fitted the truck with an electric driveline, by Goetting KG. Wabco supports the development with control of the braking system and a V2X communication partners from industry and research develop solutions for for Economic Affairs and Energy of Germany. The project device. Orten Orten fitted fitted the the truck truck with with an an electric electric driveline, driveline, partners from industry and research develop solutions for device. This work control of the braking system and a V2X communication is funded by the Federal Ministry for Economic Affairs device. Orten fitted the truck with an electric driveline, partners from industry and research develop solutions for 1 work is by Federal Ministry for Affairs This This work is funded funded by the the Federal Ministry for Economic Economic Affairs http://www.autotruck-projekt.de/ and Energy device. Orten fitted the truck with an electric driveline, 1 This workGermany. is funded by the Federal Ministry for Economic Affairs and Energy Germany. 1 http://www.autotruck-projekt.de/
and Energy Germany. 1 http://www.autotruck-projekt.de/ http://www.autotruck-projekt.de/ and Energy This workGermany. is funded by the Federal Ministry for Economic Affairs 1 http://www.autotruck-projekt.de/ and Energy Germany. 2405-8963 © © 2019 2019, IFAC IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright Copyright © 2019 Copyright © under 2019 IFAC IFAC Peer review responsibility of International Federation of Automatic Control. Copyright © 2019 IFAC 10.1016/j.ifacol.2019.08.088 Copyright © 2019 IFAC
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which allows for easier automation. The logistics company Emons provides the distribution centre for testing. Fraunhofer IVI is responsible for the overall system integration on the truck and the control algorithms. Furthermore, Fraunhofer IVI develops the management web application HelyOS. 3. DRIVELAB In order to test parts of the technology and algorithms, a test environment called DriveLab was built up before the actual truck is ready. This test environment uses 1:32 scale trucks, which can perform various manoeuvres autonomously, see Fig. 1. Even though, the real truck and the control algorithm assume a single two axle truck, a semi-trailer truck is used in the DriveLab. The trailer has a minor influence on the controller, but is needed to carry the RaspberryPi and the Lithium-Ion battery.
With the help of the DriveLab test environment the following aspects of AutoTruck could already be successfully tested: (1) The main top level concept of sending several vehicles from A to B from a simple user interface on a stationary computer. (2) The ROS system and communication including multi master synchronization between the main computer and the trucks (3) The path tracking controller This shows the feasibility of the AutoTruck concept and technological components. However, adaptations are expected to be necessary for the real vehicle. 4. PATH TRACKING CONTROLLER Parting from an optimal path, tracking steering controllers were designed. While other studies solve the path tracking problem with sophisticated control laws or using nonlinear control theory, Rouchon et al. (1993); Sampei et al. (1995); Divelbiss and Wen (1997); Werling et al. (2014); Riesmeier et al. (2016), this project looked into the achievable performance of simple and easy to implement solutions. Due to the low computation cost, this methods could be incorporated on electronic control units of real vehicles.
Fig. 1. The scale truck used in DriveLab
Table 1. Symbols
Fig. 2 shows a schematic of the DriveLab. The control software and communication is based on the Robot Operating System (ROS). The main control software runs on a stationary computer with one ROS master. The trucks use a RaspberryPi to receive the information from the main computer via WIFI. A beamer projects a map from the top to the ground to visualize different driving scenarios. A camera mounted above the scene detects QR-markers on the truck in order to calculate their current pose.
Symbol u2 δ l2 θi dk dOff KPFC KCTEC
Variable name Velocity of rear axle Steering angle Vehicle wheelbase Orientation w.r.t. fixed coordinate system Euclidean distance from front axle to next path point Cross track error distance Weight for point follow controller Weight for cross track error controller
4.1 Vehicle Model The kinematic model of the truck is shown in Fig. 3. It is based on a car-like model. While the circle represents the steerable front axle, the rectangle shows the rear axle and defines the orientation of the vehicle. ξ2 Fig. 2. Scheme of the development environment DriveLab. The usage of the DriveLab is similar to the planned functionality of HelyOS in AutoTruck. The operator completely controls the vehicles from the main computer. He can select a vehicle, define its start and desired end position, drivable areas and stationary obstacles, which need to be avoided. Then a path is planned from start to end, which is afterwards sent to the scale truck. The truck uses the path tracking controller described in the following section to follow this path. While in AutoTruck the vehicle will be able to localize itself, in DriveLab the scale truck receives its current position from the main computer, which determines it using the camera. 308
δ θ1 x1,2 l2 x2,2
x1
θ2 x2
e2 e1 x2,1 Fig. 3. Kinematic car-like model.
x1,1
ξ1
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T
By setting the input as u = (u1 u2 ) corresponding kinematic equations read x˙ 2,1 = u1 cos θ2 x˙ 2,2 = u1 sin θ2 u1 tan u2 , θ˙2 = l2
T
= (v2 δ) , the
(1)
T
with the state X = (x2,1 x2,2 θ2 ) . In the following methods, a constant velocity is applied and the remaining control variable is the steering angle. The velocity profile for the trajectory tracking is not discussed. The dimensions of the development truck is at a scale of 1:32, resulting a wheelbase of l2 = 115 mm. 4.2 Point Follow Controller (PFC) The idea behind the algorithm is to steer directly to the next path point in order to follow a given discrete path. The geometric approach is shown in Fig. 4. ξ2 xk+1 xk
rth
δ θ1
Path
309
Fig. 5. Scheme of the point follow controller. An extension of this algorithm considers various path points at the same time and computes the weighted steering angle δ = k1 δk + k2 δk+1 + k3 δk+2 + · · · . (7) This could reduce the discontinuities in the commanded steering angle but lead to higher differences w.r.t. the path. 4.3 Cross Track Error Controller (CTEC) A second approach was followed by using merely the cross track error dOff of the vehicle w.r.t. the path as input, defined as shown in Fig. 6. To converge the value of dOff to zero, a PID controller structure was used t de(t) , (8) e(τ ) dτ + Kd u(t) = Kp e(t) + Ki dt 0 which was intergrated in the overall structure, Fig. 7. ξ2
x1
l2 θ2 x2
e2
Path e1
dOff
ξ1
x1
l2
Fig. 4. Point follow controller, geometric principle
θ1
θ2
To head with the front axle to the next point xk , the condition for the orientation follows (2) ∆x1 = xk,1 − x1,1 (3) ∆x2 = xk,2 − x1,2 ∆x2 θ1,k = arctan , (4) ∆x1 and the resulting angle for the steering angle controller is (5) δ = θ1,k − θ2,k . In addition, the point xk is considered as reached when the condition dk ≤ rth holds, being dk = ∆x21 + ∆x22 (6)
the euclidean distance between the points. This relation is used in the path point controller. The complete control system has been illustrated by the scheme in Fig. 5.
Clearly, this method imposes discontinuities in δ which have to be analysed. The resulting tracking performance will highly depend on the path point density and the selected threshold rth , as well as the vehicle velocity. Intuition and measurements show that by increasing rth the path is followed more smoothly but at a bigger distance, which implies a greater cross track error. 309
x2
e2 e1
ξ1
Fig. 6. Cross track error visualisation
Fig. 7. Scheme of the cross track error controller. For the practical implementation, the PID controller is improved with an anti-windup for the integral and an input filter for the differential term, Fig. 8. The signals are: error e, reference r, controller output v, system input u, measured system output y and saturation error es . A possible tuning for the filter time constant Tf and the anti-windup gain Kt is described in Astroem and Murray (2008).
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1.2 1
y/m
0.8 Ref. path Front axle Rear axle
0.6 0.4 0.2
Fig. 8. Practical implementation of PID controller. There exist empirical and model based methods for tuning PID controllers, Lunze (2010); Zacher and Reuter (2011). As a starting point, the empirical method by ZieglerNichols was used to obtain first controller gains. After further optimisation w.r.t to the tracking performance, the best values read Kp = 10.4 rad m−1 Ki = 9.4 rad m−1 s−1 Kd = 3.8 rad m−1 s.
0
0.5
1
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2
x/m Fig. 9. Paths with PFC for rth = 80 mm in xy-plane ·10−3
15
4.4 Performance comparison 10 dOff/m
A test path was used to evaluate and compare the controllers’ behaviour with the scale trucks in the DriveLab test environment. The performance of the PFC is depicted in Tab. 2. Note that the CTE is measured w.r.t. the front axle, as it follows the reference. Its value is positive for the vehicle being at the left of the path and negative otherwise.
5
0 Table 2. Performance PFC Threshold rth / mm 50 80 100
Cross track error (CTE) dOff / mm [-15, 20] [-5, 15] [-5, 20]
Oscillation w.r.t. path strong light light
CTE in curve small small big
−5
To gain greater insight into the performance parameters, Fig. 9 shows the reference for the front axle and the followed paths for the scenario rth = 80 mm, which gives the best result for this controller. It can be seen that the path is followed quite well, except the part of the curve, for which this algorithm gives less accurate tracking.
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Fig. 10. CTE with PFC for rth = 80 mm 0.6
0.4
The switching behaviour for the commanded steering angle can be observed in Fig. 11. Although some jump sizes are in the region of ∆δ ≈ 0.20 rad, the dynamics of the steering mechanism handles them satisfactorily. On the other hand, the behaviour of the CTEC is directly shown for the best evaluated controller gains. As can be seen in Fig. 12, initially this controller tracks the path very close. In the curve the truck follows through the outer side of the path, the opposite behaviour of the PFC. The performance degrades significantly after the curve. See Fig. 13 the related cross track error. The computed steering angle for tracking the path is smoother than for the PFC, Fig. 14. 310
δ/rad
The correspondent cross track error is shown in Fig. 10. 0.2
0 −0.2 0
10
20
30 t/s
Fig. 11. δ with PFC for rth = 80 mm
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This quite opposite behaviour of both controllers contributed to the idea of combining them to get the best result of each. The following section introduces the simple combined controller and its resulting performance.
1.2 1 0.8 y/m
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4.5 Combination of PFC and CTEC
Ref. path Front axle Rear axle
0.6
The resulting controller structure combining the PFC and the CTEC is shown in Fig. 15.
0.4 0.2 0
0.5
1
1.5
2
x/m Fig. 15. Scheme of the combined controller. Fig. 12. Paths with CTEC with best PID gains in xy-plane By using KCTEC = 1 − KPID , the result for different gains is presented in Tab. 3.
·10−3
40
Table 3. Performance combination Gain KPID 0.1 0.5 0.9
dOff/m
20 0
Oscillation w.r.t. path light light light
CTE in curve very small big big
This shows that with a predominant point follow controller the behaviour is significantly improved. For comparison reasons, Fig. 16 shows the reference and the driven paths. The reference is followed very close with this setup.
−20 −40 0
10
20
30 t/s
40
50
1.2
60
1
Fig. 13. CTE with CTEC
0.8 y/m
0.6
δ/rad
CTE dOff / mm [-8, 10] [-30, 19] [-42, 30]
0.6
0.4
0.4
0.2
0.2 0
0
Ref. path Front axle Rear axle
0.5
1
1.5
2
x/m −0.2
Fig. 16. Paths with PFC+CTEC, KPID = 0.1 in xy-plane 0
10
20
30 t/s
40
50
60
The resulting cross track error is very small for the full path, Fig. 17. It stays inside a range of [-8,10] mm. Additionally, it shows that the truck remains closer to the reference path.
Fig. 14. δ with CTEC
Finally, the needed steering angle is shown in Fig. 18. 311
2019 IFAC IAV 312 Gdansk, Poland, July 3-5, 2019
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·10−3
REFERENCES
10
dOff/m
5
0
−5 0
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20
30 t/s
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Fig. 17. CTE with PFC + CTEC and KPID = 0.1
δ/rad
0.4
0.2
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Fig. 18. δ with PFC + CTEC and KPID = 0.1 5. CONCLUSION It was able to show that a combination of two simple control strategies leads to satisfactory results for a path tracking controller. The controllers were implemented in the ROS framework and were tested with 1:32 scale trucks in the Drivelab test environment. A maximum cross track error of 10 mm was achieved, which should transform to about 30 cm in real world applications – depending on the positioning system. This is considered sufficient for the application in Autotruck-project. In a next step, the control strategy will be integrated in the real world truck. Measurements will reveal the true cross track error.
ACKNOWLEDGEMENTS This work is part of the project Autotruck, funded by the Federal Ministry of Economic Affairs and Energy Germany. 312
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