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COMPARISON OF OPTICAL AND GPS BASED TIRE SLIP ANGLE ESTIMATION
COMPARISON OF OPTICAL AND GPS BASED TIRE SLIP ANGLE ESTIMATION Christophe Lamy ∗ Julien Caroux ∗ Michel Basset ∗ G´ erard-L´ eon Gissinger ∗ Damien Poli ∗∗ Pierre Romieu ∗∗
Laboratory MIPS, MIAM group, Universit´e de Haute Alsace, 12 rue des fr`eres Lumi`ere, 68093 Mulhouse Cedex, France ∗∗ Renault - Research Department, Centre Technique d’Aubevoye, Parc de Gaillon, 27940 Aubevoye, France ∗
Abstract: In order to improve the lateral behavior modeling of a road vehicle, an accurate determination of tire slip angle is needed (typically an accuracy close to 0.1◦ ). In this paper, first, we compare two industrial sensors delivering information of sideslip angle: an optical sensor and a GPS/INS sensor. For this purpose, a specific test bench was developed. The limits of both sensors with regard to the above mentioned precision requirement, are studied, as well for static as for dynamic vehicle maneuvres. Secondly, for the GPS/INS sensor giving better results, we investigate the possibility of direct tire slip angle measurement by mounting this sensor in a plane parallel to the wheel rim. The developed mechanical adapter suffers from an inherent drawback for this kind of mounting, in terms of additional movements, compared to commonly used optical sensors. In spite of this supplementary perturbation, we show that the GPS/INS sensor precision is c 2007 IFAC still better than the optical sensor’s. Copyright Keywords: Vehicle dynamics, tires, precision measurements, global positioning systems
1. INTRODUCTION Today, important efforts are made to improve vehicle services such as comfort, safety, consumption and reliability. They require increasing means of simulation and thus a search for increasingly powerful models. Within the framework of vehicle dynamics study, the integration into the global vehicle model of a model describing its interaction with the ground is vital. However, the understanding of the phenomena involved in the transmission of strains by the tire is still limited. So, the improvement of the models which describe this
interaction is imperative in order to upgrade the modeling of the dynamics which extends the field of investigation. In the literature, a number of authors have carried out research on modeling the tire and the wheelground interface. A good synthesis of the main models can be found in (Porcel et al., 2001). The models given as references are: Pacejka model (Pacejka and Bakker, 1991), a semi-empirical model, Guo (Guo and Ren, 2000) and Milliken (Milliken and Milliken, 1995) models. In all these
models, for a given grip, the inputs considered are the wheel slip, the slip angle, the camber angle and the vertical tire strain; the strains and the moments at the wheel/road interface are processed as outputs. To obtain a better understanding, and then a sharper and more robust model of the tire, the measurement or a precise estimation of the tire model inputs are necessary. The present paper deals with accurate measurement of tire slip angle by the way of the evaluation of the sensors performance. We will show that the quality of the slip angle measurement depends on the used sensor and the dynamic range of the maneuvers performed with the test vehicle. The paper is organized as follows: in the second section, a definition of the tire slip angle is introduced, and two industrial sensors, permitting the determination of tire slip angle, are presented. The third section is dedicated to the characterization phase of the sensors using a specific test bench mounted at the rear of the laboratory test car. In the last section, the above sensors are fixed in a plane parallel to the wheel rim of the same test vehicle using a mechanical installation, developed by the laboratory. The sensors measurements obtained during real tests validate the mechanical adapter in spite of its inherent drawbacks.
FY
Y
VX
O Contact surface
VYi V
X
αi
Fig. 2. Definition of the tire slip angle This angle is generally defined by the expression: VY i αi = arctan i = 1, 2, (1) VXi where VY i is the lateral velocity with respect to the front and rear wheel axis, and VXi is the tire longitudinal velocity. Concretely, industrial companies propose different solutions to measure the tire slip angle. Two methods of determination can be highlighted and are presented in the next subsection.
2.2 Industrial sensors In the context of industrial tire slip angle measurement, there are essentially two different principles of measurement: an optical cross-correlation approach and a GPS/INS approach.
2. TIRE SLIP ANGLE OVERVIEW 2.1 Tire slip angle definition When the tire is subjected to lateral promptings (cornering, camber angle, etc.), a self-aligning torque is generated due to the tire elasticity. It modifies the original direction of the wheel with an angle called tire slip angle. The contact surface between the tire and the road changes according to the solicitations on the tire. The surface can be decomposed into two parts (Fig. 1): • a tension or sliding area at the rear; • a compression or friction area at the front. friction area
Y
X α
motion direction V
drift area
Fig. 1. Contact surface between the tire and the road in grip limit condition The tire slip angle is commonly considered as the angle between the longitudinal tire axis and the velocity vector of the tire center, named O in Fig. 2.
Optical principle A contactless optical sensor is commonly used to measure tire slip angle directly (Zami, 2005). It consists in measuring the longitudinal and lateral components of the velocity vector of the wheel and computing the tire slip angle according to equation 1. The slip angle can be also obtained directly as an output of the sensor. This sensor is often used in the context of automotive control such as in (Caroux et al., 2006), (Stephant et al., 2004), (Lozia, 1998) and (Uno et al., 1994). GPS/INS principle The GPS/INS sensor consists of a Inertial Navigation System (INS) sensor assisted by Global Positioning System (GPS) data with a positioning accuracy of 2 cm. The major drawback of sideslip angle determination with only a GPS device is the low (10 Hz) update rate of most GPS receivers. On the other hand, the direct time integration of INS measurements (without GPS information) can accumulate sensor errors. Furthermore, this principle is limited by the drift in sensor bias and sensitivity. So the INS data and the GPS information are combined by a Kalman filter. The Kalman algorithm is presented in many works such as in (Ryu and Gerdes, 2004), (How et al., 2002) and (Daily and Bevly, 2004). This sensor uses GPS information and more precisely
the velocity and the attitude to determine a slip angle according to the following equation:
Step response: 5°
9 8
(2)
3. CHARACTERIZATION OF THE SENSORS Characterization corresponds to estimating the precision, the latency time and the rise time of the sensors.
3.1 Test bench presentation The system of characterization of the sensors is fixed to the rear of the test vehicle. The two mentioned sensors are mounted on this test bench. By the mean of a servomotor, the sensors can be rotated with respect to the car. This rotation generates an identical virtual slip angle for the sensors. The GPS antenna determines the direction of the vehicle velocity vector, while the sensor body measures the sensor attitude. Therefore, when the vehicle follows a trajectory with the servomotor in zero position, the slip angles measured by both GPS/INS and optical speed sensors correspond to the sideslip angle at the rear of the car. If the vehicle moves in a straight trajectory and a rotation of the servomotor is made, the sensors measure the virtual slip angle which is created. This test bench allows to generate accurate rotational angles, with a range of ±30◦ , an accuracy below 0.1◦ . Both amplitude and speed of the rotational consign are controlled.
3.2 Protocol Step input excitation First the sensors are tested with step inputs of slip angle for three different magnitudes (0.5◦ , 1◦ and 5◦ ) and three constant vehicle speeds (60, 80 and 100 km/h) while keeping vehicle attitude constant. For practical reasons, the discontinuous part of the step input is realized by a ramp with several rising speeds. Fig. 3 shows the measurements for a 5◦ step while Fig. 4 focuses on the transient state. Because of a software limitation concerning the tuning of the controller of the servomotor in such conditions, the virtual sideslip angle step presents overshoots. Transient state evaluation In order to evaluate the rise time of the sensors, different ramp slopes are applied. We are interested in sideslip angle
Sideslip angle (°)
where γ is the direction of the velocity and ψ is the yaw angle.
7 6 5 4 3 2
GPS/INS sensor Excitation signal Optical sensor
1 0 -1 27
27.5
28
28.5
29
29.5
Time (s)
30
30.5
31
31.5
32
Fig. 3. Comparison of sensors response for a step input at 80 km/h Step response: 5°, transient state
9
GPS/INS sensor Excitation signal Optical sensor
8 7
Sideslip angle (°)
β = γ − ψ,
6 5 4 3 2 1 0
-1 27.5
27.6
27.7
27.8
27.9
28
28.1
Time (s)
28.2
28.3
28.4
28.5
Fig. 4. Zoom on the transient response : rise time of 100 ◦/s variations up to 100 ◦ /s, which can only be controlled by a professional test car driver during specific real tests. To cover this range, the tested ramp slopes are up to 150 ◦ /s, that both sensors are able to follow. So, the rise time of the sensors permits to cover all the representative sideslip variation range. For the performed ramp slope range, both sensors present a latency time which can be considered as constant, for a given ramp slope, in a first approach. For all ramp slopes tested, the latency times measured are comprised between 10 and 20 ms for the GPS/INS sensor and 40 and 60 ms for the optical sensor. For the latter, the range depends furthermore on the configurable sliding mode filtering. In an on-line application, the instantaneous error caused by the latency time can possibly be too important to be neglected. Indeed, the latency time has to be correlated to the rise time of the ramp, which is about 100 ms for the example shown in Fig. 4. The slope ramp is nearly 100 ◦ /s. Put aside the influence of latency time, even if the overall behavior of the sensors in transient state is good, the instantaneous measurements are not satisfying with re-
Excitation signal Optical sensor GPS/INS sensor
0.8 0.6
Sideslip angle (°)
for the tire. The optical sensor can be approximated by a second order linear model, whose the 3 dB bandwidth is 8 Hz. For the GPS/INS sensor, a linear model can not be easily found to evaluate its bandwidth. But for all experimental tests (sinusoidal excitation up to 5 Hz), its phase delay and its static gain error are the lowest and we can conclude than the GPS/INS sensor bandwidth is much higher than 5 Hz.
Sinusoidal input
1
0.4 0.2 0
-0.2 -0.4 -0.6
4. DIRECT TIRE SLIP ANGLE MEASUREMENT
-0.8 -1 19.5
19.6
19.7
19.8
19.9
20
20.1
Time (s)
20.2
20.3
20.4
20.5
Fig. 5. Comparison of sensors response for a periodical input at 80 km/h, with a rise time of 5◦ /s gard to the precision requirement of 0.1◦ . For the example shown in Fig. 4, the maximum absolute difference for the first overshoot is 0.6◦ (8%) for the optical sensor and 0.3◦ (4%) for the GPS/INS sensor. For all the ramp slopes tested, the optical sensor always suffers from an error in overshoots greater than 0.1◦ while the GPS/INS sensor can satisfy this precision requirement when the ramp slope does not exceed 8 ◦ /s. Results obtained for a periodical input, with a maximum rise time of 5 ◦ /s are shown in Fig. 5. Steady state evaluation In steady state, the GPS/INS sensor matches the required precision of 0.1◦ . Concerning the optical sensor, the error of its mean value is also less than 0.1◦ , but instantaneous measurement with required precision is not possible because of the important fluctuation. As the frequency range of these variations is contained in the vehicle dynamic range, a simple low-pass filtering is not a solution to this problem. Bandwidth evaluation We analyzed the sensors in the time domain because ramp excitation was quite easy to generate. In fact, when using the available servomotor and control software, direct frequency analysis by sinusoidal excitation was difficult to realize, even approximately. However, characterization in either time or frequency domain is sufficient, because the two domains are related by Fourier transform. Sometimes, for instance when performing a sweep input driving maneuver, it can be advantageous to reason in terms of frequency characteristics like bandwidth. Thus the question is whether or not the sensor bandwidth allows reliable data acquisition of car behavior knowing that normal driving cars are characterized by a bandwidth up to 5 Hz, which corresponds to frequencies between 12 and 15 Hz
4.1 Context The previous tests of the characterization phase showed that, with some restrictions, the GPS/INS sensor satisfies the precision requirement of 0.1◦ . In fact, the latency time has possibly to be taken into account and the slip angle variation must be slower than 8 ◦ /s for accurate measuring in transient state. When used in automotive control domain, this kind of sensor is mounted on the car at a specific point of the vehicle (commonly near the center of gravity) in order to determine position, lateral, longitudinal and vertical velocities, sideslip angle, yaw-rate, etc. of the car at this point. When other specific vehicle points are of interest, their values are computed using geometric knowledge of the car which is supposed rigid. As we are interested in direct measurement of tire slip angle, we do not measure near the center of gravity, but, as it is commonly the case with an optical sensor, directly in the plane of the wheel rim (front right). This is done by a special mechanic adapter we developed, which fixes the sensor body near the center of the wheel in a plane parallel to the rim. A second part of the adapter fixes the GPS antenna 1 m above the sensor body, as it is advised by the constructor. The mechanical installation is shown in Fig. 6. A possible disadvantage of this kind of mounting is that the antenna, in order to keep a constant distance to the sensor body, is not longer fixed on the vehicle body, hence the sprung mass, but on an element of the unsprung mass. Therefore the antenna is exposed to much more vibrations and oscillations than for a fixation on the vehicle body. A parallel mounted optical sensor enables us to answer this question, in spite of its precision drawback. 4.2 Straight line tests First tests in straight line, for several constant vehicle speeds (40, 60 and 80 km/h) are carried out. So the tire slip angles are quasi constant and equal to 0◦ , and the variations with respect to the
Measurement of tire slip angle
1
Optical sensor GPS/INS sensor
0.8 0.6
Tire slip angle (°)
0.4 0.2 0 0.2 0.4 0.6 0.8 1
20
22
24
26
28
Time (s)
30
32
Fig. 7. Straight line test on the wheel: 40 km/h 1
Measurement of tire slip angle : circular trajectory test Optical sensor GPS/INS sensor
0.9
Fig. 6. Mechanical adapter mean values of the measures are essentially due to measurement noise. Both sensors deliver the same mean value (with respect to the precision requirement), and furthermore, when computing the variance of the random output part for both sensors, we obtain values which are equivalent to those obtained when they were mounted on the test bench.
Tire slip angle (°)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 40
41
42
43
44
45
Time (s)
46
47
48
49
50
Fig. 8. Circular trajectory test: 50 km/h
First, we have to remind that in steady state, the mean value delivered by the optical sensor satisfies the precision requirements. Secondly, this mean value is practically identical to that of the GPS/INS sensor. Hence, for straight line, we conclude that the mechanical installation is sufficiently robust to the undesired additional movements of the GPS antenna. Consequently, for this car maneuvre and because of its better instantaneous behavior, the use of a GPS/INS sensor improves the direct measurement of tire slip angle in comparison to an optical sensor. The measures for a straight line test, for a vehicle velocity of 40 km/h, are shown in Fig. 7.
submitted to a constant acceleration, which adds to the random like movement of the antenna in the straight line tests, a systematic component. Fig. 8 shows an example of a circular trajectory test for a vehicle speed of 50 km/h.
4.3 Dynamic angular tests
Comparing Fig. 7 and Fig. 8, we observe a variation around the mean value which is much more important for the circular test than for the straight line test. The explanation is the following: for circular testing, when the vehicle speed increases, the mean tire slip angle and the lateral efforts on the tire become higher. As a consequence, the increase of the vehicle speed obliges the driver to correct the steering wheel angle, in order to follow the circular trajectory efficiently.
In this kind of test, the vehicle follows a circular trajectory (a circle with a diameter of 25 m) for several constant speeds (30, 50 and 70 km/h). Hence the car is subject to a constant lateral acceleration. Considering the wheel, its tire slip angle is quasi constant and equal to a value which directly depends on the vehicle velocity. In the same way, the GPS antenna adapter is
For all tests, we measure mean values of tire slip angle which are the same (with respect to the precision requirement) for both sensors. Hence, the mechanical installation of the antenna does not cause any systematic error due to the constant lateral acceleration and we can conclude that the additional movements of the antenna can be neglected. Furthermore, in spite of the mechanical drawback, the GPS/INS sensor provides higher precision than the optical sensor.
This repeated correction causes variations around the mean trajectory and hence the overall variation of the sensors output is more important than for straight line driving.
5. CONCLUSION To obtain a better understanding, and then a sharper and more robust model of the tire, the measurements of the tire model inputs are necessary (typically an accuracy below 0.1◦ ). The present paper deals with the accurate determination of the tire slip angle. Two industrial sensors which measure the sideslip angle are compared and their statical and dynamical behavior evaluated. For this purpose, a test bench was developed and an experimental protocol permited to study their precision, their latency time, their rise time and their bandwidth. A characterization phase showed that both sensors must be used in a limited rise time range, in order to obtain measures which satisfy the precision requirement. The GPS/INS sensor, with some restrictions, satisfies the precision requirement of 0.1◦ . For this sensor, a slip angle variation lower than 8 ◦ /s gives accurate measuring in the transient state. For the optical sensor, the instantaneous measurement with the required precision is not possible because of its important fluctuation, even if it decreases with respect to the overall velocity. To measure the tire slip angle directly, a specific mechanical adapter was developed to fix the sensors near the center of the wheel in a plane parallel to the rim. Although the GPS antenna is exposed to more vibrations and oscillations than when it is fixed on the vehicle, the qualities of the GPS/INS sensor measurement, obtained in the characterization phase, are equivalent to those obtained during real tests. Globally, the GPS/INS sensor precision is better than that of the optical sensor.
6. ACKNOWLEDGMENTS The authors would like to thank the Renault Research Department in Aubevoye for the lending of both optical and GPS/INS sensors. Additionally, the authors would like to thank them for the access to their personal test tracks and for the possibility to carry out tests with Bruno Dupuis, a professional driver. Other thanks are given to Thomas Spr¨osser and Jo¨el Lambert for their contribution to the data processing and the conception of the test bench.
REFERENCES Caroux, J., T. Spr¨osser, M. Basset and G. L. Gissinger (2006). Identification of lateral vehicle behaviour for observer-based sideslip angle estimation. In: Proceedings of the 10th MINI Conference on Vehicle System Dynamics, Identification and Anomalies. Daily, R. and D. M. Bevly (2004). The use of gps for vehicle stability control systems. IEEE Transactions on Industial Electronics 51(2), 270–277. Guo, K. and L. Ren (2000). A non-steady and non-linear tire model under large lateral slip condition. SAE Transactions. How, J., N. Pohlman and C. W. Park (2002). Gps estimation algorithms for precise velocity, slip and race-track position measurements. In: SAE 2002 Motorsports Engineering Conference & Exhibition. Lozia, Z. (1998). Vehicle dynamics and motion simulation versus experiment. SAE Transactions 107, 344–360. Milliken, W.F. and D.L. Milliken (1995). Race car vehicle dynamics. SAE Publication. Pacejka, H. and E. Bakker (1991). The magic formula tyre model. In: Int. Colloq on Tyre models for Vehicle Dynamics Analysis. pp. 1– 18. Porcel, A., P. Laurence, M. Basset and G.L. Gissinger (2001). Tire model for vehicle simulation: overview and real time solution for critical situations. In: IEEE Conference in Control Applications. Mexico. Ryu, J. and J. C. Gerdes (2004). Integrating inertial sensors with gps for vehicle dynamics. Journal of Dynamics Systems, Measurement and Control 126, 243–254. Stephant, J., A. Charara and D. Meizel (2004). Virtual sensor : Application to vehicle sideslip angle and transversal forces. IEEE Transactions on Industrial Electronics 51(2), 278– 289. Uno, T., Y. Sakai, J. Takagi and T. Yanashita (1994). Road surface recognition method using optical spatial filter. JSAE Review 16(2), 221. Zami, B. (2005). Contribution `a l’identification de la liaison v´ehicule/sol d’un v´ehicule automobile. Estimation des param`etres de mod`eles de pneumatiques. PhD thesis. Universit´e de Haute Alsace.
Laboratory MIPS, MIAM group, Universit´e de Haute Alsace, 12 rue des fr`eres Lumi`ere, 68093 Mulhouse Cedex, France ∗∗ Renault - Research Department, Centre Technique d’Aubevoye, Parc de Gaillon, 27940 Aubevoye, France ∗
Abstract: In order to improve the lateral behavior modeling of a road vehicle, an accurate determination of tire slip angle is needed (typically an accuracy close to 0.1◦ ). In this paper, first, we compare two industrial sensors delivering information of sideslip angle: an optical sensor and a GPS/INS sensor. For this purpose, a specific test bench was developed. The limits of both sensors with regard to the above mentioned precision requirement, are studied, as well for static as for dynamic vehicle maneuvres. Secondly, for the GPS/INS sensor giving better results, we investigate the possibility of direct tire slip angle measurement by mounting this sensor in a plane parallel to the wheel rim. The developed mechanical adapter suffers from an inherent drawback for this kind of mounting, in terms of additional movements, compared to commonly used optical sensors. In spite of this supplementary perturbation, we show that the GPS/INS sensor precision is c 2007 IFAC still better than the optical sensor’s. Copyright Keywords: Vehicle dynamics, tires, precision measurements, global positioning systems
1. INTRODUCTION Today, important efforts are made to improve vehicle services such as comfort, safety, consumption and reliability. They require increasing means of simulation and thus a search for increasingly powerful models. Within the framework of vehicle dynamics study, the integration into the global vehicle model of a model describing its interaction with the ground is vital. However, the understanding of the phenomena involved in the transmission of strains by the tire is still limited. So, the improvement of the models which describe this
interaction is imperative in order to upgrade the modeling of the dynamics which extends the field of investigation. In the literature, a number of authors have carried out research on modeling the tire and the wheelground interface. A good synthesis of the main models can be found in (Porcel et al., 2001). The models given as references are: Pacejka model (Pacejka and Bakker, 1991), a semi-empirical model, Guo (Guo and Ren, 2000) and Milliken (Milliken and Milliken, 1995) models. In all these
models, for a given grip, the inputs considered are the wheel slip, the slip angle, the camber angle and the vertical tire strain; the strains and the moments at the wheel/road interface are processed as outputs. To obtain a better understanding, and then a sharper and more robust model of the tire, the measurement or a precise estimation of the tire model inputs are necessary. The present paper deals with accurate measurement of tire slip angle by the way of the evaluation of the sensors performance. We will show that the quality of the slip angle measurement depends on the used sensor and the dynamic range of the maneuvers performed with the test vehicle. The paper is organized as follows: in the second section, a definition of the tire slip angle is introduced, and two industrial sensors, permitting the determination of tire slip angle, are presented. The third section is dedicated to the characterization phase of the sensors using a specific test bench mounted at the rear of the laboratory test car. In the last section, the above sensors are fixed in a plane parallel to the wheel rim of the same test vehicle using a mechanical installation, developed by the laboratory. The sensors measurements obtained during real tests validate the mechanical adapter in spite of its inherent drawbacks.
FY
Y
VX
O Contact surface
VYi V
X
αi
Fig. 2. Definition of the tire slip angle This angle is generally defined by the expression: VY i αi = arctan i = 1, 2, (1) VXi where VY i is the lateral velocity with respect to the front and rear wheel axis, and VXi is the tire longitudinal velocity. Concretely, industrial companies propose different solutions to measure the tire slip angle. Two methods of determination can be highlighted and are presented in the next subsection.
2.2 Industrial sensors In the context of industrial tire slip angle measurement, there are essentially two different principles of measurement: an optical cross-correlation approach and a GPS/INS approach.
2. TIRE SLIP ANGLE OVERVIEW 2.1 Tire slip angle definition When the tire is subjected to lateral promptings (cornering, camber angle, etc.), a self-aligning torque is generated due to the tire elasticity. It modifies the original direction of the wheel with an angle called tire slip angle. The contact surface between the tire and the road changes according to the solicitations on the tire. The surface can be decomposed into two parts (Fig. 1): • a tension or sliding area at the rear; • a compression or friction area at the front. friction area
Y
X α
motion direction V
drift area
Fig. 1. Contact surface between the tire and the road in grip limit condition The tire slip angle is commonly considered as the angle between the longitudinal tire axis and the velocity vector of the tire center, named O in Fig. 2.
Optical principle A contactless optical sensor is commonly used to measure tire slip angle directly (Zami, 2005). It consists in measuring the longitudinal and lateral components of the velocity vector of the wheel and computing the tire slip angle according to equation 1. The slip angle can be also obtained directly as an output of the sensor. This sensor is often used in the context of automotive control such as in (Caroux et al., 2006), (Stephant et al., 2004), (Lozia, 1998) and (Uno et al., 1994). GPS/INS principle The GPS/INS sensor consists of a Inertial Navigation System (INS) sensor assisted by Global Positioning System (GPS) data with a positioning accuracy of 2 cm. The major drawback of sideslip angle determination with only a GPS device is the low (10 Hz) update rate of most GPS receivers. On the other hand, the direct time integration of INS measurements (without GPS information) can accumulate sensor errors. Furthermore, this principle is limited by the drift in sensor bias and sensitivity. So the INS data and the GPS information are combined by a Kalman filter. The Kalman algorithm is presented in many works such as in (Ryu and Gerdes, 2004), (How et al., 2002) and (Daily and Bevly, 2004). This sensor uses GPS information and more precisely
the velocity and the attitude to determine a slip angle according to the following equation:
Step response: 5°
9 8
(2)
3. CHARACTERIZATION OF THE SENSORS Characterization corresponds to estimating the precision, the latency time and the rise time of the sensors.
3.1 Test bench presentation The system of characterization of the sensors is fixed to the rear of the test vehicle. The two mentioned sensors are mounted on this test bench. By the mean of a servomotor, the sensors can be rotated with respect to the car. This rotation generates an identical virtual slip angle for the sensors. The GPS antenna determines the direction of the vehicle velocity vector, while the sensor body measures the sensor attitude. Therefore, when the vehicle follows a trajectory with the servomotor in zero position, the slip angles measured by both GPS/INS and optical speed sensors correspond to the sideslip angle at the rear of the car. If the vehicle moves in a straight trajectory and a rotation of the servomotor is made, the sensors measure the virtual slip angle which is created. This test bench allows to generate accurate rotational angles, with a range of ±30◦ , an accuracy below 0.1◦ . Both amplitude and speed of the rotational consign are controlled.
3.2 Protocol Step input excitation First the sensors are tested with step inputs of slip angle for three different magnitudes (0.5◦ , 1◦ and 5◦ ) and three constant vehicle speeds (60, 80 and 100 km/h) while keeping vehicle attitude constant. For practical reasons, the discontinuous part of the step input is realized by a ramp with several rising speeds. Fig. 3 shows the measurements for a 5◦ step while Fig. 4 focuses on the transient state. Because of a software limitation concerning the tuning of the controller of the servomotor in such conditions, the virtual sideslip angle step presents overshoots. Transient state evaluation In order to evaluate the rise time of the sensors, different ramp slopes are applied. We are interested in sideslip angle
Sideslip angle (°)
where γ is the direction of the velocity and ψ is the yaw angle.
7 6 5 4 3 2
GPS/INS sensor Excitation signal Optical sensor
1 0 -1 27
27.5
28
28.5
29
29.5
Time (s)
30
30.5
31
31.5
32
Fig. 3. Comparison of sensors response for a step input at 80 km/h Step response: 5°, transient state
9
GPS/INS sensor Excitation signal Optical sensor
8 7
Sideslip angle (°)
β = γ − ψ,
6 5 4 3 2 1 0
-1 27.5
27.6
27.7
27.8
27.9
28
28.1
Time (s)
28.2
28.3
28.4
28.5
Fig. 4. Zoom on the transient response : rise time of 100 ◦/s variations up to 100 ◦ /s, which can only be controlled by a professional test car driver during specific real tests. To cover this range, the tested ramp slopes are up to 150 ◦ /s, that both sensors are able to follow. So, the rise time of the sensors permits to cover all the representative sideslip variation range. For the performed ramp slope range, both sensors present a latency time which can be considered as constant, for a given ramp slope, in a first approach. For all ramp slopes tested, the latency times measured are comprised between 10 and 20 ms for the GPS/INS sensor and 40 and 60 ms for the optical sensor. For the latter, the range depends furthermore on the configurable sliding mode filtering. In an on-line application, the instantaneous error caused by the latency time can possibly be too important to be neglected. Indeed, the latency time has to be correlated to the rise time of the ramp, which is about 100 ms for the example shown in Fig. 4. The slope ramp is nearly 100 ◦ /s. Put aside the influence of latency time, even if the overall behavior of the sensors in transient state is good, the instantaneous measurements are not satisfying with re-
Excitation signal Optical sensor GPS/INS sensor
0.8 0.6
Sideslip angle (°)
for the tire. The optical sensor can be approximated by a second order linear model, whose the 3 dB bandwidth is 8 Hz. For the GPS/INS sensor, a linear model can not be easily found to evaluate its bandwidth. But for all experimental tests (sinusoidal excitation up to 5 Hz), its phase delay and its static gain error are the lowest and we can conclude than the GPS/INS sensor bandwidth is much higher than 5 Hz.
Sinusoidal input
1
0.4 0.2 0
-0.2 -0.4 -0.6
4. DIRECT TIRE SLIP ANGLE MEASUREMENT
-0.8 -1 19.5
19.6
19.7
19.8
19.9
20
20.1
Time (s)
20.2
20.3
20.4
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Fig. 5. Comparison of sensors response for a periodical input at 80 km/h, with a rise time of 5◦ /s gard to the precision requirement of 0.1◦ . For the example shown in Fig. 4, the maximum absolute difference for the first overshoot is 0.6◦ (8%) for the optical sensor and 0.3◦ (4%) for the GPS/INS sensor. For all the ramp slopes tested, the optical sensor always suffers from an error in overshoots greater than 0.1◦ while the GPS/INS sensor can satisfy this precision requirement when the ramp slope does not exceed 8 ◦ /s. Results obtained for a periodical input, with a maximum rise time of 5 ◦ /s are shown in Fig. 5. Steady state evaluation In steady state, the GPS/INS sensor matches the required precision of 0.1◦ . Concerning the optical sensor, the error of its mean value is also less than 0.1◦ , but instantaneous measurement with required precision is not possible because of the important fluctuation. As the frequency range of these variations is contained in the vehicle dynamic range, a simple low-pass filtering is not a solution to this problem. Bandwidth evaluation We analyzed the sensors in the time domain because ramp excitation was quite easy to generate. In fact, when using the available servomotor and control software, direct frequency analysis by sinusoidal excitation was difficult to realize, even approximately. However, characterization in either time or frequency domain is sufficient, because the two domains are related by Fourier transform. Sometimes, for instance when performing a sweep input driving maneuver, it can be advantageous to reason in terms of frequency characteristics like bandwidth. Thus the question is whether or not the sensor bandwidth allows reliable data acquisition of car behavior knowing that normal driving cars are characterized by a bandwidth up to 5 Hz, which corresponds to frequencies between 12 and 15 Hz
4.1 Context The previous tests of the characterization phase showed that, with some restrictions, the GPS/INS sensor satisfies the precision requirement of 0.1◦ . In fact, the latency time has possibly to be taken into account and the slip angle variation must be slower than 8 ◦ /s for accurate measuring in transient state. When used in automotive control domain, this kind of sensor is mounted on the car at a specific point of the vehicle (commonly near the center of gravity) in order to determine position, lateral, longitudinal and vertical velocities, sideslip angle, yaw-rate, etc. of the car at this point. When other specific vehicle points are of interest, their values are computed using geometric knowledge of the car which is supposed rigid. As we are interested in direct measurement of tire slip angle, we do not measure near the center of gravity, but, as it is commonly the case with an optical sensor, directly in the plane of the wheel rim (front right). This is done by a special mechanic adapter we developed, which fixes the sensor body near the center of the wheel in a plane parallel to the rim. A second part of the adapter fixes the GPS antenna 1 m above the sensor body, as it is advised by the constructor. The mechanical installation is shown in Fig. 6. A possible disadvantage of this kind of mounting is that the antenna, in order to keep a constant distance to the sensor body, is not longer fixed on the vehicle body, hence the sprung mass, but on an element of the unsprung mass. Therefore the antenna is exposed to much more vibrations and oscillations than for a fixation on the vehicle body. A parallel mounted optical sensor enables us to answer this question, in spite of its precision drawback. 4.2 Straight line tests First tests in straight line, for several constant vehicle speeds (40, 60 and 80 km/h) are carried out. So the tire slip angles are quasi constant and equal to 0◦ , and the variations with respect to the
Measurement of tire slip angle
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Fig. 7. Straight line test on the wheel: 40 km/h 1
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Fig. 6. Mechanical adapter mean values of the measures are essentially due to measurement noise. Both sensors deliver the same mean value (with respect to the precision requirement), and furthermore, when computing the variance of the random output part for both sensors, we obtain values which are equivalent to those obtained when they were mounted on the test bench.
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Fig. 8. Circular trajectory test: 50 km/h
First, we have to remind that in steady state, the mean value delivered by the optical sensor satisfies the precision requirements. Secondly, this mean value is practically identical to that of the GPS/INS sensor. Hence, for straight line, we conclude that the mechanical installation is sufficiently robust to the undesired additional movements of the GPS antenna. Consequently, for this car maneuvre and because of its better instantaneous behavior, the use of a GPS/INS sensor improves the direct measurement of tire slip angle in comparison to an optical sensor. The measures for a straight line test, for a vehicle velocity of 40 km/h, are shown in Fig. 7.
submitted to a constant acceleration, which adds to the random like movement of the antenna in the straight line tests, a systematic component. Fig. 8 shows an example of a circular trajectory test for a vehicle speed of 50 km/h.
4.3 Dynamic angular tests
Comparing Fig. 7 and Fig. 8, we observe a variation around the mean value which is much more important for the circular test than for the straight line test. The explanation is the following: for circular testing, when the vehicle speed increases, the mean tire slip angle and the lateral efforts on the tire become higher. As a consequence, the increase of the vehicle speed obliges the driver to correct the steering wheel angle, in order to follow the circular trajectory efficiently.
In this kind of test, the vehicle follows a circular trajectory (a circle with a diameter of 25 m) for several constant speeds (30, 50 and 70 km/h). Hence the car is subject to a constant lateral acceleration. Considering the wheel, its tire slip angle is quasi constant and equal to a value which directly depends on the vehicle velocity. In the same way, the GPS antenna adapter is
For all tests, we measure mean values of tire slip angle which are the same (with respect to the precision requirement) for both sensors. Hence, the mechanical installation of the antenna does not cause any systematic error due to the constant lateral acceleration and we can conclude that the additional movements of the antenna can be neglected. Furthermore, in spite of the mechanical drawback, the GPS/INS sensor provides higher precision than the optical sensor.
This repeated correction causes variations around the mean trajectory and hence the overall variation of the sensors output is more important than for straight line driving.
5. CONCLUSION To obtain a better understanding, and then a sharper and more robust model of the tire, the measurements of the tire model inputs are necessary (typically an accuracy below 0.1◦ ). The present paper deals with the accurate determination of the tire slip angle. Two industrial sensors which measure the sideslip angle are compared and their statical and dynamical behavior evaluated. For this purpose, a test bench was developed and an experimental protocol permited to study their precision, their latency time, their rise time and their bandwidth. A characterization phase showed that both sensors must be used in a limited rise time range, in order to obtain measures which satisfy the precision requirement. The GPS/INS sensor, with some restrictions, satisfies the precision requirement of 0.1◦ . For this sensor, a slip angle variation lower than 8 ◦ /s gives accurate measuring in the transient state. For the optical sensor, the instantaneous measurement with the required precision is not possible because of its important fluctuation, even if it decreases with respect to the overall velocity. To measure the tire slip angle directly, a specific mechanical adapter was developed to fix the sensors near the center of the wheel in a plane parallel to the rim. Although the GPS antenna is exposed to more vibrations and oscillations than when it is fixed on the vehicle, the qualities of the GPS/INS sensor measurement, obtained in the characterization phase, are equivalent to those obtained during real tests. Globally, the GPS/INS sensor precision is better than that of the optical sensor.
6. ACKNOWLEDGMENTS The authors would like to thank the Renault Research Department in Aubevoye for the lending of both optical and GPS/INS sensors. Additionally, the authors would like to thank them for the access to their personal test tracks and for the possibility to carry out tests with Bruno Dupuis, a professional driver. Other thanks are given to Thomas Spr¨osser and Jo¨el Lambert for their contribution to the data processing and the conception of the test bench.
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