TECHNICAL FIELD

The present disclosure relates to vehicle roll-over prevention, and in particular to roll-over prevention in autonomous vehicles. The invention can be applied in heavy-duty vehicles, such as trucks, buses and construction equipment. Although the invention will be described mainly with respect to articulated vehicles, the invention is not restricted to this particular type of vehicle. BACKGROUND

A vehicle roll-over is an event where a vehicle tips over onto its side or roof. Vehicle roll overs are divided into two categories: tripped and untripped. Tripped rollovers are caused by forces from an external object, such as a curb or a collision with another vehicle, whereas untripped roll-overs are the result of steering input, speed, and friction with the ground, e.g., when a vehicle with a high centre of gravity is subject to large lateral acceleration due to turning at high velocity. The present disclosure mainly focuses on untripped roll-over events.

Vehicles for cargo transport may become sensitive to roll-over in case the vehicle load is located relatively high up from the ground, i.e., when the height of the vehicle centre of gravity (CoG) is substantial. Erroneously loaded vehicles may be subject to increased risk of roll-over.

Experienced drivers are often able to determine from experience and general ‘feel’ of the vehicle that a roll-over is imminent and may therefore be able to act in time to avoid the roll-over event. Roll-over is, however, foreseen to be an issue with autonomous vehicles where no driver is present to take corrective action.

There is a need for improved roll-over prevention systems that can be automated and used in autonomous vehicles.

Some known roll-over prevention methods react to imminent rollover. The methods estimate the risk of the vehicle rolling over based on, e.g., measurements of vehicle current lateral acceleration. Various braking intervention policies are then automatically applied in case the risk is deemed too high. US 2004/0068359 discloses a method for predictive speed control of a vehicle. The method comprises preventing vehicle roll-over by limiting vehicle speed depending on driving scenario. The control is based on what the upcoming road looks like up to a prediction horizon. However, there is a continuing need for more refined methods of roll-over prevention. Also, less complex methods for roll-over prevention are preferred in order to not overly burden on-board vehicle processing systems and control units.

SUMMARY It is an object of the present disclosure to provide improved methods for roll-over prevention. This object is obtained by a method for vehicle roll-over prevention. The method comprises obtaining a reference trajectory r and a reference speed profile v to be followed by a vehicle, predicting a vehicle lateral acceleration a _y along the reference trajectory r based on the reference speed profile v, and obtaining a vehicle roll-motion model, wherein the vehicle roll-motion model is configured to predict a roll-motion by the vehicle based on the predicted lateral acceleration a _y . The method also comprises controlling the vehicle to avoid roll-over based on the predicted vehicle roll-motion, determining a vehicle state x along the reference trajectory r, and updating the vehicle roll-motion model based on the vehicle state x. This way a proactive roll-over prevention mechanism is enabled which is able to predict roll-over prone vehicle operation before it happens and take corrective action before the vehicle enters into a condition associated with an increased risk of vehicle roll-over. The method builds on generating a model of vehicle roll-over which is not static but updated in real-time based on measurements or estimates of a current state of the vehicle. This means that a more refined and a more relevant model of vehicle roll-motion is obtained, which is an advantage.

According to some aspects, the reference trajectory r and the reference speed profile v is obtained from an autonomous drive (AD) function or from an advanced driver assistance system (ADAS). As mentioned above, vehicles implementing AD or ADAS may be prone to vehicle roll-over since there is no driver which can take preventive action. However, by the proposed methods, the risk of roll-over by AD or ADAS equipped vehicles is alleviated. According to some other aspects, predicting the vehicle lateral acceleration a _y comprises determining a target lateral acceleration required in order to follow the reference trajectory r at the reference speed profile v. Predicting lateral acceleration in this way can often be implemented in a computationally efficient manner, which is an advantage. Yet, this way of predicting lateral acceleration often provides accurate results suitable for proactive roll over prevention.

According to some further aspects, the vehicle roll-motion model is an adaptive model given as a function of the predicted lateral acceleration a _y . Various vehicle roll-motion models, of varying complexity, will be discussed below. The models may, e.g., be linearized models, and may comprise joint prediction of both roll motion, Load Transfer Ratio (LTR), and/or vehicle CoG height.

Aspects of the disclosed methods also comprise adjusting the reference speed profile v and/or reference trajectory r to meet a pre-determined requirement on predicted roll angle and/or roll angle rate for a j:th axle of the vehicle along the reference trajectory r. This way the risk of vehicle roll-over can be significantly reduced. Notably, the methods not only comprise adjusting velocity, e.g., reducing velocity to prevent roll-over. The trajectory itself may also be adjusted, for instance by straightening out planned (i.e., future) high-curvature turns and the like, if such options are available given the driving scenario.

According to aspects, the controlling comprises determining an LTR associated with a load force difference on an axle of the vehicle and controlling the vehicle to keep the determined LTR below a threshold. LTR is a particularly relevant metric for vehicle roll over prevention. By keeping LTR below a threshold, the risk of vehicle roll-over is mitigated. For instance, the controlling may comprise adjusting the reference speed profile v and/or the reference trajectory r to meet a pre-determined requirement on vehicle LTR and/or on vehicle roll angle.

Aspects of the disclosed methods also comprise determining any of; a current vehicle roll angle, a current vehicle LTR, and a current vehicle lateral acceleration, and updating the model based on the measured vehicle state values.

There are also disclosed herein control units, vehicles, computer program products, and systems for pro-active roll-over prevention associated with the above-mentioned advantages. Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the element, apparatus, component, means, step, etc." are to be interpreted openly as referring to at least one instance of the element, apparatus, component, means, step, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated. Further features of, and advantages with, the present invention will become apparent when studying the appended claims and the following description. The skilled person realizes that different features of the present invention may be combined to create embodiments other than those described in the following, without departing from the scope of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

With reference to the appended drawings, below follows a more detailed description of embodiments of the invention cited as examples. In the drawings:

Figure 1 schematically illustrates an articulated vehicle;

Figures 2- 4 show forces acting on a vehicle;

Figures 5A,5B show an example reference trajectory and associated speed profile;

Figure 6 schematically illustrates a system for roll-over prevention; Figure 7 shows a simplified model of vehicle dynamics;

Figure 8A shows a vehicle following an example trajectory;

Figure 8B shows an example vehicle lateral acceleration;

Figure 9 is a flow chart illustrating methods;

Figure 10 schematically illustrates a control unit; and Figure 11 shows an example computer program product;

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION

The invention will now be described more fully hereinafter with reference to the accompanying drawings, in which certain aspects of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments and aspects set forth herein; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout the description.

It is to be understood that the present invention is not limited to the embodiments described herein and illustrated in the drawings; rather, the skilled person will recognize that many changes and modifications may be made within the scope of the appended claims.

Figure 1 schematically illustrates an articulated vehicle 100 comprising two vehicle units. The first unit 101 is here exemplified by a tractor unit and the second unit 102 is a trailer unit. Throughout the present disclosure vehicle units are indexed by variable i. The tractor is vehicle unit i=1 , and the trailer is vehicle unit i=2. The two units undergo rotation around respective axes X,, Y, and Z,, i.e., roll, pitch and yaw, respectively.

Each vehicle unit 101, 102 comprises axles 130, 131. Herein, vehicle unit axles are indexed by variable j; the first axle from the front of the vehicle is vehicle axle j=1 , and second vehicle axle is vehicle axle j=2. Each axle is associated with a load transfer ratio (LTR), which indicates a shift in load from one side of the axle to the other side of the axle. LTR will be discussed in more detail below.

It is appreciated that the techniques disclosed herein are applicable to many different types of vehicles, with two or more axle units, such as articulated vehicles with three or more units, possibly also comprising one or more dolly units arranged in-between vehicle units. The techniques disclosed herein also apply to single unit vehicles, such as trucks without any towed vehicle units.

A somewhat simplified notation is used herein in order to not obscure the main concepts. All variables will be given without accent, e.g., a. This value may be, e.g., measured by some sensor or obtained from some model. Predictions of future values of the variable a are then at times denoted by a. It will be clear from context whether a prediction of a future variable value or a current variable value is discussed.

The vehicle 100 comprises a control unit 110 configured to control one or more operations of the vehicle. The vehicle 100 also comprises one or more sensors, state data generation modules, and/or state estimator modules 120, configured to measure vehicle state x. The vehicle state x may comprise any of vehicle lateral acceleration a _y , vehicle roll motion f, and vehicle load transfer ratio (LTR), associated with one or more of the vehicle axles 130, 131. The vehicle 100 is optionally connected via, e.g., wireless link to a remote server 140. The remote server may perform one or more functions and signal processing operations associated with vehicle control discussed herein. The remote server 140 may also store one or more parameters of the vehicle 100, such as present cargo, center of gravity height of a vehicle unit, and data regarding vehicle load.

Under some unfortunate circumstances, for instance when a vehicle enters a turn at too high velocity, one or more vehicle units may experience a roll-over condition. When this happens, the force distribution on one or more axles is such that all force is on one end of the axle and no force is on the other end of the axle. It is an objective of this disclosure to predict such events before they happen and control vehicle functions to avoid vehicle roll over.

Heavy vehicles are complex systems from a mechanical perspective. It is an object of the present disclosure to provide models of roll motion which are manageable in terms of, e.g., computation complexity and verifiability.

Some examples of vehicle roll motion will now be given in connection to Figures 2-4;

Figure 2 schematically illustrates a vehicle 200 with mass m at a center of gravity (CoG). The vehicle 200 undergoes roll motion, i.e., the vehicle tilts by a roll angle f to the right due to a lateral acceleration a _y . The Earth gravitational constant is denoted by g, the track width is l _t , and the CoG height is h _cg . In Figure 2, it is assumed that the axles 210 and tyres 220 have negligible mass compared to the overall vehicle chassis. A flat road surface with zero bank angle is also assumed, as well as a rigid vehicle body without suspension and with stiff tyres. Extension to sloping road surfaces are straight forward. Thus, the only Degree of Freedom (DoF) with respect to roll motion in response to lateral acceleration a _y will be the roll angle f. According to this model, vehicle roll-over happens when the lateral acceleration reaches the level

Thus, there is a threshold imposed on allowable lateral acceleration a _y . If lateral acceleration goes above this threshold, then one or more of the wheels starts lifting off from the ground. More dynamics can be incorporated into the vehicle roll motion model if one regards the two main compliances allowing a dynamic roll motion; Tyre compliance and chassis suspension. The mechanical moments causing roll are the restoring moment, resulting from the lateral load transfer between left and right side tires, as schematically illustrated in Figure 3, and the overturning moment, originating from the lateral acceleration of the CoG, and lateral displacement moment, due to the lateral shift of the CoG.

These two moments result in two, clearly distinguishable DoF: (Φt (“unsprung” roll angle due to tyre compliance) about rotation center O at ground plane, and Φ _s (“sprung” roll angle of the chassis suspension) about rotation center R at height h _rc , which are indicated in Figures 3 and 4. It is noted that some of these roll-motion values are notoriously hard to measure by sensors or to obtain by other means such as estimators and the like.

An autonomous drive (AD) vehicle, or a vehicle implementing advanced driver assistance systems (ADAS) monitors vehicle surroundings and generates a trajectory and an associated speed profile to be followed. Figure 5A schematically illustrates an example trajectory in terms of coordinates x _ref ,y _ref , in meters, with an associated path heading angle h _ref in degrees. With reference to Figure 5B, a longitudinal speed profile v _x,ref in m/s is also given as function of path parameter s, where s is defined on the interval [0, s _/ ], with si being the trajectory length up to some trajectory horizon at time fn.

Known path-following algorithms can be applied to make the vehicle follow a pre- determined trajectory at some speed profile. However, if the speed profile and the trajectory are such as to generate excessive lateral acceleration, vehicle roll-over risk is increased.

With reference to Figure 5A, according to an example, a planned track or trajectory rfrom a starting location A to a target location B can be represented by a matrix of state vectors x indexed by time t, i.e.; r(t) = where denotes position vector and denotes longitudinal and lateral velocity vector as function of time t. The trajectory data may sometimes also comprise a target acceleration vector to be followed by the vehicle, i.e., , where denotes acceleration vector as function of time t. The trajectory may also comprise other quantities such as steering wheel angle, turn rate, heading, and so on. An error vector at time t can be defined as a difference between a vehicle state vector at time t, , and the corresponding planned trajectory at time t;

A control algorithm for executing a maneuver where the vehicle 100 follows the planned track r(t) can be based on minimizing, e.g., a squared error e(t) ^T e(t). Such control algorithms can be based on a plurality of known tracking filter methods, such as Kalman filters, extended Kalman filters, Wiener filters, and variants of a particle filter. It may be important to consider the characteristics of the control algorithm used to follow the trajectory, since it will have an effect on the discrepancy between trajectory and actual vehicle state along the trajectory.

It is appreciated that the different components in the matrix of state vectors can be given different priorities or weights when deciding on actions and control decisions. For instance, lateral position may be more important than, e.g., longitudinal stopping distance, when planning a maneuver. These various configurations will also have an effect on the characteristics of the error e(t).

It is furthermore appreciated that the trajectory r(t) can be parameterized by some discrete index k, or by some other path parameter, like the parameter s mentioned above, instead of by time t.

The herein proposed techniques build on the realization that vehicle roll-over risk can be estimated or ‘predicted’ in advance based on a trajectory r(t) comprising a path x _T and a speed profile v _T to be followed by the vehicle. The techniques presented herein are based on creating a model of vehicle roll-motion in run time, i.e., as the vehicle is operated, and predicting vehicle roll motion based on the model. The model of vehicle roll-motion is thus adapted to the actual vehicle behavior, which is an advantage. If the roll-over risk is deemed too high, action can be taken proactively to, e.g., reducing vehicle velocity at critical points along the trajectory and/or changing the trajectory to reduce lateral acceleration at one or more key points along the trajectory. Most commonly is perhaps to reduce speed along certain sections of the path, but changes to the path can also be considered, e.g., straightening out some critical curves or the like. For instance, a vehicle may be driving along a relatively wide road, perhaps with a broad road shoulder. This allows the vehicle to plan turns such that lateral acceleration is kept below dangerous levels even if the speed profile is not adjusted.

With reference again to Figures 3 and 4, the left and right wheel normal forces to the ground are labeled F _z,l and F _z,r' respectively. When one of these two forces become small, the risk of roll-over is large. The dimensionless lateral Load Transfer Ratio (LTR) is defined herein for each axle (130, 131) of a vehicle combination as the lateral load transfer normalized by the total vertical load;

AF ^* = ±100% corresponds to wheel lift off on the corresponding axle, i.e., vehicle rollover or at least severe risk of vehicle roll-over. An advantage of LTR as roll-over index or roll-over risk indicator compared to other measures is that it directly incorporates roll dynamics, at least to some degree of accuracy.

It is appreciated that the methods disclosed herein could also stop at predicting roll angle, and not continue to LTR.

To ensure vehicle roll safety, the allowed lateral load transfer can be set to a value below wheel lift-off with some margin. It is possible to instrument an axle to provide an estimate of the vertical tyre forces, and, therefore, of LTR. However, when measurement of large deviation in LTR are obtained, it may be too late to avoid roll-over due to, e.g., system inertia, control delay, and other vehicle time constants.

The present disclosure formulates an approximation of LTR in terms of measurable quantities that can also be predicted based on the trajectory information discussed above in connection to Figures 5A and 5B.

It is possible to predict LTR, here denoted up to some time horizon, for a vehicle unit i and axle j in terms of predicted roll angle vehicle unit CoG height h _{cg i} and track width l _{t ,i} as where â _y,i,j is the lateral acceleration predicted for axle j of vehicle unit i, and g is the Earth gravitational constant.

The gravity of Earth, denoted by small g, is the net acceleration that is imparted to objects due to the combined effect of gravitation (from distribution of mass within Earth) and the centrifugal force (from the Earth's rotation). In SI units this acceleration is measured in meters per second squared, m/s ² , or equivalently in newtons per kilogram N/kg. Near Earth's surface, gravitational acceleration is approximately 9.8 m/s ² , which means that, ignoring the effects of air resistance, the speed of an object falling freely will increase by about 9.8 m/s every second. The quantity is a vehicle unit specific parameter. To account for model errors and transient dynamics, a safety margin can be included in X _i . Thus, for a two unit articulated vehicle such as the vehicle 100 shown in Figure 1, the vehicle specific constants may be set as X ₁ = c _{s ,1} X ₁ for the tractor 101 (vehicle unit i=1 ) and X ₂ = c _s,2 X ₂ for the trailer (vehicle unit i=2). The safety margins may be set as fixed values or may be dynamically adapted. The values assigned to the safety margin factors c _{s ,i} may be obtained from experimentation and/or from computer simulation.

Figure 6 schematically illustrates a system 600 for vehicle roll-over prevention. Estimates of vehicle state x (comprising, e.g., roll-angle Φ _i,j and other vehicle parameters) are obtained from sensors or from other sub-systems and fed into the system 600 as input data. The trajectory r (comprising the speed profile) discussed above in connection to Figures 5A and 5B are also supplied as inputs to the system. A yaw model 610 then predicts lateral acceleration â _y , and a roll-motion model 620 predicts vehicle roll angle f. The yaw model 610 and the roll-motion model 620 together represent a vehicle prediction model 630. The vehicle prediction model can, according to an example, then be used in an LTR prediction model 640 to predict LTR along the trajectory r as will be discussed in more detail below. According to another example, the prediction of LTR based on vehicle state and lateral acceleration can also be incorporated into the vehicle prediction model 630. Then, optionally, a vehicle control unit 650 or other functional module may adjust the vehicle target speed profile to meet requirements on, e.g., LTR or roll angle. The output 660 of such a function may, e.g., be a maximum velocity to be kept during parts of the trajectory, or some alternative trajectory parameters, like less abrupt turns or the like. Vehicle lateral acceleration along a reference trajectory can be predicted in many different ways based on the reference trajectory and on the speed profile. The lateral acceleration may also be obtained as part of the trajectory to be followed. The present disclosure is not limited to any particular method for predicting vehicle lateral acceleration.

One example approach to predicting lateral acceleration comprises transforming a reference trajectory into a lateral acceleration reference a _{y, ref} (t). This basically entails deducing the lateral acceleration that needs to be achieved at each point in time in order to follow the required path x _T (t ) at the desired speed profile v _T (t), i.e., counting ‘backwards’ using the trajectory with its turns and the associated target speed profile. More or less advanced models of vehicle dynamics can be assumed in the prediction of lateral acceleration.

Figure 7 shows a simplified ‘single-track’ vehicle model with associated forces. Single track vehicle models are known in general and will therefore not be discussed in more detail herein. Based on the model in Figure7, for a vehicle with mass m, the following system of equations can be assumed; where I _zz is the yaw moment of inertia about the CoG, v _x and v _y are the longitudinal and lateral velocities of the CoG, respectively, f is the yaw rate, F _y,F and F _{y R} are front and back lateral forces, and a and b geometrical parameters. Note that the front and back lateral forces correspond to axles j=1 and j=2, respectively.

Vehicle lateral acceleration can be determined from the above simplified set of equations, assuming v _y = 0, as

If predictions of vehicle velocity v _x are available, they can be ‘transformed’ into predictions of lateral accelerations â _y , based on the yaw rate , i.e.,

Figure 8A schematically illustrates a vehicle 810 moving along a trajectory r over coordinates [x _ref ,y _ref ]. The distance d between adjacent vehicle symbols 810 provide some idea about target velocity that the vehicle attempts to follow. Figure 8B shows an example lateral acceleration a _y 820 and a prediction a _y 830 thereof, for part of the trajectory in Figure 8A.

With reference to Figures 8A and 8B, â _y = v _x Φ can approximately predict actual lateral acceleration for the trajectory up to some time horizon t _H . However, the approximation does not account for effects like closed-loop dynamics. For instance, some over-shoots 840, 850 where the prediction is not very accurate can be observed in Figure 8B.

More advanced methods for predicting lateral acceleration may also account for effects like lateral jerk. More advanced vehicle dynamic models may also be used to further refine the prediction of lateral acceleration based on the trajectory and the speed profile.

A problem with basing lateral acceleration prediction on expressions like a _y = n _c Φ is that it assumes knowledge of the vehicle speed v _x up to the prediction horizon t _H , which is dependent on the closed-loop behaviour of the vehicle, including, e.g., cruise control and other vehicle control functions. Assuming a small tracking error, using the information in v _x,ref (t) given by the trajectory data is an option. However, there may be a delay between actual vehicle velocity and reference velocity, which may cause error in vehicle velocity prediction, especially when longitudinal acceleration levels are high.

An option is to linearly extrapolate the current speed of the vehicle using the current vehicle acceleration vector; v _x (t) = v _x (0) + a _x (0)t, t e [0, t _H ] where v _x (t) is the predicted future speed of the vehicle at time f, predicted based on the current vehicle speed v _x (0) and acceleration a _x ( 0). The prediction is made up to a time horizon t _H . Advantageously, this approach is quite general and is independent of the used cruise control method.

A more advanced method for predicting lateral acceleration also captures “swings” in the lateral acceleration. This implies accounting for lateral jerk. A linear system that meets these criteria is second order, having no zeros. The following standard single-input singleoutput (SISO) transfer function description is assumed, where G _a is a Laplace-domain transfer function, A _y,j (s) is the Laplace transform of the vehicle lateral acceleration value, A _{y ref} (s ) is the Laplace transform of the vehicle lateral acceleration reference value, s a complex number, A _G the steady-state gain of the system, x the damping factor and ω _n the undamped natural frequency. Choosing these parameters affects the accuracy of the prediction. An example set of parameters which have shown to give good results for predicting lateral acceleration are and 0.5 ≤ w _n ≤ 3 rad/s.

The predicted lateral acceleration is obtained by subjecting the prediction model above to the acceleration reference value; where vehicle unit and axle indices have been skipped for brevity, L ^-1 is the inverse Laplace transform, and G _a,p corresponds to the model with a given undamped natural frequency value from a set of undamped natural frequency values, indexed by variable p over a set of undamped natural frequencies. In practice, this prediction is calculated at k discrete time points, by discretizing a finite number of models G _{a, q} using zero-order-hold, obtaining the form where H _a,p is the discretized transfer function corresponding to G _a,P , q the time-shift operator and n _1,p , n _2,P , d _1,p , d _2,p , d _3,p are scalar coefficients, corresponding to a particular ω _n,p bandwidth. This leads to the difference equation with where T _s is a sample time of the system, i.e., an update interval. Initial conditions and may be obtained by computer simulation and/or practical experimentation.

The above is of course again an oversimplification of the ‘real’ dynamics of the vehicle, but reasonably accurate predictions of vehicle lateral acceleration can be achieved by this method.

Consider now an example roll-model for vehicle axle j of some unit comprised the heavy vehicle 100 given by where a _{y j} is the lateral acceleration for the j:th axle and where vehicle unit index i has been skipped for brevity. Here, the parameters k _Φ , b _Φ , and h _cg may be difficult to obtain with sufficient precision, for instance by measurements. It may therefore be efficient to linearize the prediction model. The above model can be re-formulated as where c _1, c ₂ , c ₃ are scalar model coefficients. The expression can be rearranged as

The system matrices and can be discretized, yielding: where Φ _j ( k) is the vehicle roll angle for axle j at sample k, is the corresponding roll angle rate at sample k, A _d and B _d are system matrices, x _Φ is a vehicle state space variable, and a _{y j} (k ) is the predicted lateral acceleration for the j:th axle at sample k.

There are many known methods by which the system matrices can be identified. Defining

, where y(k) is a measurement vector, (Φ(k) is a data vector comprising previous data, and Θ(k) is the vector of values desired to estimate, the parameter identification becomes where e _id (k) e _id (k ) = y(k) - (p ^T (k)Θ(k - 1) can be seen as a prediction error describing the difference between model output and actual measurement data. Once the system matrices A _d and B _d have been identified or estimated for a given vehicle combination, roll motion can be estimated based on predicted lateral acceleration â _y , e.g., as where, again, vehicle unit index i has been skipped for brevity. The system matrices A _d , B _d can be initialized based on previous vehicle data, based on theoretical derivation, and/or based on computer simulation. The system matrices may also be initialized based on information received from the remote server 140, which may store suitable initialization values.

A predicted LTR (for vehicle unit i and vehicle unit axle j) along the trajectory r can now be determined as where Xi is a vehicle unit specific constant which may be known a-priori, may be obtained from the remote server 140, or may be estimated during vehicle operation.

LTR along the trajectory r may also be predicted directly from a joint model of roll motion and LTR, i.e., where and comprise and , respectively, and one or more higher order terms, and where vehicle unit index i has been skipped for brevity and where x _Φ,LTR represents vehicle state comprising LTR. The state variables and are now vectors comprising the variables and , but also higher order terms up to some level n, like The system matrices A _d , B _d may be identified using any of the above techniques. It is appreciated that the system matrix coefficients may be complex, and according to some aspects may comprise vectors. This will, for instance, be the case if some linearization is implicitly performed by the system matrices. The vehicle CoG height over ground, h _cg , can also be comprised in the model;

Other methods to predict roll angle LTR , and other vehicle parameters related to roll-over comprises Kalman filtering and particle filters. In case LTR is included in the prediction model together with roll angle, an extended Kalman filter may be suitable, since the expression for LTR as function of roll angle comprises non-linear functions, i.e., cosine functions.

A covariance matrix can also be associated with the predicted quantities. A covariance matrix is, for instance, obtained when using a Kalman filter or extended Kalman filter, driven by the error signal e _id (k), to estimate and continuously update the system matrices of the roll-motion model.

A covariance matrix estimate P _kIk in a Kalman filter algorithm at discrete time index k, given data input up to time k, is determined as where P _{k |k-1} is the covariance matrix estimate at time k given data up to time k-1, / is the identity matrix, K _k is the Kalman gain at time step k, H _k is the observation matrix at time step k, R _k is the assumed covariance matrix of the measurement noise, i.e., describing the uncertainty in the input sensor signals, F _k is a state transition matrix at time step k, and Q _k is a process noise at time step k.

Note that the estimate of covariance matrix P _kIk does not depend on the actual realization of sensor data, only on the assumed statistics of the error distributions and processes. Kalman filters, extended Kalman filters, and the like are known in general and will therefore not be discussed in more detail herein.

Figure 9 is a flow chart which summarizes the various methods and aspects discussed above. There is illustrated a method for vehicle roll-over prevention. The method comprises obtaining S1 a reference trajectory r and a reference speed profile v to be followed by a vehicle 100. The reference trajectory r and the reference speed profile v may, e.g., be obtained from an autonomous drive (AD) function S11 or from an advanced driver assistance system (ADAS) S12.

The method also comprises predicting S2 a vehicle lateral acceleration a _y along the reference trajectory r based on the reference speed profile v. Predicting vehicle lateral acceleration can be performed in several different ways, as discussed above in connection to Figure 6. Vehicle lateral acceleration can be predicted per vehicle unit in a vehicle combination.

According to some aspects, predicting the vehicle lateral acceleration a _y comprises determining S21 a target lateral acceleration required in order to follow the reference trajectory rat the reference speed profile v.

The vehicle lateral acceleration a _y and the roll-motion may also be predicted individually S22 for each vehicle unit 101 , 102 of the vehicle 100, and/or for one or more axles 130, 131 on the vehicle 100.

The method further comprises obtaining S3 a vehicle roll-motion model, wherein the vehicle roll-motion model is configured to predict a roll-motion by the vehicle 100 based on the predicted lateral acceleration a _y .

Thus, the method is able to predict vehicle roll motion based on the trajectory and the target speed profile. This way it can be determined in advance if a given trajectory with corresponding speed profile will lead to excessive roll motion or not. Vehicle roll-over preventive action is thus enabled in an automated fashion, which is an advantage.

According to some aspects, the vehicle roll-motion model is an adaptive model, given S31 as a function of the predicted lateral acceleration a _y . By using an adaptive model which can be adjusted based on vehicle behavior in real-time, a more accurate prediction of roll motion is obtained. For instance, by monitoring vehicle dynamic behavior and adjusting the model accordingly, a more relevant model is obtained which is able to account for current vehicle state with much higher precision compared to if a pre-determ ined model of vehicle roll-motion had been used.

Roll-motion models of varying complexity can be considered. For instance, optionally, the model of roll motion for a j:th axle of the vehicle 100 is a linearized model of roll motion given by S32 where Φ _j ( k) is the vehicle roll angle at axle j and at sample k, Φ _j (k) is the corresponding vehicle roll angle rate at sample k, A _d and B _d are system matrices, and a _{y j} (k ) is the predicted lateral acceleration at sample k for axle j. The model may be used to obtain corresponding predictions;

This linearized model allows for efficient computation and therefore does not require extensive processing resources, which is an advantage. Yet, the model has shown reasonably accurate, and is able to predict vehicle roll motion up to time horizons of reasonable length. Linearized models such as the above can be efficiently identified using known methods such as recursive least squares (RLS). The linearized model also allows for an efficient update routine, which is an advantage.

According to other aspects, the vehicle roll-motion model is configured to predict S33 a Load Transfer Ratio (LTR) by the vehicle 100 based on the predicted lateral acceleration a _y . Thus, a joint prediction of both roll motion and LTR is obtained from a single model, which is an advantage. For instance, the linearized model of roll motion for a j:th axle of the vehicle 100 may be given by S34 where and comprise Φ _j (k) and Φ _j (k), respectively, and one or more higher order terms, and where is it appreciated that at least some of the model coefficients a _d may be vector coefficients implementing a linearization of variables which depend on each other by a non-linear relationship. The model may be used to obtain corresponding predictions; Even more advanced models may optionally be contemplated. According to some aspects, the vehicle roll-motion model is configured to estimate S35 a center of gravity height, h _cg , of the vehicle 100 based on any of; the predicted lateral acceleration a _y , the predicted roll-motion by the vehicle 100, and/or the predicted LTR. Such linearized models of roll motion for a j:th axle of the vehicle 100 may, for instance, be given by S36 where, again, at least some of the coefficients may be vector parameters implementing a linearization operation. Again, predictions can be obtained, e.g., as The method further comprises controlling S4 the vehicle 100 to avoid roll-over based on the predicted vehicle roll-motion. It is appreciated that vehicle control based on LTR is comprised as a special case of the feature of controlling based on roll motion. According to aspects, the controlling comprises adjusting S41 the reference speed profile v and/or reference trajectory r to meet a pre-determined requirement on predicted roll angle and/or roll angle rate for a j:th axle of the vehicle 100 along the reference trajectory r. According to other aspects, the controlling comprises determining S42 LTR associated with a load force difference on an axle 130, 131 of the vehicle 100, and controlling the vehicle 100 to keep the determined LTR below a threshold.

The LTR for the j:th axle on vehicle unit i of the vehicle 100, may for instance be determined S43 as where 2 h _{cg i} is a center of gravity height for vehicle unit i, l _{t ,i} is a track width associated with axles on the vehicle unit i, a _y,i,j is the predicted lateral acceleration for the j:th axle on the i:th vehicle unit, g is the gravitational constant, and is the predicted vehicle roll angle at axle j on vehicle unit i. As noted above, the LTR is optionally determined S44 directly from the linearized model of roll motion.

According to some aspects, the controlling comprises adjusting S45 the reference speed profile v and/or adjusting S46 the reference trajectory r to meet a pre-determ ined requirement on vehicle LTR and/or on vehicle roll angle.

The method also comprises determining S5 a vehicle state x along the reference trajectory r. The vehicle state may comprise, e.g., any of; a current vehicle roll angle S51 , a current vehicle LTR S52, and/or a current vehicle lateral acceleration S53.

The method comprises updating S6 the vehicle roll-motion model based on the vehicle state x. This step is key to the proposed proactive roll-over prevention methods discussed herein. By updating the vehicle roll-motion model, the model can be generated to account for current vehicle dynamics, which improves modelling accuracy.

According to some aspects, the updating comprises generating S61 an error as a difference between a predicted vehicle state and a measured vehicle state and updating the vehicle roll-motion model to reduce the error.

According to some aspects, the updating comprises generating S62 the error signal as a difference between a predicted vehicle roll angle and a measured vehicle roll angle and updating the vehicle roll-motion model to reduce the error.

According to some aspects, the updating comprises generating S63 the error signal as a difference between a predicted vehicle LTR and a measured vehicle LTR and updating the model F to reduce the error.

The error signal may be used to drive, e.g., a Kalman filter, an extended Kalman filter, or a particle filter in order to identify roll-motion model system matrices.

Figure 10 schematically illustrates, in terms of a number of functional units, the components of a control unit 110 according to embodiments of the discussions herein. This control unit 110 may be comprised in the articulated vehicle 100. Processing circuitry 1010 is provided using any combination of one or more of a suitable central processing unit CPU, multiprocessor, microcontroller, digital signal processor DSP, etc., capable of executing software instructions stored in a computer program product, e.g. in the form of a storage medium 1030. The processing circuitry 1010 may further be provided as at least one application specific integrated circuit ASIC, or field programmable gate array FPGA. Particularly, the processing circuitry 1010 is configured to cause the control unit 110 to perform a set of operations, or steps, such as the methods discussed in connection to Figure 8. For example, the storage medium 1030 may store the set of operations, and the processing circuitry 1010 may be configured to retrieve the set of operations from the storage medium 1030 to cause the control unit 110 to perform the set of operations. The set of operations may be provided as a set of executable instructions. Thus, the processing circuitry 1010 is thereby arranged to execute methods as herein disclosed.

The storage medium 1030 may also comprise persistent storage, which, for example, can be any single one or combination of magnetic memory, optical memory, solid state memory or even remotely mounted memory.

The control unit 110 may further comprise an interface 1020 for communications with at least one external device, such as the antenna array comprising the phase controllers and the mechanically rotatable base plate. As such the interface 1020 may comprise one or more transmitters and receivers, comprising analogue and digital components and a suitable number of ports for wireline or wireless communication.

The processing circuitry 1010 controls the general operation of the control unit 110, e.g., by sending data and control signals to the interface 1020 and the storage medium 1030, by receiving data and reports from the interface 1020, and by retrieving data and instructions from the storage medium 1030. Other components, as well as the related functionality, of the control node are omitted in order not to obscure the concepts presented herein.

In summary, Figure 10 schematically illustrates a control unit 110 configured for vehicle roll-over prevention. The control unit 110 comprises processing circuitry 1010 configured to; obtain a reference trajectory rand a reference speed profile v to be followed by a vehicle

100, predict a vehicle lateral acceleration a _y along the reference trajectory r based on the reference speed profile v, obtain a vehicle roll-motion model, wherein the roll-motion model is configured to predict a roll-motion by the vehicle 100 based on the predicted lateral acceleration a _y , control the vehicle 100 to avoid roll-over based on the predicted vehicle roll-motion, determine a vehicle state x along the reference trajectory r, and update the vehicle roll-motion model based on the vehicle state x.

Figure 11 illustrates a computer readable medium 1110 carrying a computer program comprising program code means 1120 for performing the methods illustrated in Figure 9, when said program product is run on a computer. The computer readable medium and the code means may together form a computer program product 1000.