Pitch Dynamics Analysis for an Agricultural Tractor with Image Processing Validation through an Off-Board Camera

9th IFAC International Symposium on Advances in Automotive 9th IFAC International Symposium on Advances in Automotive Control 9th IFAC International Symposium on Advances in Automotive Control Available online at www.sciencedirect.com 9th IFAC France, International Orléans, June Symposium 23-27, 2019 on Advances in Automotive Control Orléans, France, June 23-27, 2019 Control Orléans, France, June 23-27, 2019 Orléans, France, June 23-27, 2019

ScienceDirect

IFAC PapersOnLine 52-5 (2019) 492–497

Pitch Dynamics Analysis for an Pitch Pitch Dynamics Dynamics Analysis Analysis for for an an Agricultural Tractor with Image Processing Pitch Dynamics Analysis for an Agricultural Tractor with Image Processing Agricultural Tractor with Image Processing Validation through Off-Board Camera Agricultural Tractor an with Image Processing Validation Validation through through an an Off-Board Off-Board Camera Camera Validation through an Off-Board Camera L. Onesto ∗∗ M. Corno ∗∗ S. Savaresi ∗∗

L. Onesto ∗ M. Corno ∗ S. Savaresi ∗ L. Onesto M. Corno S. Savaresi L. Onesto ∗ M. Corno ∗ S. Savaresi ∗ ∗ ∗ Dipartimento di Elettronica Informazione e Bioingegneria, Dipartimento di Elettronica Informazione e Bioingegneria, ∗ Dipartimento divia Elettronica Informazione e Bioingegneria, Politecnico di Milano, G. 34/5, Italy. Politecnico di Milano, via G. Ponzio Ponzio 34/5, 20133, 20133, Milan, Milan, Italy. Email: Email: ∗ Dipartimento Elettronica Informazione Bioingegneria, Politecnico di Milano,dimatteo.corno, via G. Ponzio 34/5, 20133,e Milan, Italy. Email: {luca.onesto, sergio.savaresi}@polimi.it. {luca.onesto, matteo.corno, sergio.savaresi}@polimi.it. Politecnico di Milano,matteo.corno, via G. Ponziosergio.savaresi}@polimi.it. 34/5, 20133, Milan, Italy. Email: {luca.onesto, {luca.onesto, matteo.corno, sergio.savaresi}@polimi.it. Abstract: This This work work proposes proposes an an analysis analysis of of the the pitch pitch dynamics dynamics of of aa heavy-duty heavy-duty vehicle, vehicle, Abstract: Abstract: This work proposes an analysis of the pitchperformed dynamics on of aa flat-asphalt heavy-duty surface, vehicle, namely an an agricultural agricultural tractor. Considering Considering maneuvers namely tractor. maneuvers performed on a flat-asphalt surface, Abstract: This work proposes anananalysis of the pitch dynamics ofanalysis heavy-duty vehicle, namely an agricultural tractor. maneuvers performed on aa flat-asphalt the analysis analysis is performed performed throughConsidering image processing processing approach. The focusessurface, on the the the is through an image approach. The analysis focuses on namely an agricultural tractor. Considering maneuvers performed on a flat-asphalt surface, the analysis is performed through an image processing approach. The analysis focuses on and the cabin displacement and on the vehicle body displacement. Moreover, the tires compression cabin displacement and onthrough the vehicle body displacement. Moreover, theanalysis tires compression and the is performed an image processing approach. The focuses the cabin displacement and on vehicle body displacement. Moreover, the compression and the analysis vehicle longitudinal sliptheare are evaluated. The analysis shows how thetires cabin and the theonbody body the vehicle longitudinal slip evaluated. The analysis shows how the cabin and cabin displacement andinon theare vehicle body displacement. Moreover, compression and the vehicle longitudinal slip evaluated. The longitudinal analysis shows howthe thetires cabin anddue thetobody displacements change function of the vehicle acceleration and how, the displacements change in slip function of the vehicle longitudinal acceleration and the the vehicle longitudinal are the evaluated. The analysis shows how the cabinhow, anddue theto displacements change in function of body the vehicle longitudinal acceleration and how, due tobody the tires compression, the cabin and can oscillate, at the end of a braking maneuver. The tires compression, the in cabin and the can oscillate, at theacceleration end of a braking maneuver. displacements change function of body the vehicle longitudinal and how, dueinertial to The the tires compression, cabin and body can at the end of a braking maneuver. The results are used used tothe evaluate the the feasibility of aaoscillate, road gradient gradient estimator based on the the results are to evaluate the feasibility of road estimator based on inertial tires compression, the cabin and the body can oscillate, at the end of aInbraking maneuver. The results are used to evaluate theaccelerometer feasibility of ainstalled road gradient estimator based on the inertial measurement of a mono axial in the cabin. particular, the cabin measurement of to a mono axial in the estimator cabin. In based particular, theinertial cabin results are used evaluate theaccelerometer feasibility ainstalled road gradient on cabin the measurement of a mono axial accelerometer installed in the which cabin.measures In particular, the speed cabin displacement needs to be be considered considered and an anofadditional additional sensor the displacement needs to and sensor which measures the cabin speed measurement of a mono axial accelerometer installed in the cabin. In particular, the cabin displacement needs to be considered and an additional sensor which measures the cabin speed is required to avoid a drop of performance. is required to avoid to a drop of performance. displacement be considered and an additional sensor which measures the cabin speed is required to needs avoid a drop of performance. © required 2019, IFAC of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. is to(International avoid a dropFederation of performance. Keywords: Vehicle Vehicle dynamics, dynamics, Pitch, Pitch, Estimation Estimation Algorithms, Algorithms, Kalman Kalman Filters, Filters, Image Image Processing Processing Keywords: Keywords: Vehicle dynamics, Pitch, Estimation Algorithms, Kalman Filters, Image Processing Keywords: Vehicle dynamics, Pitch, Estimation Algorithms, Kalman Filters, Image Processing 1. INTRODUCTION INTRODUCTION vides aa direct direct measurement measurement of of the the longitudinal longitudinal (specific) (specific) 1. vides 1. INTRODUCTION vides directinmeasurement of theon longitudinal force. aWhile, While, the method method based based the torque torque (specific) measureforce. in the on the measure1. INTRODUCTION vides aWhile, direct measurement of theon longitudinal (specific) force. in the method based the torque measurement, the force is obtained relying on a vehicle model. Modern Agricultural Agricultural tractors tractors are are complex complex machines. machines. They They ment, the force is obtained relying on a vehicle model. Modern force. While, inmodel the method based on theatorque measurement, the force is obtained relying on vehicle model. Hence, all the uncertainties affects the results. For Modern Agricultural tractors are complex machines. They are designed designed to to operate operate on on aa wide wide array array of of terrains terrains and and concon- Hence, all the model uncertainties affects the results. For are the force is obtained relying on a the vehicle model. Hence, all the model uncertainties affects results. For Modern Agricultural tractors are array complex machines. this reason, it is stated that the slope estimation accuracy are designed to operate on a wide ofthey terrains andThey con- ment, ditions. To better face these situations, are equipped this reason, it is stateduncertainties that the slope estimation accuracy ditions. To better face these situations, they are equipped Hence, allwhen the affects the results. For reason, it ismodel statedanthat the slope estimation accuracy are tohydraulic operate on a wide arrayand ofthey terrains and conincreases using accelerometer. ditions. To better face these situations, are equipped withdesigned complex transmissions suspension sys- this increases when using anthat accelerometer. with complex hydraulic transmissions and suspension systhis reason, it is stated the slope estimation accuracy increases when using an accelerometer. ditions. To better face these situations, they are equipped with complex hydraulic transmissions and suspension systems. Understanding Understanding the the pitch pitch dynamics dynamics of of tractors tractors in in In Corno et al. (2014) the usage of a reduced sensor set tems. accelerometer. In Corno when et al. using (2014)anthe usage of a reduced sensor set with complex hydraulicthe transmissions and suspension systems. Understanding pitch to dynamics of and tractors in increases these varied conditions is useful the design tuning In Corno et al. (2014) the usage of a reduced sensor set (i.e. longitudinal acceleration and speed) speed) is used used to to develop these varied conditions is useful to the design and tuning (i.e. longitudinal acceleration and is develop tems. Understanding the pitch to dynamics of and tractors in In these varied conditions is useful the design tuning of many of the tractor subsystems: for example the cabin Corno et al. (2014) the usage ofconsiders a reduced sensor set (i.e. longitudinal acceleration and speed) is usedthe to develop a Kalman-filtering approach that vehicle of many of the tractor subsystems: for example the cabin a Kalman-filtering approachand that considers the vehicle these varied conditions isLanger useful to the design and tuning of many of the tractor subsystems: for example the cabin a(i.e. suspension control (see et al. (2016)), traction longitudinal acceleration speed) is used to develop Kalman-filtering approach that considers the vehicle longitudinal dynamics, dynamics, coupled coupled with with aa fictitious fictitious road road slope slope suspension control (see Langer et for al. example (2016)),the traction of manyand of the tractor cabin suspension control (seesubsystems: Langer et al. traction control automatic gear shifting (see(2016)), Andersen et al. al. longitudinal alongitudinal Kalman-filtering approach that the dynamics, coupled with considers a fictitious roadvehicle slope dynamics. The algorithm is developed for the case study control and automatic gear shifting (see Andersen et dynamics. The algorithm is developed for the case study suspension (seegear Langer et al. traction control automatic shifting (see(2016)), Andersen et al. longitudinal (2003)).and control dynamics, with a fictitious road study slope dynamics. The algorithm is developed for the case of an an Electrically Electrically Powercoupled Assisted Cycle. (2003)). of Power Assisted Cycle. control (2003)).and automatic gear shifting (see Andersen et al. dynamics. The algorithm is developed for the case study of an Electrically Power Assisted Cycle. One of of the the most most useful useful information information on on the the tractor tractor state state is is This work focuses on the the vehicle pitch dynamics. (2003)). One an Electrically Power Assisted Cycle. pitch dynamics. This work focuses on the the vehicle One of the mostThe useful information the tractor is of the road road grade. open scientific on literature offersstate many This work dynamics focuses onanalysis the theis vehicle pitchthrough dynamics. The pitch pitch performed an the grade. The open scientific literature offers many The dynamics analysis is performed through an One of the most useful information on the tractor state is the road grade. The open that scientific literature offers grade many This examples of subsystems subsystems employ the terrain terrain work focuses onanalysis the that theisallows vehicle pitch dynamics. The pitch dynamics performed through an image processing approach the reconstruction examples of that employ the grade imagepitch processing approach thatisallows the reconstruction the road grade. The openthe scientific literature offersand many examples of to subsystems that employ the terrain grade information improve tractor performance or The dynamics analysis performed through an image processing approach thesensors. reconstruction of signals signals not available withthat the allows onboard information to improve the tractor performance and or of not available with the onboard sensors. examples of subsystems that employ the terrain grade information to improve the tractor performance and or safety. In Druzhinina et al. (2000) a braking system for image processing approach that allows the reconstruction of signals not available with the onboard sensors. safety. In Druzhinina et al. (2000) a braking system for information to improve tractor and for or of The pitchnot dynamics ofwith tractor are different different from the the safety. et the al. the (2000) braking system truckIn is Druzhinina developed, where roadaperformance gradient, estimated signals availableof the onboard sensors.from The pitch dynamics aa tractor are aa truck is developed, where the road gradient, estimated The pitch dynamics of awell tractor are different from the safety. In Druzhinina et al. (2000) a braking system for ones of a car (that are studied in the literature). aastruck is developed, where the roadisgradient, estimated a constant unknown parameter, used to modulate ones pitch of a car (that are well studied in the literature). astruck a constant unknown parameter, is used to estimated modulate The dynamics ofdiffers awell tractor are different from the of a car (that are studied in the literature). a is developed, where the the road In particular, particular, tractor from onroad vehicles under as constant unknown parameter, isgradient, used toofmodulate theacontrol control action. Additionally, knowledge the road road ones In aa(that tractor differs from onroad vehicles under the action. Additionally, the knowledge of the ones of a car are well studied in the literature). In particular, a tractor differs from onroad vehicles under as a constant unknown parameter, is used to modulate several aspects: the control action. Additionally, the knowledge of the road slope can can be be used used to to prevent prevent needless needless shifting shifting of of automatic automatic several aspects: slope In particular, a tractor differs from onroad vehicles under several aspects: the control the knowledge the road slope can beaction. used toAdditionally, prevent needless shifting ofof automatic transmission. For this this purpose, in Ohnishi et al. (2000) two • The The cabin and and the the vehicle vehicle body body have have aa different different pitch pitch transmission. For purpose, in Ohnishi et al. (2000) two several aspects: slope can be used to prevent needless shifting of automatic • cabin transmission. For this purpose, in Ohnishi al. case (2000) two estimation algorithms algorithms are developed developed for etthe the study • The cabin and the vehicle body have a different pitch angle, because of the cabin suspension system. estimation are for case study transmission. For this purpose, in Ohnishi al.longitudinal (2000) two angle, because of the cabin suspension system. pitch estimation algorithms are forofetthe case study of aa car. car. One One exploits the developed information •• The and the vehicle have a different angle, because of cabinbody suspension system. Manycabin tractors arethe equipped with a front front axles only only of exploits the information ofthe aa longitudinal estimation algorithms are developed for case study • Many tractors are equipped with a axles of a car. One exploits the information of a longitudinal accelerometer, the the others others exploits exploits the the vehicle vehicle estimated estimated angle, because of cabin suspension system. with a front axles only • Many tractors arethe equipped load leveling suspension system. accelerometer, of a car.They Oneconclude exploits the exploits information of ameasurement longitudinal load leveling suspension system. accelerometer, the others vehicle estimated torque. that with thethe inertial •• Many tractors are equipped withare a front axles load leveling suspension system. The tires tires of heavy-duty heavy-duty vehicles subject to only non torque. They conclude that with the inertial measurement accelerometer, the others vehicle estimated • load The of vehicles are subject to non torque. They conclude thatexploits withThe thethe inertial measurement the estimation is more accurate. usage of torque and of leveling suspension system. • The tires compressions of heavy-dutyinvehicles are subject to non negligible both vertical and longituthe estimation is more accurate. The usage of torque and of torque. They conclude that withcompared the usage inertial measurement negligible compressions invehicles both vertical and longituthe estimation is more isaccurate. The of Lingman torque and of inertial measurement deeply in and • The of heavy-dutyin are subject to non negligible compressions both vertical and longitudinaltires direction. inertial measurement isaccurate. deeply compared in Lingman and the estimation is more is The usage of Lingman torque and of dinal direction. inertial measurement deeply on compared in and Schmidtbauer (2002), focusing heavy duty vehicles. For negligible compressions in both vertical and longitudinal direction. Being off-highway off-highway vehicles, vehicles, the the tyres tyres are are subject subject to to Schmidtbauer (2002), is focusing on heavy duty vehicles. and For inertial measurement deeply on compared in Lingman •• dinal Being Schmidtbauer (2002), focusing heavy duty For both approaches, approaches, an estimator estimator is performed invehicles. Kalmandirection. • Being off-highway vehicles, the tyres are subject to considerable longitudinal slip. both an is performed in aa KalmanSchmidtbauer (2002), focusing on heavy duty vehicles. For considerable longitudinal slip. both approaches, an estimator is performed a Kalmanfilter fashion. fashion. Moreover, the estimation estimation of the theinvehicle vehicle mass • Being off-highway vehicles, the tyres are subject to considerable longitudinal slip. filter Moreover, the of mass both approaches, an estimation estimator isofperformed invehicle a is Kalmanfilter fashion. Moreover, the estimation of the mass This This considerable paper is organized as follows. In Section Section 2, 2, the the is also included. The the road slope related longitudinal slip. paper is organized as follows. In is alsofashion. included. The estimation of the road slope is related filter Moreover, theforce. estimation of the vehicle mass This paper islayout organized follows. Section Section 2, the Thevehicle estimation of The the road slope is related is also included. experimental of the theasvehicle vehicle is In presented. to the longitudinal inertial sensor proexperimental layout of is presented. Section to the included. longitudinal vehicle force. The inertial sensor pro- experimental paper islayout organized follows. Section Section 2, the is Thevehicle estimation the road slope is related of theasvehicle is In presented. to also the longitudinal force.of The inertial sensor pro- This experimental layout of the vehicle is presented. Section to the longitudinal vehicle force. The inertial sensor pro2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

Copyright © 2019 IFAC 492 Copyright 2019 responsibility IFAC 492Control. Peer review©under of International Federation of Automatic Copyright © 2019 IFAC 492 10.1016/j.ifacol.2019.09.078 Copyright © 2019 IFAC 492

2019 IFAC AAC Orléans, France, June 23-27, 2019

L. Onesto et al. / IFAC PapersOnLine 52-5 (2019) 492–497

3 presents and validates the image processing approach. Section 4 shows the experimental results of the pitch dynamics analysis. Finally, in Section 5, the results of the analysis are exploited to evaluate the feasibility of a road gradient estimator. 2. EXPERIMENTAL LAYOUT The heavy-duty off-highway vehicle considered in this work consists in a tractor (model: Deutz-Fahr 6140). Figure 1 shows the elements that characterize the pitch dynamics of the tractor, namely: the cabin, the cabin suspension, the vehicle body, the front and the rear wheels, the front suspension. Note the tractor is not equipped with

493

∆yF , ∆xR and ∆yR respectively, are considered. Please note that with the onboard sensors it is not possible to obtain all the mentioned variables, hence additional instrumentation is required. This can be avoided recording the maneuvers of the tractor through an external camera. In this Section, the image processing algorithm used to extract the informations from the videos is presented. Please note that with the proposed method it is possible to evaluate the longitudinal compression of the tires only when the wheels are locked. The maneuvers are performed on the same flat-asphalt surface and registered by a camera (model: SONY RX100), fixed on a support, with a frame-rate of 250 frames per second. Figure 2 shows the experimental layout used for

Cabin

Body

Wheel

Fig. 2. Experimental layout for image processing Fig. 1. Experimental layout a rear suspension. The front suspension is pneumatic and a load-levelling control is in charge of keeping the suspension leveled. The load-levelling control consists of a quasi-static law and its response time is in the order of 5 seconds. The vehicle is equipped with the following sensors: • A mono axial accelerometer installed inside the cabin, that provides the longitudinal acceleration of the cabin Axc . This is the only accelerometer installed in the production vehicle. • A 6 axis Inertial Measurement Unit (IMU) installed on the vehicle body. In the following analysis only the pitch rate θ˙B and the longitudinal acceleration AxB of the tractor body are considered. This IMU is installed only on the prototype and not on the production vehicle. • An encoder installed in the transmission system, that provides the longitudinal speed VxE of the wheels. The encored is installed both on the prototype and on the production vehicle. Moreover the vehicle is equipped with a cruise control system and a continuously variable transmission system. They allows the driver to set a reference speed to the tractor. In particular, this aspect will be exploited to perform speed inversion tests without acting on the brakes.

the image analysis. Six markers (Mi , i = 1, .., 6) are installed on the vehicle. Table 1 indicates for each marker, the supportive element, the height with respect to the road, when the vehicle is at standstill, and the depth with respect to the side of the tires. Analysing the position of the markers it is possible to measure the variables of interests. The position of the marker in world coordinates is obtained following the steps: (1) Lens distortion correction. (2) Detection of the position of the markers on the image plane. (3) Reprojection of the markers’ position in world coordinates. To accomplish the first and the third step of the procedure, the camera needs to be calibrated. According to the Pinhole Camera Model (see Heikkila and Silven (1997)), the relationship between the image plane and the world coordinates is:   R [x y 1] = [X Y Z 1] K (1) t

3. IMAGE ANALYSYS ALGORITHM

where [x y 1] are the coordinates in the image plane in pixel, [X Y Z 1] are the world coordinates in meters, K is the intrinsic matrix (composed by the intrinsic parameters), while R and t are the Rotation matrix and the translation vector and compose the extrinsic parameters.

To perform the vehicle pitch dynamics, the cabin’s pitch angle θC , the body’s pitch angle θB , the longitudinal and the vertical compression of the front and rear wheels, ∆xF ,

The world points are transformed to camera coordinates using the extrinsics parameters. The camera coordinates are mapped into the image plane using the intrinsics parameters.

493

2019 IFAC AAC 494 Orléans, France, June 23-27, 2019

L. Onesto et al. / IFAC PapersOnLine 52-5 (2019) 492–497

In this work, the extrinsic and intrinsic parameters are obtained as discussed in Zhang (2000). In particular: • the intrinsic parameters, describing the internal camera geometric and optical characteristics, are estimated using a training set of 80 pictures of a checkerboard pattern in different positions. The resulting reprojection error has a mean value of 0.3 pixel which is considered satisfactory for this application. • the extrinsic parameters allow for the reprojection of the markers’ position in world coordinates. Since the markers lay in five different (and parallel) vertical planes, five different sets of extrinsic parameters are defined. This is accomplished exploiting the information of the depth with respect to the tires side. Hence, for each marker the following translation vector ti is defined:     tx 0 ti = ty + 0 , i = 1, .., 6 (2) tz δz i where tx , ty and tz are the parameters of the translation vector, obtained from the camera calibration procedure. As regards the Rotation matrix R, since the five planes are parallel, it is the same for all the markers. The calibration procedure is performed placing a checkerboard on the side of the tires (see Figure 2). The resulting reprojection error has a mean value of 2.48 [mm]. Table 1. Markers configuration Marker M1 M2 M3 M4 M5 M6

Element Cabin Cabin Body Body Front Wheel Body

Height [mm] 2715 2700 1110 1095 625 825

δz [mm] 655 525 1190 1190 260 335

As regards the second step of the procedure, for each frame, the position of the markers in the image plane is extracted through an Aggregate Channel Features (ACF) detector (see Doll´ ar et al. (2014)). The detector, trained with 21 labelled images, provides the position (in pixels) of the candidate objects and their confidence score. Defining a threshold on the confidence score, it is possible to properly detect the location of the six markers within the image, as Figure 3 shows. Once the markers’ position in world coordinates are available, it is possible to measure the variables of interest as follows. The measurement of the cabin’s pitch angle θC is obtained considering the line connecting M1 and M2 . Defining (x1 , y1 ) and (x2 , y2 ) their position coordinates, the line linking M1 M2 can be expressed as: y = m12 · x + q where its slope can be calculated as y1 − y 2 m12 = x1 − x2 Finally the cabin’s pitch angle θC is obtained as

(3) (4)

(5) θC = − arctan(m12 ) Then, trough differentiation, it is possible calculate the cabin’s pitch rate θ˙C . 494

Fig. 3. Markers extraction trough ACF detector: on the top all the candidate objects, on the bottom only the markers selected checking the confidence scores Following the same procedure, considering the pairs (M3 , M4 ) and (M3 , M6 ) it is possible to calculate the body’s pitch rate θ˙B = θ˙34 = θ˙36 . Since the mentioned pairs are not aligned with respect to the vehicle’s body, the body pitch angle θB can be computed as: θB = θB0 + θ34 − θ340 = θB0 + θ36 − θ360 where θB0 , θ340 and θ360 are respectively the displacement of the body and of the two lines when the tractor is standing still. The compression of the front and rear tires can be measured from the motion, in the longitudinal and in the vertical direction, of M5 and M6 respectively. 3.1 Validation of the Image Analysys Algorithm Firstly, the performance of the camera calibration procedure are evaluated. From a random video frame, the position of the markers are manually obtained. Then, exploiting the intrinsic and the extrinsic parameters, the distance from the i-th and the j-th marker, called dij is measured and compared to the real one. The accuracy of the measurements is in the order of the centimeters. In particular the root mean square error is equal to 0.17 [m]. The second phase of the validation is based on the velocity computation. It is possible to compare the velocity of the markers to directly measured values: • the longitudinal speed VxE measured through a wheel encoder, and the longitudinal speed of the markers, which is obtained trough the differentiation of their longitudinal position, during a test without wheel slip. • the body pitch rate θ˙B measured by the 6-axis IMU to the ones measured through video processing θ˙34 and θ˙36 .

2019 IFAC AAC Orléans, France, June 23-27, 2019

L. Onesto et al. / IFAC PapersOnLine 52-5 (2019) 492–497

2

495

15 M1 M5 M6 V xE

1

10

5

Pitch rate [deg/s]

Speed [m/s]

0

-1

-2

0

-5

-10 -3

-15

-4 6

6.5

7

7.5

8

8.5

9

9.5

-20 29.5

10

30

30.5

31

31.5

Time [s]

32

32.5

33

33.5

34

34.5

35

Time [s]

• Both the measured pitch rate θ˙34 and θ˙36 are consistent with the one measured by the IMU. In particular, the root mean square error in the time  window from deg 30 to 35 seconds is equal to 1.79 s . • Even in this case the image processing SNR is worse with respect to the one measured by the IMU. Overall, the image processing tool provides a reliable, albeit noisy, method to measure the position and velocities of part of the tractor that cannot be directly measured with onboard sensors. 4. PITCH DYNAMICS ANALYSIS The pitch dynamics of the tractor is analysed in the following case studies: • Speed inversion • Braking (to complete stop)

Speed [m/s]

2

M1

M5

V xE

M6

0 -2 -4 5.5

Pitch rate [deg/s]

Figure 5 shows the comparison of the body pitch rate measurements at the end of a braking maneuver. The following remarks are due:

• As regards the body displacement, at the end of the acceleration transient the vehicle body displacement increases by 1 degree. This fact is confirmed by the body pitch rate.

6

6.5

7

7.5

8

8.5

9

9.5

10

6

6.5

7

7.5

8

8.5

9

9.5

10

6

6.5

7

7.5

8

8.5

9

9.5

10

8

8.5

9

9.5

10

7 3 -1 -5 -9 5.5 6

A x [m/s2 ]

• The longitudinal speeds obtained from M1 , M4 and M5 are consistent with the one measured by the wheel encoder, however the Signal to Noise Ratio (SNR) is worse. In particular the root mean square error obtained considering all the six markers in the  time  window from 6 to 10 seconds is equal to 0.20 m s . • The wheels speed VxE is provided by an encoder.   Hence, this measurement is not reliable around 0 m s (i.e. between 8.5 and 9 seconds).

Fig. 5. Validation: pitch rate comparison at the end of an hard braking maneuver

4 2 0 -2 5.5

Pitch angle [deg]

Fig. 4. Validation: speed comparison in a speed inversion test Figure 4 shows the comparison of the longitudinal speed measured by the wheel encoder and by three markers, in a speed inversion test. The following remarks are due:

4 12

3

34

36

2 1 0 -1 5.5

6

6.5

7

7.5

Time [s]

Fig. 6. Pitch dynamics analysis of a speed inversion test

4.1 Speed inversion tests analysis Figure 6 shows the pitch dynamics analysis of a speed inversion test. The following remarks are due: • At the end of the acceleration transient the variation of the cabin displacement is around 2 degrees. 495

4.2 Cabin and body displacement analysis through inertial measurements The analysis of the body and of the cabin displacements can be performed using inertial measurements. The measurement of the accelerometer located in the cabin depends

2019 IFAC AAC 496 Orléans, France, June 23-27, 2019

L. Onesto et al. / IFAC PapersOnLine 52-5 (2019) 492–497

on 3 factors: the road gradient θ, the vehicle’s longitudinal acceleration V˙ x and the cabin displacement θC . The relationship is described by the following equation: V˙ x = Ax − g · sin(θ + θC )

the image processing approach. In particular, the cabin displacement θC affects the cabin acceleration AxC . 4.3 Braking Maneuvers analysis

C

In particular, the relationship between the vehicle’s acceleration and the cabin displacement (i.e. θC = θC (V˙ x )) is analysed. If the longitudinal slip is negligible, the vehicle’s longitudinal acceleration can be obtained filtering the longitudinal wheels speed VxE . As regards the experimental tests: • The tests are performed in plane, so the road gradient is zero. Hence, the cabin displacement can be analysed comparing the cabin acceleration AxC and the vehicle longitudinal acceleration. • The cruise control is in charge to track the reference speed (respectively ±5, ±10 and ±20 km h ) set by the driver. As showed in the following, the wheel slip effect can be neglected for this kind of tests. Considering the vehicle body acceleration AxB , with the same procedure, it is possible to analyse the displacement of the vehicle body during the maneuvers. Figure 7 presents the comparison between the three accelerations. The following remarks are due:

3

3

2

2

2

1

1

1

0

AxC [m/s2]

3

AxB [m/s2]

AxC [m/s2]

• In first approximation, a linear relationship between the accelerations holds. • The plot on the left shows how the cabin acceleration differs from the vehicle’s one. This is due to the cabin displacement θC . • The plot in the center shows that the body acceleration is almost the same of the vehicle’s one, save for an offset. In other words, the vehicle body pitch dynamics is not perceptible from this analysis. This is may due to the measurement noise that characterizes both the measurements. • The plot on the right shows that the body and the cabin accelerations are almost the same, except for an offset. This means that the body and the cabin displacements are different in absolute value, but they are subject to almost the same pitch angle variation.

0

-1

-1

-2

-2

-2

-3 -3 -2 -1

0

1

2

3

-3 -3 -2 -1

0

1

2

3

• The difference between the wheels speed and the markers speed indicates the presence of slip. • Figure 9 shows the wheel slip λ, calculated respect to the speed of M5 . In first approximation, it is possible to consider the wheel slip constant. In particular, the ¯ = 0.25 while the mean deceleration is mean slip is λ m ¯ ˙ Vx = −6 s2 . • The image processing approach shows how the cabin and the vehicle body have a variation of displacement of -2 and -1 degrees respectively. • At the beginning of the braking maneuver, the front and the rear tire has a compression of +3 and -3 centimeters. This fact is due to the load transfer. During the Locked Wheel Phase: • At the beginning of the phase, both the wheels and the markers speeds are zero. This means that the vehicle does not go forward anymore when the wheels are locked. However the vehicle body and the cabin are affected by oscillation. This is due to the tires compression. • In particular, the front and the rear tires have a longitudinal compression of 5 centimeters. Hence, even if the wheels are locked, the cabin and the vehicle body are subject to accelerations. • The body and the cabin oscillations last for 3 seconds circa. 5. FINAL CONSIDERATIONS ON TERRAIN GRADE ESTIMATION This Section discusses the feasibility of a road gradient estimator based on the longitudinal accelerometer installed inside the cabin. The considered approach is the one presented in Corno et al. (2014), where the developed algorithm is based on the vehicles longitudinal dynamics: V˙ x = Ax − g · sin(θ) (6) M

0

-1

Figure 8 shows the pitch analysis of a braking maneuver test. The maneuver can be divided in two parts: the Deceleration Phase and the Locked Wheel Phase. The Deceleration Phase starts when the driver acts on the brakes and it ends when the wheels are locked. Then, the Locked Wheel Phase begins. During the Deceleration Phase:

-3 -3 -2 -1

0

1

2

3

AxB [m/s2]

Fig. 7. Cabin and body displacement analysis performed through inertial measurements during speed inversion tests. Overall, the analysis performed through the inertial measurements is consistent with the results obtained through 496

where AxM is the measured longitudinal   acceleration, g is the gravitational acceleration in sm2 , V˙ x is the time derivative of the vehicle’s longitudinal speed and θ is the road slope. Defining the variable θ as: θ = sin(θ) the model becomes linear. Including a fictitious road slope dynamics, (6) can be rewritten in state space form:   V˙ x = AxM − g · θ + ηx1  θ˙ = ηx2   y = Vx + ηy where ηx1 , ηx2 and ηy are Gaussian noises. A Kalman filter can be designed to estimate the state variables of the

2019 IFAC AAC Orléans, France, June 23-27, 2019

L. Onesto et al. / IFAC PapersOnLine 52-5 (2019) 492–497

497

2

6

0

-2 7.5 18

8

8.5

9

9.5

10

10.5

11

11.5

4 M1 M5 M6 V xE

2 0

12

8

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.5

8.6

8.7

8.8

Time [s]

12 6

0.6

0 -6

Slip [-]

Pitch rate [deg/s]

M1 M5 M6 V xE

4

Speed [m/s]

Speed [m/s]

6

-12 -18 7.5 10

8

8.5

9

9.5

10

10.5

11

11.5

0.4 0.2

12

0 8

Ax [m/s2]

3

8.3

8.4

-4

Pitch angle [deg]

-18 7.5 4

Fig. 9. Experimental results: slip during the Deceleration phase 8

8.5

9

9.5

10

10.5

11

11.5

12

REFERENCES

12

3

34

2

36

1 0

-1 7.5 0.1

Tires X Comp [mm]

8.2

Time [s]

-11

8

8.5

9

9.5

10

10.5

11

11.5

12

9

9.5

10

10.5

11

11.5

12

0.05 0 xF

-0.05

xR

-0.1 7.5 0.06

Tires Y Comp [mm]

8.1

8

8.5

yF

0.04

yR

0.02 0 -0.02 7.5

8

8.5

9

9.5

10

10.5

11

11.5

12

Time [s]

Fig. 8. Pitch dynamics analysis of a braking test system, namely Vx and θ . The inputs of the algorithm are the measurements of the longitudinal speed VxE and of the longitudinal acceleration AxC . Then, the following consideration can be done: • As shown in Subsection 4.2, the cabin displacement θC affects the cabin acceleration AxC . Hence, a compensation of the cabin displacement is required to preserve the estimation performances. V −V • Due to the wheel slip λ, defined as λ = x Vx xE , the real speed of the vehicle Vx is not available. Since it is not computable from the available signals, it is not possible to compensate its effect. However, in low slip conditions, the estimation performance of the proposed approach is satisfactory. If the wheel slip is not negligible, an additional sensor providing the cabin speed is required to avoid a drop of performance. 497

Andersen, T.O., Hansen, M.R., and Conrad, F. (2003). Robust control of oscillations in agricultural tractors. In ASME 2003 International Mechanical Engineering Congress and Exposition, 89–95. American Society of Mechanical Engineers. Corno, M., Spagnol, P., and Savaresi, S.M. (2014). Road slope estimation in bicycles without torque measurements. IFAC Proceedings Volumes, 47(3), 6295–6300. Doll´ar, P., Appel, R., Belongie, S., and Perona, P. (2014). Fast feature pyramids for object detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36(8), 1532–1545. Druzhinina, M., Moklegaard, L., and Stefanopoulou, A. (2000). Compression braking control for heavy-duty vehicles. In American Control Conference, 2000. Proceedings of the 2000, volume 4, 2543–2547. IEEE. Heikkila, J. and Silven, O. (1997). A four-step camera calibration procedure with implicit image correction. In Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on, 1106–1112. IEEE. Langer, T., Holm-Petersen, K., and Metker, D. (2016). Comfort evaluation criteria for pitching vibration damping of agricultural tractors. 74th Internationale Tagung Landtechnik (Agricultural Engineering), VDI Berichte, (2273), 437–44. Lingman, P. and Schmidtbauer, B. (2002). Road slope and vehicle mass estimation using kalman filtering. Vehicle System Dynamics, 37(sup1), 12–23. Ohnishi, H., Ishii, J., Kayano, M., and Katayama, H. (2000). A study on road slope estimation for automatic transmission control. JSAE review, 21(2), 235–240. Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on pattern analysis and machine intelligence, 22.