Method for estimating the chassis pitch angle of a vehicle and the road hill angle of a road travelled by the vehicle

Abstract

A method for estimating a chassis pitch angle (θv) of a vehicle (2) and a road hill angle (θR) of a road travelled by the vehicle (2), wherein a longitudinal dynamic of the vehicle (2) is modelled as a continuous-time linear dynamic system comprising a scalar input (u) defined by a variation of longitudinal velocity (αx) of the vehicle (2), a state vector (x) defined by a plurality of variables including the chassis pitch angle (θv), a chassis pitch rate (θv) of the vehicle (2), the road hill angle (θR) and a road hill rate (θR), an output vector (y) defined by a plurality of variables selected within a group consisting of the longitudinal acceleration (αxm) of the vehicle (2) and a total pitch rate (θm) of the vehicle (2) represented by the sum of the chassis pitch rate (θv) and the road pitch rate (̇θR). The scalar input (u) is measured by means of a wheel speed sensor (13) of the vehicle (2), the output vector (y) is measured by means of an inertial measurement unit (3) of the vehicle (2), the continuous-time linear dynamic system is discretized, a Kalman Filter is real-time applied to the discrete-time linear dynamic system by using the measured scalar input (u) and the measured output vector (y) for estimating the state 15 vector (x), and values of the chassis pitch angle (θv) and the road hill angle (θR) are extracted from the estimated state vector (x).

Description

[0001]“METHOD FOR ESTIMATING THE CHASSIS PITCH ANGLE OF A VEHICLE AND THE ROADHILLANGLE OFAROAD TRAVELLED BY THE VEHICLE”CROSS-REFERENCE TORELATEDAPPLICATIONSThis Patent Application claims priority from Italian Patent Application No. 102024000012304 filed on May 29, 2024, the entire disclosure of which is incorporated herein by reference TECHNICAL FIELD OF THE INVENTION The present invention relates to a method for estimating the chassis pitch angle of a vehicle and a road hill angle of the road travelled by the vehicle. The invention finds application in any type of road motor vehicles, regardless of whether it is used for the transportation of people, such as a car, a bus, a camper, etc., or for the transportation of goods, such as an industrial vehicle (truck, B-train, trailer truck, etc.) or a light or medium-heavy commercial vehicle (light van, van, pick-up trucks, etc.). In particular, the invention finds advantageously application in motor vehicles equipped with inertial sensors, wheel speed sensors and steering wheel angle sensors, i.e. widely available sensors due to their small size and low cost. STATE OF THEARTAs is known, inertial sensors, such as accelerometers and gyroscopes, are widely used in many different domains, from ambulatory to biomedical, from robotics to automotive field, and the number of applications is increasing exponentially as the inertial sensors continuously shrink their size and cost. Automated and autonomous driving technology has attracted much attention recently. In this field, the electronic stability controller (ESC) is used for ensuring vehicle stability in chassis controller, while adaptive cruise control (ACC) and / or lane keeping system (LKS) are used for ensuring convenience in an advanced driver assistant system (ADAS). To improve the performance of these controllers, the vehicle state must be estimated with a high accuracy. Among them, accurate side slip angle and attitude estimations are highly significant. For example, image processing and feature recognition from camera sensor could be aided by the external pitch and roll angles of the vehicle body. Also, side slip angle and attitude are prerequisites for determining vehicle location. Typically, the term inertial sensor is used to denote the combination of a three- axis accelerometer and a three-axis gyroscope. Devices containing these sensors are commonly referred to as inertial measurement units (IMUs), and they are largely used to estimate vehicle side slip angle and vehicle attitude, as well as pose estimation. However, raw sensor data are typically affected by noise, bias, signal delays, etc., which can affect the accuracy of the estimators. On one hand, the three-axis gyroscope is dynamic-independent, but drifts over time due to bias variation and numerical integration. On the other hand, accelerometers are drift-free, but vulnerable to disturbances. Indeed, if a transition in attitude (roll and pitch) occurs, the gravitational acceleration is reflected in the sensor value. Therefore, research community has put considerable effort to improve the accuracy of the aforementioned estimates, and different approaches combining inertial sensors with additional information sources have been proposed. For example, it is known to compensate pitch and roll angles by using the gravitational acceleration vector components from the measurement of the accelerometers, where complementary filters or Kalman filters (KFs) are normally employed. The most common assumption is to neglect the measured body’s acceleration with respect to the gravitational acceleration in order to approximate the accelerometer measurement with gravity acceleration. Another approach is to combine angular rate measurements with accelerometer measurements with magnetometers, or IMUs with the global navigation satellite system (GNSS). However, the GNSS signal may be weak and easily blocked or may suffer from multipath effects, and their sample rates is typically lower than the sample rate of IMU. In addition, due to the recent developments in artificial intelligence and neural networks, data-driven estimators have been used for state estimation. These estimators have the advantage of having high accuracy by training the data directly in situations where accurate mathematical modelling is difficult. However, they require extensive tests on each type or version of vehicle they are designed for. Given that the number of possible configurations in a vehicle is very high (road surface, active suspensions, different tires, etc.), data-driven methods difficultly scale on real production systems. A thesis presented to the University of Waterloo, Ontario, Canada, by Amin Habibnejad Korayem, titled “State and Parameter Estimation of Vehicle-Trailer Systems”, and published on 5 March 2021, proposes two methods to estimate trailer mass for arbitrary vehicle-trailer configurations: model-based and Machine Learning (ML). The stability of the model-based estimation algorithm is analysed, establishing the convergence of the estimation error to zero. In the proposed ML-based approach, a deep neural network is designed to estimate trailer mass. The inputs of the ML-based method are selected based on the vehicle-trailer model and are normalized by the vehicle mass, tire sizes, and geometry so that retraining of the network is not needed for different towing vehicles. Ultrasonic sensors along with kinematics and dynamics equations of a towing vehicle are used to develop approaches for estimating hitch angle, lateral tire forces and hitch-forces of a vehicle-trailer system. SUBJECT-MATTER AND SUMMARY OF THE INVENTION The aim of the present invention is to provide a robust method to estimate the attitude of a vehicle to be used in an automated automotive driving system of a vehicle, which is free from the drawbacks described above and, at the same time, is easy and economical to implement. According to the present invention, a method for estimating the chassis pitch angle of a vehicle and the road hill angle of a road travelled by the vehicle, a computer program and an automotive driving system for a vehicle are provided, as claimed in the appended claims. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 shows a block diagram of an automotive driving system. Figure 2 shows a so called dynamic bicycle model of a vehicle. Figure 3 shows a vehicle chassis pitch schematic. Figure 4 shows a vehicle chassis roll schematic. DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION The present invention will now be described in detail with reference to the attached figures to allow a person skilled in the art to make and use it. Various modifications to the described embodiments will be immediately apparent to the persons skilled in the art and the generic principles described can be applied to other embodiments and applications without departing from the protective scope of the present invention, as defined in the attached claims. Therefore, the present invention should not be considered limited to the described and illustrated embodiments, but it must be accorded the widest protective scope in accordance with the described and claimed characteristics. Where not defined otherwise, all the technical and scientific terms used herein have the same meaning commonly used by persons skilled in the art pertaining to the present invention. In the event of a conflict, this description, including the definitions provided, will be binding. Furthermore, the examples are provided for illustrative purposes only and as such should not be considered limiting. In particular, the block diagrams included in the attached figures and described below are not intended as a representation of structural characteristics or constructive limitations, but must be interpreted as a representation of functional characteristics, i.e. intrinsic properties of the devices and defined by the obtained effects or functional limitations, which can be implemented in different ways so as to protect their functionalities (operating abilities). In order to facilitate the understanding of the embodiments described herein, reference will be made to some specific embodiments and a specific language will be used to describe the same. The terminology used in the present document has the purpose of describing only particular embodiments, and is not intended to limit the scope of the present invention. Figure 1 shows a block diagram of an automotive driving system 1 of a motor vehicle 2. As shown in Figure 1, the automotive driving system 1 comprises: at least one Inertial Measurement Units (IMU) 3 for measuring in general accelerations along three reciprocally orthogonal axes; automotive actuators 4, which comprise an Electric Power Steering (EPS) 5, a Braking System Module (BSM) 6, and a Powertrain (PWT) 7; an automotive Electronic Control Unit (ECU) 8; and an automotive on-board communication network 9, such as for instance a high-speed CAN, also known as C-CAN, or a FlexRAy, for allowing the ECU 8 to communicate with the IMU 3 and the automotive actuators 4, directly or indirectly, i.e., via dedicated automotive electronic control units. The IMU 3 is of a known type and typically comprises a triaxial accelerometer 10 for measuring accelerations of the vehicle 2 with respect to three-dimensional cartesian reference system fixed with respect to the vehicle 2, and a gyroscope 11 for measuring the yaw rate and preferably also a total pitch rate of the vehicle 2. The EPS 5 comprises an electric motor (not shown) operatively coupled to either a steering gear or a steering column, a steering gear sensor or steering column sensor, generically called steering wheel angle sensor 12 in the following, for measuring the front wheel angle of the vehicle 2 and a torque sensor (not shown) for sensing the torque applied to the steering column. The BSM 6 comprises wheel speed sensor 13 for measuring the longitudinal velocity of the vehicle 2. The ECU 8 is configured to implement the method of the present invention for estimating a chassis pitch angle of the vehicle 2 and a road hill angle of a road travelled by the vehicle 2; the method is disclosed in details in the following with reference to Figure 2 and 3. It is worth noticing that, throughout the rest of the present document, all the vehicle variables and measurements are defined using the standard ISO-8855. Vehicle pitch refers to the front and rear oscillation motion that a vehicle is subjected to while driving. A first main cause of pitching is acceleration and deceleration of the vehicle: while the vehicle accelerates or brakes the weight is transferred to the rear / front of the vehicle, causing a pitching motion uneven road conditions. A second main cause of pitching are uneven road conditions: obstacles on the road, such as bumps or potholes, can cause pitching due to the change in wheel load and the suspension’s response to irregularities. A third main cause of pitching is the vehicle design: vehicle characteristics, such as suspension geometry, chassis stiffness and centre of gravity height, can influence the pitching behaviour. In automated driving applications, the dynamics of a vehicle are commonly approximated using the well-known three-degrees of freedom dynamic bicycle model, shown in Figure 2, where the vehicle 2 is represented as a single track model with left wheel and right wheel of each axle (front and rear) fused together into a single wheel positioned at the centre of the axles. In figure 2, the following variables and quantities are shown: - YVand XVare lateral and longitudinal cartesian axes fixed with respect to the vehicle 2; -^^ ∈ [^^^^^^^^, ^^^^^^^^] ⊆ [−^^, ^^] is front wheel angle, assuming that the rear wheelangle is zero; - Ffand Frare the front axle lateral force and, respectively, the rear axle lateral force; - lfand lrrepresent the distances of the front and, respectively, rear axles from the centre of gravity 20 of the vehicle 2; - ^̇^ is the yaw rate of the vehicle 2; - ^^ is the velocity of the vehicle 2 with its longitudinal and lateral components ^^^^and, respectively, ^^^^; and -^^ ∈ [−^^, ^^] is side slip angle, which is the angle between the vehicle longitudinal direction and the vehicle travelling direction during the motion of the vehicle 2. The variables and quantities are expressed with respect to three-dimensional cartesian reference system fixed with respect to the vehicle 2 and comprising YVand XV cartesian axes. In order to capture the chassis pitch angle of the vehicle 2 and the road hill angle of the road travelled by the vehicle 2, a state-space vehicle pitch model is designed. The vehicle pitch model is represented by a linear equation describing the longitudinal dynamics of the vehicle 2 and will be used in a linear Kalman filter observer for the motion of the vehicle along a longitudinal direction in order toestimate a chassis pitch angle ^^^^ ∈ [−^^, ^^] of the vehicle 2 and a road hill angle ^^^^ ∈[−^^, ^^] of a road travelled by the vehicle 2.Such equation is derived on the basis of the following two assumptions: the tires of the vehicle 2 are planar to the ground and steady on the ground; and the road hill angle ^^^^and the chassis pitch angle ^^^^are small angles, i.e. it is assumed, forinstance, that sin(^^^^) ≈^^^^ and cos(^^^^) ≈1. The first assumption is very common inthe field of automated driving, since the longitudinal and lateral dynamics involved in the most of the automated driving levels do not allow vehicle tires to severe from the road, in both urban and highway scenarios. With regard to the second assumption, the chassis pitch angle ^^^^typically ranges in the order of the degree, then the approximation error is near-zero. Thus, the most tight assumption is the one related to the road hill angle ^^^^. However, the longitudinal slopes exceeding 30%, which corresponds to a road hill angle ^^^^of about 16°, are unusual in public roads. Thus, it can be assumed that the latter assumption does not jeopardize the generality and reliability of the method of the invention. The vehicle chassis pitch schematic is illustrated in Figure 3, where the pitching behaviour is described as a mass-spring-damper model influenced by the longitudinal and vertical accelerations. In figure 3, the following cartesian axes, variables and quantities are shown: - XRand ZRare longitudinal and vertical cartesian axes fixed with respect to the road hill; - XV and ZV are longitudinal and vertical cartesian axes fixed with respect to the road vehicle 2; - ^^^^is the sprung mass of the vehicle 2, i.e. the portion of the total mass of the vehicle 2 that is supported by the suspension; - g is the gravity acceleration; - ^^^^is the longitudinal acceleration of the vehicle 2; - ℎ^^is the distance between the pitch centre 21 and the centre of gravity 20 of the chassis of the vehicle 2; - ^^^^is the pitch stiffness of the vehicle 2; - ^^^^is the pitch damping of the vehicle 2; - ^^^^is the road hill angle; and - ^^^^is the chassis pitch angle; and - ^̇^ is the total pitch rate. A total pitch angle ^^ of the vehicle 2 when travelling on a road having a certainroad hill angle ^^^^ is therefore obtainable by the sum ^^ = ^^^^ + ^^^^.The linear equation of the vehicle pitch model relates to the moment along the Y-axis of the cartesian reference system fixed with respect to the vehicle 2. The equilibrium equation of the moment along the Y-axis can be expressed as: −^^^^^^^̈^^^ − ^^^^^̇^^^ − ^^^^^^^^ + ℎ^^^^^^(−^^^^^^^^^^^^^^ + ^^^^^^^^(^^^^ + ^^^^)) = 0 , (1)wherein ^^^^^^is a moment of inertia along the Y-axis of the vehicle 2. The factor^^^^^^^^(^^^^ + ^^^^) provides useful information about the acceleration caused by the chassispitch angle and the road hill angle, represented by the component of the gravitational acceleration parallel to the ground. By applying the small angles assumption to equation (1), the linear equation of the vehicle pitch model is obtained and can be expressed as: The pitch stiffness ^^^^and the pitch damping ^^^^of the vehicle 2 are identified from experimental test data. In particular, these parameters are derivable by performing constant intensive braking manoeuvres from different initial longitudinal velocities till standstill in ABS mode, and manual shaking of the vehicle body along the Y-axis. The vehicle pitch model represented by the equation (2) will be used in a linear Kalman filter observer. A traditional Kalman filter is commonly used to estimate the state of a dynamic system based on a series of noisy and / or incomplete measurements. The Kalman filter consists of an algorithm which recursively performs two main steps: a prediction step and a measurement update step. The prediction step uses a dynamic model of the system to estimate the state of the systems and the measurement update step refines and corrects the estimates leveraging the measurement model. The algorithm operate in real time, using only current input measurements coming from sensors and the state calculated previously and its uncertainty matrix. As new measurements arrive, at each iteration the algorithm reduces the state uncertainty. In particular, the longitudinal dynamics of the vehicle 2 is modelled as a continuous-time linear dynamic system defined as: ^̇^ = ^^^^ + ^^^^, (3)^^ = ^^^^ + ^^^^, (4)wherein in general u is the input of the system (^^ ∈ ℝ^^), x is the state of thesystem (x ∈ ℝ^^), y is the output of the system (y ∈ ℝ^^), and A, B, C and D (^^ ∈ ℝ^^^^^^,^^ ∈ ℝ^^^^^^, ^^ ∈ ℝ^^^^^^, ^^ are dynamic system matrices. The Kalman filter isreal-time applied to the continuous-time linear dynamic system defined by equations (3) and (4) by using the measured input vector and the measured output vector for estimating the state vector according to a measurement period. Hence, the continuous-time linear dynamic system defined by equations (3) and (4) is discretized before applying the Kalman filter. In particular, the prediction step starts with an initial estimate of the state (often based on prior knowledge or initial measurements), and predicts the next state based on equation (3). The prediction step includes both the state estimation and the computation of its associated uncertainty, expressed as a covariance matrix, as follows: where Ad, Bd, Cdand Ddare the discretized version of the system matrices of the dynamic system matrices A, B, C and D , P is the state covariance matrix, and Q is the process noise covariance matrix. The measurement update step is carried out as follows. Given the estimated state, when new measurements become available, the Kalman filter combines the estimates with the current available measurements, using a weighted average through the Kalman gain K, which balances the trust between the prediction and the measurements and is calculated as follows: wherein, R is the measurement noise covariance matrix. This measurement update step enhances the estimate accuracy with respect to prediction step alone. Finally, taking into account both the prediction error and the measurement error, the state covariance matrix P is updated as follows: The matrixes Q and R are obtainable in a manner known in art, particularly through a fine tuning for the specific conditions to which the Kalman filter is applied to or through iterative attempts. In order to model the longitudinal dynamic of the vehicle, which is described by equation (2), as the continuous-time linear dynamic system defined by (3) and (4), the input u, the state x, and the output y of the system are defined as follows: - u is scalar input defined by the variation of longitudinal velocity, hereinafter indicated with ^^^^; - x is a state vector defined by a plurality of variables including: - the chassis pitch angle ^^^^of the vehicle 2, - the chassis pitch rate ^̇^^^of the vehicle 2, - the road hill angle ^^^^, and - the road hill rate ^^^^; - y is an output vector defined by a plurality of measured variables selected within a group consisting of: - the measured longitudinal acceleration ^^^^^^of the vehicle 2, and - the measured total pitch rate ^^^^of the vehicle 2. Accordingly, A and C are dynamic system matrices and B and D are dynamic system vectors. The output vector y is also called measurement vector because it collects the variables which are measured in the measurement update step. During the measurement update step also the scalar input u is measured. The variables of the measurement vector y are put in relationship with the state of the system by using the following linear equation: ^̇^^^ = ^̇^^^ + ^̇^^^ . (9)According to equation (8), the measured longitudinal acceleration ^^^^^^is expressed by the sum of the components of the variation of the longitudinal velocity ^^^^and the vertical acceleration parallel to the ground. The equation (8) is then developed by using the small angle assumption. In particular, the variation of the longitudinal velocity ^^^^comprises two contributions: the first derivative of the longitudinal velocity ^̇^^^of the vehicle 2 and the factor ^̇^^^^^, which combines the yaw rate ^̇^ and the lateral velocity ^^^^of the vehicle 2. Using the bicycle model of Figure 2, the lateral velocity ^^^^is bound to the longitudinal velocity ^^^^through the side slip angle ^^ according to a trigonometric relationship, i.e. ^^^^ = tan(^^) ^^^^ .Equation (9) means that the measured total pitch rate ^̇^^^is represented by the sum of two state variables, i.e. the chassis pitch rate ^̇^^^and the road hill rate ^̇^^^. The above definition of scalar input u, state vector x and output vector y together with the state linear equation (2) and the measurement linear equation (8) and (9) give rise to the following dynamic system matrices A and C and dynamic system vectors B and D: To summarize, the method of the invention for estimating a chassis pitch angle ^^^^of a vehicle 2 and a road hill angle ^^^^of a road travelled by the vehicle 2, after modelling the longitudinal dynamic of the vehicle 2 as the continuous-time linear dynamic system defined by (3) and (4) and described above, further comprises: - measuring the scalar input u , i.e. obtaining the variation of longitudinal velocity ^^^^, by means of the IMU 3 according to a certain measurement period; - measuring the variables of the output vector y, i.e. obtaining the measured longitudinal acceleration ^^^^^^and the measured total pitch rate ^̇^^^, by means of the IMU 3 according to the measurement period; - discretizing the continuous-time linear dynamic system to obtain a discrete-time linear dynamic system; - real-time applying the Kalman Filter to the discrete-time linear dynamic system by using the measured scalar input u and the measured output vector y for estimating the state vector x according to the measurement period; and - extracting values of the chassis pitch angle ^^^^and the road hill angle ^^^^from the estimated state vector x. In particular, the triaxial accelerometer 10 provides a signal representing the measured longitudinal acceleration ^^^^^^and the gyroscope 11 provides a signal representing the measured total pitch rate ^̇^^^. In more details, measuring the scalar input u comprises: - measuring the first derivative of the longitudinal velocity ^̇^^^by means of the wheel speed sensor 13 of the vehicle 2; - measuring the yaw rate ^̇^ of the vehicle 2 by means of the IMU 3, in particular by means of the gyroscope 11; and - determining the lateral velocity ^^^^as a function of measurements of the IMU 3 and of the wheel speed sensor 13 or as a function of measurements of the IMU 3 and of a steering wheel angle sensor 12. In the first alternative, the determination of the lateral velocity ^^^^comprises: - estimating a side slip angle ^^ of the vehicle 2 as a function of measurements of the IMU 3; - measuring the longitudinal velocity ^^^^of the vehicle 2 by means of the wheel speed sensor 13; and - calculating the lateral velocity ^^^^as a function of the side slip angle ^^ and thelongitudinal velocity ^^^^, i.e. according to the relationship ^^^^ = tan(^^) ^^^^ .The side slip angle ^^ is estimated by means of a side slip angle estimator known in the art and implementable through software means. In the second alternative, the determination of the lateral velocity ^^^^consists in estimating the lateral velocity ^^^^as a function of measurements of the IMU 3 and of the steering wheel angle sensor 12. The lateral velocity ^^^^is estimated in a manner similar to that disclosed above for the chassis pitch angle of the vehicle 2 and the road hill angle. In particular, the starting point is a state-space vehicle roll model represented by linear equations describing the lateral dynamics of the vehicle 2. The vehicle roll model will be used in a linear Kalman filter observer for the motion of the vehicle along a lateral direction in order to estimate the lateral velocity ^^^^. Such equations are derived on the basis of the same assumptions made for the vehicle pitch model, i.e. the assumption that the tires of the vehicle 2 are planar to the ground and steady on the ground and the small angle assumption. With regard to the second assumption, the chassis roll angle ^^^^typically ranges in the order of the degree, then the approximation error is near- zero. Thus, the most tight assumption is the one related to the front wheel angle ^^ and the road bank angle ^^^^. However, the front wheel angle ^^ is commonly limited in the range from -30° to 30° and banked roads are unusual in public roads. Thus, given that at front wheel angle ^^ equal to 20° the approximation error is it can be assumed that the latter assumption does not jeopardize the generality and reliability of the method of the invention. The vehicle chassis roll schematic is illustrated in Figure 4, where the lateral movement of the suspension system is described as a mass-spring-damper model. In figure 4, the following cartesian axes, variables and quantities are shown: - YR and ZR are lateral and vertical cartesian axes fixed with respect to the road bank; - YV and ZV are lateral and vertical cartesian axes fixed with respect to the road vehicle 2; - ^^^^is the sprung mass of the vehicle 2, i.e. the portion of the total mass of the vehicle 2 that is supported by the suspension; - g is the gravity acceleration; - ^^^^is the lateral acceleration of the vehicle 2; - ℎ^^^^^^^^is the distance between the roll centre 21 and the centre of gravity 20 of the chassis of the vehicle 2; - ^^^^^^^^^^is the roll stiffness of the vehicle 2; - ^^^^^^^^^^is the roll damping of the vehicle 2; - ^^^^is the road bank angle; - ^^^^is the chassis roll angle; and - ^̇^ is the total roll rate. A total roll angle ^^ of the vehicle 2 when travelling on a road having a certainroad bank angle ^^^^ is therefore obtainable by the sum ^^ = ^^^^ + ^^^^.According to the dynamic bicycle model of the vehicle 2, the front axle lateral forces and the rear axles later force are expressed as: ) wherein ^^^^and ^^^^are the front and rear cornering stiffness. Then the equilibrium equation of the lateral acceleration is derived from the second Newton’s laws of motion: By putting equations (12a) and (12b) into equation (13) and using small angles assumption, a first linear equation of the vehicle roll model is obtained and can be expressed as: wherein m is the total mass of the vehicle 2. According to equation (14), the first derivative of the lateral velocity, indicated by ^̇^^^, depends on the road bank angle ^^^^through the gravity acceleration. The factor ^^^^^^provides useful information about the acceleration caused by the road bank angle, represented by the component of the gravitational acceleration parallel to the ground. A second linear equation of the vehicle roll model relates to the moment along the Z-axis of the cartesian reference system fixed with respect to the vehicle 2, which is influenced by the front wheel angle ^^, i.e. the steering input, and the lateral forces Ffand Fr. The equilibrium equation of the moment along the Z-axis can be expressed as: wherein ^^^^^^is a moment of inertia along the vertical axis of the vehicle 2, i.e. the yaw moment of inertia. By putting equations (12a) and (12b) into equation (15), the second linear equation is obtained and can be expressed as: A third linear equation of the vehicle roll model relates to the moment along the X-axis of the cartesian reference system fixed with respect to the vehicle 2. Therefore, the third linear equation is obtained by starting from the equilibrium equation of the moment around the Z-axis, expressed as: wherein ^^^^is the vertical acceleration of the vehicle and ^^^^^^is the moment of inertia along the longitudinal axis X of the vehicle 2. By putting equations (12a), (12b) and (2) into equation (6), the third linear equation is obtained and can be expressed as: According to equation (18), the first derivative of the chassis roll rate, indicated by ^̈^^^, depends on the chassis roll angle ^^^^through the gravity acceleration. The factor ^^^^^^ℎ^^^^^^^^ − ^^^^^^^^^^^^ ^^^^^^^^is a contribution which depends on the vertical acceleration and so takes into account not only the chassis roll angle ^^^^but also the road bank angle ^^^^. The roll stiffness ^^^^^^^^^^and the roll damping ^^^^^^^^^^of the vehicle 2 are identified from experimental test data. In particular, these parameters are obtainable by performing steering wheel angle ramps and sweep manoeuvres at different longitudinal velocities. The vehicle roll model represented by the three equations (14) (16) and (18) will be used in a linear Kalman filter observer. In order to model the lateral dynamic of the vehicle, which is described by equations (14), (16), (18), as a continuous-time linear dynamic system similar to (3) and (4), that is a further system defined as: ^^^̇^ = ^^^^^^^^ + ^^^^^^^^ (^^^^)^^^^ = ^^^^^^^^ + ^^^^^^^^ (^^^^)a further input, a further state, and a further output of the system are defined as follows: - ^^^^is further scalar input defined by the front wheel angle ^^; - ^^^^, is a further state vector defined by a plurality of variables including: - the lateral velocity ^^^^of the vehicle 2, - the yaw rate ^̇^ of the vehicle 2, - the chassis roll angle ^^^^of the vehicle 2, - the chassis roll rate ^̇^^^of the vehicle 2, - the road bank angle ^^^^, and - the road bank rate ^̇^^^; - ^^^^is a further output or measurement vector defined by a plurality of measured variables selected within a group consisting of: - the measured lateral acceleration ^^^^^^of the vehicle 2, - the measured yaw rate ^̇^^^of the vehicle 2, and - the measured total roll rate ^̇^^^of the vehicle 2. Accordingly, ^^^^and ^^^^are dynamic system matrices and ^^^^and ^^^^are dynamic system vectors. During the measurement update step the output vector ^^^^scalar input ^^^^are measured. The variables of the measurement vector ^^^^are put in relationship with the state of the system by using the following linear equations: According to equation (21), the measured lateral acceleration ^^^^^^is expressed by the sum of the components of the lateral acceleration and the vertical acceleration parallel to the ground. The equation (21) is developed by using equation (13) and the small angle assumption. Equation (22) means that the measured yaw rate ^̇^^^is represented by the state variable yaw rate ^̇^. Equation (23) means that the measured total roll rate ^̇^^^is represented by the sum of two state variables, i.e. the chassis roll rate ^̇^^^and the road bank rate ^̇^^^. The above definition of scalar input u, state vector x and output vector y together with the state linear equations (14) (16) and (18) and the measurement linear equations (21), (22) and (23) give rise to the following dynamic system matrices ^^^^and ^^^^and dynamic system vectors ^^^^and ^^^^: wherein To summarize, the estimating the lateral velocity ^^^^, after modelling the lateral dynamic of the vehicle 2 as the continuous-time linear dynamic system defined by (19) and (20) and described above, further comprises: - measuring the scalar input ^^^^, i.e. the front wheel angle ^^, by means of the steering wheel angle sensor 12 of the EPS 5 according to the measurement period; - measuring the variables of the output vector ^^^^, i.e. obtaining the measured lateral acceleration ^^^^^^, the measured yaw rate ^̇^^^and the measured total roll rate ^̇^^^, by means of the IMU 3 according to the measurement period; - discretizing the further continuous-time linear dynamic system to obtain a further discrete-time linear dynamic system; - real-time applying the Kalman Filter to the further discrete-time linear dynamic system by using the measured scalar input ^^^^and the measured output vector ^^^^for estimating the state vector ^^^^according to the measurement period; and - extracting values of the estimated lateral velocity ^^^^from the estimated further state vector (^^^^). In particular, the triaxial accelerometer 10 provides a signal representing the measured lateral acceleration ^^^^^^and the gyroscope 11 provides a signal representing the measured yaw rate ^̇^^^and preferably also a signal representing the measured total roll rate ^̇^^^. As can be seen from the detailed matrices and vectors (24) and (25), part of elements of the dynamic system matrices ^^^^and ^^^^are inversely proportional to the longitudinal velocity ^^^^of the vehicle 2, which means that the longitudinal velocity ^^^^is a parameter for the continuous-time linear dynamic system to which the Kalman filter is applied to. However, in general the longitudinal velocity ^^^^is a variable during the travelling of the vehicle 2 and therefore it is measured by means of the wheel speed sensor 13 according the same measurement period of the measurement vector ^^^^. That means the further discrete-time linear dynamic system to which the Kalman filter is applied to is a time-variant dynamic system. Therefore, the discretization step for obtaining the discrete-time linear dynamic system is carried out at each time step according to the measurement period. It is worth to note that automated driving applications substantially need to estimate the chassis pitch angle ^^^^and the road hill angle ^^^^, when the vehicle 2 accelerates or brakes and / or runs into uneven road conditions, such as for instance bumps or potholes, during normal traveling of the vehicle 2. In these situations, the contribution of the factor ^̇^^^^^of equation (8) is negligible. According to a further embodiment of the present invention, based on the assumption that the contribution of the factor ^̇^^^^^of equation (8) is negligible during normal travelling of the vehicle 2, the variation of the longitudinal velocity ^^^^substantially coincides with the first derivative of the longitudinal velocity ^̇^^^and therefore the variation of the longitudinal velocity ^^^^is measured simply by means of the wheel speed sensor 13. According to a further aspect of the invention, the ECU 8 is designed to store and execute a computer program or software comprising instructions which, when executed by the ECU 8, cause the latter to become configured to carry out the method described above for estimating a chassis pitch angle ^^^^of the vehicle 2 and a road hill angle ^^^^of a road travelled by the vehicle 2. The advantages of the method and the corresponding automotive driving system 1 described above with respect to state of the art are substantially twofold. First of all, the vehicle pitch model merges in single state matrices both the vehicle attitude and the road slope. Secondly, due to the linearity of the vehicle pitch model it turns out that the overall computational burden of the algorithms is low, and the estimates can be easily computed in real-time by using common and inexpensive sensors without the need of specific high- performance hardware in the vehicle. A further advantages is that the method is scalable, namely the measurement equation (4) of the continuous-time linear dynamic system can be scaled down based on the available measurements; for instance, in case the measured total pitch rate ^̇^^^is not available, the dynamic system matrix C and the dynamic system vector D are reduced. Moreover, due to the low computational burden and the scalability, the method and the corresponding automotive driving system are suitable for any type of motor vehicle, equipped or not with an automated driving system.

Claims

CLAIMS 1. Method for estimating a chassis pitch angle of a vehicle and a road hill angle of a road travelled by the vehicle, the method comprising: - modelling a longitudinal dynamic of the vehicle (2) as a continuous-time linear dynamic system defined as ^̇^ = ^^^^ + ^^^^^^ = ^^^^ + ^^^^wherein u is a scalar input defined by a variation of longitudinal velocity (^^^^) of the vehicle (2), x is a state vector defined by a plurality of variables including the chassis pitch angle (^^^^), a chassis pitch rate (^̇^^^) of the vehicle (2), the road hill angle (^^^^) and a road hill rate (^̇^^^), y is an output vector defined by a plurality of variables selected within a group consisting of the longitudinal acceleration (^^^^^^) of the vehicle (2) and a total pitch rate (^̇^^^) of the vehicle (2) represented by the sum of the chassis pitch rate (^̇^^^) and the road pitch rate (^̇^^^), A and C are first and second dynamic system matrices, respectively, and B and D are first and second dynamic system vectors, respectively; - measuring the scalar input (u) by means of a wheel speed sensor (13) of the vehicle (2) according to a certain measurement period; - measuring the output vector (y) by means of the inertial measurement unit (3) of the vehicle (2) according to the measurement period; - discretizing the continuous-time linear dynamic system to obtain a discrete-time linear dynamic system; - real-time applying a Kalman Filter to the discrete-time linear dynamic system by using the measured scalar input (u) and the measured output vector (y) for estimating the state vector (x) according to the measurement period; and - extracting values of the chassis pitch angle (^^^^) and the road hill angle (^^^^) from the estimated state vector (x).

2. The method according to claim 1, wherein the inertial measurement unit (3) comprises a triaxial accelerometer (10) for measuring the longitudinal accelerationand preferably a gyroscope (11) for measuring the total pitch rate (^̇^^^).

3. The method according to claim 1 or 2, wherein part of the elements of said first dynamic system matrix (A) and part of the elements the first dynamic system vector (B)are defined by at least a first linear equation, which binds the first derivative of the chassis pitch rate (^̈^^^) to the chassis pitch angle (^^^^), the chassis pitch rate (^̇^^^), the road hill angle (^^^^) and the longitudinal acceleration (^^^^) through a first plurality of parameters of the vehicle (2) comprising a sprung mass (^^^^) of the vehicle (2), the gravity acceleration (g), a pitch stiffness (^^^^) of the vehicle (2), a (^^^^) pitch damping of the vehicle (2), a distance (ℎ^^) between the pitch centre (21) and the centre of gravity (20) of the vehicle (2), and a moment of inertia along a lateral axis (^^^^^^) of the vehicle (2).

4. The method according to claim 3, wherein the first linear equation is as follows:wherein ^̈^^^is the first derivative of the chassis pitch rate, ^^^^is the chassis pitch angle, ^̇^^^is the chassis pitch rate, ^^^^is the road hill angle, ^^^^is the longitudinal acceleration, ^^^^is the sprung mass, g the gravity acceleration, ^^^^the pitch stiffness , ^^^^is the pitch damping, ℎ^^is a distance between the pitch centre (21) and the centre of gravity (20) of the vehicle (2), and ^^^^^^is a moment of inertia along a lateral axis of the vehicle (2).

5. The method according to any of the claims 1 to 4, wherein part of the elements of said second dynamic system matrix (C) and part of the elements the second dynamic system vector (D) are defined by a second linear equation, which binds the longitudinal acceleration (^^^^^^), as output variable, to the longitudinal acceleration (^^^^), as input variable, the chassis pitch angle (^^^^) and the road hill angle (^^^^) through a second plurality of parameters comprising the gravity acceleration (g).

6. The method according to claim 5, wherein the second linear equation is as follows:wherein ^^^^^^is the longitudinal acceleration, as output variable, ^^^^is the longitudinal acceleration, as input variable, ^^^^is the chassis pitch angle, ^^^^is the road hill angle and g is the gravity acceleration.

7. The method according to any of the claims 1 to 6, wherein the variation oflongitudinal velocity (^^^^) of the vehicle (2) is determined as a function of a first derivative of the longitudinal velocity (^̇^^^) of the vehicle (2) and a factor combining a yaw rate (^̇^) of the vehicle (2) and a lateral velocityof the vehicle (2); measuring the scalar input (u) comprising: - measuring the first derivative of the longitudinal velocity (^̇^^^) by means of the wheel speed sensor (13) of the vehicle (2); - measuring the yaw rate (^̇^) by means of the inertial measurement unit (3), in particular by means of a gyroscope (11) of the inertial measurement unit (3); and - determining the lateral velocityas a function of measurements of the inertial measurements units (3) and of a steering wheel angle sensor (12) of the vehicle (2) or as a function of measurements of the inertial measurements units (3) and of the wheel speed sensor (13) of the vehicle (2).

8. The method according to claim 7, wherein determining the lateral velocitycomprises: - estimating the lateral velocityas a function of measurements of the inertial measurements units (3) and of a steering wheel angle sensor (12) of the vehicle (2); or - estimating a side slip angle (^^) of the vehicle (2) as a function of measurements of the inertial measurements units (3), measuring the longitudinal velocity (^^^^) of the vehicle (2) by means of the wheel speed sensor (13) and calculating the lateral velocity as a function of the side slip angle (^^) and the longitudinal velocity (^^^^).

9. The method according to claim 8, wherein estimating the lateral velocityas a function of measurements of the inertial measurements units (3) of a steering wheel angle sensor (12) comprises: - modelling a lateral dynamic of the vehicle (2) as a further continuous-time linear dynamic system defined as ^^^̇^ = ^^^^^^^^ + ^^^^^^^^^^^^ = ^^^^^^^^ + ^^^^^^^^wherein ^^^^is a further scalar input defined by a front wheel angle (^^) of the vehicle (2), ^^^^is a further state vector defined by a plurality of variables including a lateral velocityof the vehicle (2), a yaw rate (^̇^) of the vehicle (2), a chassis roll angle (^^^^) of the vehicle (2), a chassis roll rate (^̇^^^) of the vehicle (2), a road bank angle (^^^^) and a road bank rate (^̇^^^), ^^^^is a further output vector defined by a plurality ofvariables selected within a group consisting of a lateral acceleration (^^^^^^) of the vehicle (2), a yaw rate (^̇^^^) of the vehicle (2) and a total roll rateof the vehicle (2) represented by the sum of the chassis roll rate (^̇^^^) and the road bank rate (^̇^^^), ^^^^and ^^^^are third and fourth dynamic system matrices, respectively, and ^^^^and ^^^^are third and fourth dynamic system vectors, respectively; - measuring the further scalar input (^^^^) by means of the steering wheel angle sensor (12) of the vehicle (2) according the measurement period; - measuring the further output vector (^^^^) by means of the inertial measurement unit (3) of the vehicle (2) according to the measurement period; - discretizing the further continuous-time linear dynamic system to obtain a further discrete-time linear dynamic system; - real-time applying a Kalman Filter to the further discrete-time linear dynamic system by using the measured further scalar input (^^^^) and the measured further output vector (^^^^) for estimating the further state vector (^^^^) according to the measurement period; and - extracting values of the estimated lateral velocityfrom the estimated further state vector (^^^^).

10. A computer program comprising instructions which, when executed by an automotive electronic control unit (8) of a vehicle (2) comprising an inertial measurement unit (3) communicating with the automotive electronic control unit (8), cause the automotive electronic control unit (8) to carry out the method of any of the claims 1 to 9.

11. An automotive driving system for a vehicle, comprising an automotive electronic control unit (8), at least one inertial measurement unit (3) and an automotive on-board communication network (9), which communicatively connect the automotive electronic control unit (8) with the inertial measurement unit (3); the automotive electronic control unit (8) being configured to implement the method according to any of the claims 1 to 9.

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