Patent Description:
Heavy-duty vehicles, such as trucks and semi-trailer vehicles, are designed to carry heavy loads. The heavily laden vehicles must be able to start from standstill also in uphill conditions and accelerate reliably on various types of road surfaces.

Excessive wheel slip occurs when too much torque is applied to an axle, or to a wheel compared to what is supported by the current road friction and normal load. Excessive wheel slip is undesired since it results in an unpredictable vehicle behavior, loss of tractive force, and also in an energy inefficient operation.

<CIT> discusses wheel slip and proposes methods for limiting a maximum regenerative braking torque which can be applied to a wheel. The controller uses a tyre model to determine a maximum usable traction for each wheel and calculates the maximum regenerative braking force to be applied to each wheel based on this tyre model.

A differential drive arrangement allows a single power source, such as a combustion engine or an electric machine, to power both wheels on a driven axle. An open differential drive arrangement distributes torque evenly over the drive axle. However, in scenarios where one wheel starts to spin faster than the other wheel, for instance due to varying friction conditions, the power transferred to the wheels will differ. This problem may become especially pronounced in so-called split friction conditions, where severely sub-optimal propulsion can be experienced.

<CIT> discloses a method for controlling motion of a heavy-duty vehicle, where the vehicle comprises an open differential driven axle, and where the vehicle wheel forces are controlled based on a wheel slip target.

<CIT> discusses a reduction of the target slip value in response to a large wheel speed difference.

<CIT> discloses methods for controlling wheel slip of a vehicle.

However, despite the advancements to-date, there is a continuing need for further improvements in vehicle motion management in heavy-duty vehicles, and in particular for vehicles comprising open differential drive arrangements.

It is an object of the present disclosure to provide techniques which alleviate or overcome at least some of the above-mentioned problems. This object is at least in part obtained by a method for controlling propulsion of a heavy-duty vehicle, where the heavy-duty vehicle comprises a differential drive arrangement arranged in connection to a drive axle with a left wheel and a right wheel. The method comprises determining a nominal shaft slip corresponding to a desired wheel force to be generated by the drive axle wheels, wherein the nominal shaft slip is indicative of a difference between a current vehicle velocity and a vehicle velocity corresponding to the shaft speed. The method also comprises determining a difference between a speed of the left wheel and a speed of the right wheel, and adjusting the nominal shaft slip in dependence of a magnitude of the wheel speed difference to a target shaft slip and also controlling the shaft speed based on the target shaft slip.

The vehicle control systems discussed herein are able to react quickly to a detected wheel speed difference in order to, e.g., maintain traction. The proposed system advantageously complements known traction control systems which apply friction brakes or the like to transfer torque away from a spinning wheel of an open differential. The proposed methods adjust shaft speed already for relatively small wheel speed differences, and is thereby able to improve traction before the actual traction control system kicks in. It is an advantage that the shaft speed control can be actuated with low latency, since the forward motion of a heavy-duty vehicle in, e.g., an uphill driving condition with uneven friction on the sides of the vehicle, can be maintained. The target shaft slip may for instance be obtained by multiplying the nominal shaft slip by a reduction factor α ≤ <NUM>, where the reduction factor α decreases with the magnitude of the wheel speed difference. The actual function for determining the reduction factor may be configured specifically for a given vehicle, or for a given type of vehicle, thus customizing the control methods for even higher performance. The method may also comprise controlling the shaft speed based on the target shaft slip by adjusting the shaft speed to obtain the target shaft slip. The shaft slip may, e.g., be defined as <MAT> where K represents a conversion factor between axle speed ω<NUM> and vehicle speed vx, such that Kω<NUM> = vx at zero wheel slip for both wheels and at equal wheel speeds.

According to aspects, the reduction factor α is determined as <MAT> and the target shaft slip λT relates to the nominal shaft slip λ<NUM> as <MAT>.

According to aspects, the difference between the speed of the left wheel and the speed of the right wheel is adjusted based on a vehicle path curvature and/or on a vehicle steering angle. Thus, wheel speed differences due to steering are compensated for. This improves the performance of the methods when the vehicle is cornering.

According to aspects, the method also comprises configuring the target shaft slip equal to the nominal shaft slip if the magnitude of the difference between the speed of the left wheel and the speed of the right wheel is below a pre-determined threshold. This way the shaft slip is not reduced until the wheel slip difference is deemed significant. The frequency of control intervention is thereby reduced, which can be an advantage in some scenarios.

According to aspects, the target shaft slip is adapted according to a bandwidth constraint, where the bandwidth constraint is smaller for a decreasing target shaft slip compared to an increasing target shaft slip. This way the shaft slip is quickly reduced in response to detecting an increase in wheel speed difference, but more slow to increase again if the wheel speed difference becomes smaller. This provides a more robust control of the heavy-duty vehicle.

According to aspects, the target shaft slip is adapted such that neither of the speed of the left wheel and the speed of the right wheel exceeds a wheel slip limit configured in dependence of the nominal shaft slip. This means that neither of the two wheels will experience a too high slip, and risk loose traction, which is an advantage. This also simplifies the overall slip control of the shaft slip.

According to aspects, the method comprises triggering a service brake intervention procedure in case the magnitude of the difference between the speed of the left wheel and the speed of the right wheel exceeds a split-µ condition threshold. In other words, the herein proposed methods may be used with advantage together with legacy traction control system, which apply brake torque to the spinning wheel in order to transfer torque over to the wheel with more traction.

There is also disclosed herein control units, computer programs, computer readable media, computer program products, and vehicles associated with the above discussed advantages.

The skilled person realizes that modifications are possible within the scope of the present invention, as defined by the appended claims.

<FIG> illustrates a heavy-duty vehicle <NUM>. This particular example comprises a tractor unit <NUM> which is arranged to tow a trailer unit <NUM>. The tractor <NUM> comprises a vehicle electronic control unit (ECU) <NUM> arranged to control various functions of the vehicle <NUM>. For instance, the ECU may be arranged to perform a vehicle motion management (VMM) function comprising control of wheel slip, vehicle unit stability, and so on. The trailer unit <NUM> optionally also comprises an ECU <NUM>, which then controls one or more functions on the trailer <NUM>. The ECU or ECUs may be communicatively coupled, e.g., via wireless link, to a remote server <NUM>. This remote server may be arranged to perform configuration of the ECU, and to provide various forms of data to the ECU <NUM>, such as providing data regarding the make and type of tyres mounted on the vehicle <NUM>, and information related to a relationship between generated wheel force and wheel slip, i.e., an inverse tyre model, as will be discussed in more detail below in connection to <FIG>.

The vehicle combination <NUM> may of course also comprise additional vehicle units, such as one or more dolly units and more than one trailer unit. The techniques disclosed herein are applicable to rigid trucks, and also to passenger cars, although the main benefit of the proposed technique is obtained when used with heavy-duty vehicle for cargo transport.

Propulsion of a heavy-duty vehicle like the vehicle <NUM> has traditionally been controlled using control loops based on torque requests. However, the torque-based control loops of a heavy duty vehicle are normally associated with time constants on the order of <NUM> or so. In some scenarios this time constant reduces overall vehicle control bandwidth to a point where the startability and overall vehicle motion management of the heavy duty vehicle may be negatively affected, especially when road friction is uneven. To improve control during, e.g., vehicle launch, it is proposed herein to base propulsion control on wheel slip requests (or, equivalently, wheel speed relative the vehicle speed) instead of on torque. This means that the propulsion device on the vehicle <NUM> is requested by the ECU <NUM> to maintain wheel slip at a target wheel slip value λtarget which has been determined in order to obtain a desired motion by the vehicle. For instance, if the target wheel slip is set at <NUM>, then the wheel rotational velocity will be continuously set at a relative difference of <NUM> above the vehicle velocity so that the wheel will always be slipping by the configured amount. Notably, this control strategy is different compared to just imposing a wheel slip limit, and performing torque-based on control of the propulsion as long as the wheel slip stays below the configured wheel slip limit.

<FIG> schematically illustrates functionality <NUM> for controlling a left wheel <NUM> and a right wheel <NUM> on a driven axle <NUM> by some example MSDs, here comprising friction brakes <NUM> (such as disc brakes or drum brakes) and a propulsion device <NUM> such as an electric machine (EM) or a combustion engine (CE). The friction brakes <NUM>, <NUM> and the propulsion device <NUM> are examples of wheel torque generating devices, which may also be referred to as actuators and which can be controlled by one or more motion support device control units <NUM>, <NUM>. In this example the service brakes SB1, SB2 are assumed to be controlled by respective wheel end module (WEM) controllers <NUM>, <NUM>, while the propulsion device <NUM> comprises an integrated control unit not shown in <FIG>.

The propulsion device <NUM> is connected to the drive axle <NUM> via a differential drive arrangement <NUM>. This differential drive arrangement may, e.g., be an open differential which distributes torque evenly over the two wheels.

A traffic situation management (TSM) function <NUM> plans driving operations with a time horizon of, e.g., <NUM>-<NUM> seconds or so. This time frame corresponds to, e.g., the time it takes for the vehicle <NUM> to negotiate a curve. The vehicle maneuvers, planned and executed by the TSM, can be associated with acceleration profiles and curvature profiles which describe a desired vehicle velocity and turning for a given maneuver. The TSM continuously requests the desired acceleration profiles areq and curvature profiles creq from the VMM function <NUM> which performs force allocation to meet the requests from the TSM in a safe and robust manner, based at least in part based on capability reports (CAP) received from the various MSD control units.

Desired acceleration profiles and curvature profiles may optionally be determined based on input from a driver via a human machine interface of the heavy-duty vehicle via normal control input devices such as a steering wheel, accelerator pedal and brake pedal, although the techniques disclosed herein are just as applicable with autonomous or semi-autonomous vehicles. The exact methods used for determining the acceleration profiles and curvature profiles is not within scope of the present disclosure and will therefore not be discussed in more detail herein.

The control commands, i.e., the requests sent to the MSD controllers <NUM>, <NUM>, <NUM> from the VMM function <NUM> comprises wheel slips λ to be maintained by the respective MSDs.

Both the friction brakes and the propulsion device interact with the road surface via wheels <NUM>, <NUM> comprising respective tyres. Thus, the tyre properties and behavioral characteristics has an impact on how the different control actions by the friction brakes and the propulsion device generate vehicle motion. A software-based tyre model is optionally comprised in the system. This tyre model provides information about the tyre currently mounted on the wheel, its properties, and behavioral characteristics. The tyre model may, as mentioned above, be implemented as a look-up table or other type of function. The tyre model is parameterized, i.e., defined, by one or more tyre parameters. This means that the function itself varies in dependence of the tyre properties. The tyre model can be used to model various relationships, as exemplified above, such as a relationship or mapping between wheel slip and generated wheel force, and/or a mapping between tyre wear rate and vehicle state such as tyre normal load, vehicle speed, and wheel slip. It is appreciated that the present disclosure is not limited to any particular form of tyre model structure. Rather, it is appreciated that many different types of mathematical and/or experimentally based functions and mappings can be used as the tyre model.

A tyre model can be used to define a relationship between longitudinal tyre force Fx for a given wheel and an equivalent longitudinal wheel slip for the wheel. Longitudinal wheel slip λx relates to a difference between wheel rotational velocity and speed over ground and will be discussed in more detail below. Wheel, axle or shaft rotation speed ω is a rotational speed given in units of, e.g., rotations per minute (rpm) or angular velocity in terms radians/second (rad/sec) or degrees/second (deg/sec). The wheel behavior in terms of wheel force generated in longitudinal direction (in the rolling direction) and/or lateral direction (orthogonal to the longitudinal direction) as function of wheel slip is discussed in "<NPL>. See, e.g., chapter <NUM> where the relationship between wheel slip and longitudinal force is discussed.

Longitudinal wheel slip λx may, in accordance with SAE J670 (<NPL>) be defined as <MAT> where R is an effective wheel radius in meters, ωx is the angular velocity of the wheel, and vx is the longitudinal speed of the wheel (in the coordinate system of the wheel). Thus, λx is bounded between -<NUM> and <NUM> and quantifies how much the wheel is slipping with respect to the road surface. Wheel slip is, in essence, a speed difference measured between the wheel and the vehicle. Thus, the herein disclosed techniques can be adapted for use with any type of wheel slip definition. It is also appreciated that a wheel slip value is equivalent to a wheel speed value given a velocity of the wheel over the surface, in the coordinate system of the wheel.

It is also possible to define a nominal shaft slip <MAT> where K represents a conversion factor between axle speed ω<NUM> and vehicle speed vx, including any in-between gear ratios and the like, such that Kω<NUM> = vx at zero wheel slip for both wheels and at equal wheel speeds.

Lateral wheel slip λy can be defined as <MAT> where vy is the lateral speed of the wheel (in the coordinate system of the wheel), measured on a direction orthogonal to the direction of the longitudinal speed vx. The present disclosure relates primarily to longitudinal wheel slip, although it is appreciated that the two are connected, mainly since the ability to generate lateral wheel force depends strongly on the longitudinal wheel slip.

A tyre is subject to a longitudinal force Fx, a lateral force Fy, and a normal force Fz. The normal force Fz is key to determining some important vehicle properties. For instance, the normal force to a large extent determines the achievable longitudinal tyre force Fx by the wheel since, normally, Fx ≤ µ Fz, where µ is a friction coefficient associated with a road friction condition. The maximum available lateral force for a given lateral slip can be described by the so-called Magic Formula as described in "<NPL>.

In order for a wheel (or tyre) to produce a wheel force, slip must occur. For smaller slip values the relationship between slip and generated force are approximately linear, where the proportionality constant is often denoted as the slip stiffness of the tyre. <FIG> shows a graph <NUM> illustrating an example of achievable tyre forces Fx, Fy as function of wheel slip. The longitudinal tyre force Fx shows an almost linearly increasing part <NUM> for small wheel slips, followed by a part <NUM> with more non-linear behavior for larger wheel slips. The obtainable lateral tyre force Fy decreases rapidly even at relatively small longitudinal wheel slips. It is desirable to maintain vehicle operation in the linear region <NUM>, where the obtainable longitudinal force in response to an applied brake command is easier to predict, and where enough lateral tyre force can be generated if needed. To ensure operation in this region, a wheel slip limit λLIM on the order of, e.g., <NUM>, can be imposed on a given wheel, which ensures operation in the linear region <NUM>.

A tyre model of this kind can be determined by practical experimentation, analytical derivation, computer simulation, or a combination of the above. In practice, the tyre model may be represented by a look-up table (LUT) indexed by the tyre parameters, or as a set of coefficients describing a polynomial or the like. There the set of coefficients are selected based on the tyre parameters, and where the polynomial then describes the relationship between tyre behavior and vehicle state.

With reference again to <FIG>, a difficulty when using wheel slip-based control together with open differential drive arrangements is that the wheels may end up spinning at different speeds, due to varying friction and/or normal load on the wheels. Also, different tyre conditions on the left- and right-hand side wheels may affect the wheel speeds. This means that, if a nominal shaft speed ω<NUM> is configured based on some nominal inverse tyre model Fx, which corresponds to a desired wheel slip on the inverse tyre model, then the desired wheel force may not be obtained due to variation in friction, normal load, or tyre condition at the two wheels of the drive axle. <FIG> illustrates an example of this type of situation, where the shaft speed has been configured to maximize wheel force for a nominal inverse tyre model Fx, i.e., at the wheel slip indicated as <NUM>. However, one wheel is spinning much faster than the other due to varying friction conditions (µ<NUM> compared to µ<NUM>) and/or varying normal load (Fz<NUM> compared to Fz<NUM>), and therefore has a different inverse tyre model curve Fx', which has resulted in that one wheel is operating at the point <NUM> while the other is operating at the point <NUM>, i.e., about <NUM> kN in wheel force less compared to the optimal traction case where both wheels provide a wheel force close to <NUM> kN, giving a propulsion force on the order of <NUM> kN. Also, the capability of generating lateral force by the wheel associated with the operating point <NUM> is severely limited, which may jeopardize safe vehicle motion management.

To improve the vehicle propulsion control when friction, tyre properties, and/or normal load on the wheels differs on the left- and right-hand side of a driven axle, it is proposed herein to rapidly reduce the shaft slip when a difference in wheel speed is detected over the driven axle. This will move the slipping wheel back closer to the linear region <NUM>, where the traction is much better, and is also likely to reduce the relative difference in wheel speeds. The concept is illustrated in <FIG>, which shows a graph <NUM> of wheel speed (<FIG>) and drive shaft slip (<FIG> ). At time T0, the vehicle encounters a split friction driving condition. This causes one of the wheel speeds <NUM>, dashed line, to diverge from the other wheel speed <NUM>, solid line, whereby a wheel speed difference <NUM> arises. This difference then starts to become smaller at time T1, and eventually goes away entirely at time T2 when the two wheel speeds have again converged.

During this time period T1 to T3 when there is a difference in wheel speeds, the respective operating points on the inverse tyre model curve will diverge, as discussed in connection to <FIG> above, away from the desired operating point. Most likely, the total generated wheel force by the two wheels will be sub-optimal due to the wheel speed difference, and the sub-optimally configured shaft slip. For instance, one wheel may be slipping severely while another wheel may be more or less free-rolling, i.e., not slipping at all and therefore not generating any traction force at all. To rapidly bring the slipping wheel under control again, it is proposed to temporarily reduce the nominal shaft slip λ<NUM> <NUM> by an amount <NUM> determined as a function of the magnitude of the wheel speed difference <NUM> to a target shaft slip λT, <NUM>.

<FIG> shows an example of a vehicle control stack <NUM> comprising the above-mentioned TSM and VMM functions, where the proposed technique may be implemented with advantage. Sensors <NUM> arranged to provide data about the vehicle environment provides input to the overall control stack <NUM>, and a connection to remote processing resources, such as cloud-based processing resources like the remote server <NUM> in <FIG> are also optionally comprised in the control stack.

As mentioned above, the VMM function <NUM> operates with a time horizon of about <NUM>,<NUM>-<NUM>,<NUM> seconds or so, and continuously transforms the acceleration profiles areq and curvature profiles creq into control commands for controlling vehicle motion functions, actuated by the different MSDs of the vehicle <NUM> which report back capabilities to the VMM, which in turn are used as constraints in the vehicle control. The accuracy of this control is improved by means of the advanced tyre models <NUM> discussed herein.

The VMM function <NUM> performs vehicle state or motion estimation <NUM>, i.e., the VMM function <NUM> continuously determines a vehicle state s (often a vector variable) comprising positions, speeds, accelerations, yaw motions, normal forces and articulation angles of the different units in the vehicle combination by monitoring vehicle state and behavior using various sensors <NUM> arranged on the vehicle <NUM>, often but not always in connection to the MSDs.

The result of the motion estimation <NUM>, i.e., the estimated vehicle state s, is input to a global force generation module <NUM> which determines the required global forces on the vehicle units which need to be generated in order to meet the motion requests from the TSM <NUM>. An MSD coordination function <NUM> allocates, e.g., wheel forces and coordinates other MSDs such as steering and suspension. The coordinated MSDs then together provide the desired lateral Fy and longitudinal Fx forces on the vehicle units, as well as the required moments Mz, to obtain the desired motion by the vehicle combination <NUM>. As indicated in <FIG>, the MSD coordination function <NUM> may output any of wheel slips λi, wheel rotation speeds ω, and/or steering angles δI to the different MSDs.

A split-µ control module <NUM> is arranged to monitor wheel speed differences, and to intervene in case the wheel speeds diverge. When this happens, a control signal is sent to the MSD coordination module <NUM> which will reduce the configured shaft slip in response to the control signal <NUM>. Thus, the wheel speed is rapidly brought back under control.

<FIG> illustrates an example split-µ scenario <NUM>, where a heavy-duty vehicle <NUM> drives straight on a road <NUM> in a forward direction with vehicle velocity vx <NUM>. A region of low friction <NUM> is encountered by the left wheels of the vehicle <NUM>. When this happens, the left-hand side wheels may start to spin faster than the right-hand side wheels. giving rise to the sub-optimal operating points illustrated in <FIG>, i.e., where one wheel is to the right of the nominal desired slip and the other wheel is to the left of the desired operating point. The herein proposed techniques will then quickly step in and reduce the shaft slip down to a level where the speed of the spinning wheel is reduced, thus improving overall traction very fast, much faster than would have been possible using legacy traction control system based on slow torque-based control of service brakes. The methods proposed herein also act in a more continuous manner, and may be configured to activate already at small wheel speed differences. Traction control system often require larger wheel speed differences before they kick in, due to robustness reasons.

<FIG> illustrates another example scenario <NUM>, but now the vehicle is cornering, i.e., follows a path associated with a curvature. The curvature itself gives rise to a difference in wheel speeds. This wheel speed difference is preferably accounted for by the method, i.e., such wheel speed differences due to planned curve taking will optionally not result in a modified shaft slip. However, the vehicle <NUM> encounters a region <NUM> of low friction, which causes the wheel speed difference to deviate from that expected from the curvature, which may cause a reduction in shaft slip request to the propulsion device.

<FIG> is a flow chart which summarizes the herein disclosed techniques. There is illustrated a method for controlling propulsion of a heavy-duty vehicle <NUM>, where the heavy-duty vehicle <NUM> comprises a differential drive arrangement <NUM> arranged in connection to a drive axle <NUM> with a left wheel <NUM> and a right wheel <NUM>, as discussed above in connection to <FIG>. The method comprises determining S1 a nominal shaft slip λ<NUM>, <NUM> corresponding to a desired wheel force Fx to be generated by the drive axle wheels <NUM>, <NUM>, wherein the nominal shaft slip is indicative of a difference between a current vehicle velocity vx and a vehicle velocity corresponding to the shaft speed ω<NUM>.

Shaft slip is a measure of the difference between how fast the shaft is rotating compared to how fast the vehicle is moving, of course accounting for the total gear ratio, wheel radius, and so on. Shaft slip is akin to a measure of wheel slip, albeit measured in the drive shaft instead of on the wheel axle. Shaft slip may, e.g., be defined S11 as <MAT> where K represents a conversion factor between axle speed ω<NUM> and vehicle speed vx, such that Kω<NUM> = vx at zero wheel slip for both wheels and equal wheel speeds. The nominal shaft slip may, e.g., be determined by the MSD coordination module <NUM> discussed in connection to <FIG> in order to obtain a desired total wheel force from the wheels on the driven axle. A tyre model such as that discussed in connection to <FIG> may be used to translate between desired tyre force and shaft slip.

The method also comprises determining S2 a difference between a speed ω<NUM> of the left wheel and a speed ω<NUM> of the right wheel. This wheel speed difference, or at least the magnitude thereof, is preferably determined by using left and right-hand side wheel speed sensors. The difference in wheel speeds may then be determined with high bandwidth, i.e., with an update latency on the order of <NUM> or less, by the MSD control units <NUM> and/or by the VMM unit <NUM>. The vehicle ECU <NUM> also has access to accurate information about the speed of the vehicle in the forward direction, which means that accurate determination of shaft slip is enabled.

It is appreciated that some vehicle maneuvers, like cornering, will involve a difference in wheel speed which is not due to wheel slippage. Thus, optionally, the difference between the speed ω<NUM> of the left wheel and the speed ω<NUM> of the right wheel is adjusted S32 based on a vehicle path curvature creq and/or on a vehicle steering angle δ. The actual adjustment may be obtained from a model of the vehicle, comprising vehicle dimensions and the like, or simply tabulated based on practical experimentation. An example scenario comprising cornering when encountering split friction conditions were discussed above in connection to <FIG>.

Due to the above-mentioned problems relating to wheel speed differences in slip-controlled differential drive arrangement, the method comprises adjusting S3 the nominal shaft slip λ<NUM>, <NUM> in dependence of a magnitude of the wheel speed difference to a target shaft slip λT, <NUM>, and controlling S4 the shaft speed ω0 based on the target shaft slip λT, <NUM>, e.g., by adjusting the shaft speed ω<NUM> to obtain the target shaft slip λT, <NUM>. Thus, as soon as one wheel starts to slip due to encountering lower friction (after the optional compensation for expected wheel speed difference due to steering), the proposed method immediately reduces the nominal shaft slip down to a lower target shaft slip. This means that the rightmost operating point on the inverse tyre model curve is shifted to the left, with a resulting improved vehicle propulsion. The control can be made very fast, i.e., with very small latency.

According to aspects, the target shaft slip λT, <NUM> is obtained S31 by multiplying the nominal shaft slip λ<NUM>, <NUM> by a reduction factor α ≤ <NUM>, where the reduction factor α decreases with the magnitude of the wheel speed difference. This reduction factor is generally a function of the wheel speed difference magnitude. For instance, the reduction factor α may be determined as <MAT> with <MAT>.

The method may also comprise configuring S33 the target shaft slip λT, <NUM> to be equal to the nominal shaft slip λ<NUM>, <NUM> if the magnitude of the difference between the speed ω<NUM> of the left wheel and the speed ω<NUM> of the right wheel is below a pre-determined threshold. Thus, in other words, the herein disclosed methods can be triggered only if the wheel speed difference exceeds some value considered substantial, and be left inactivated as long as the wheel speeds only differ by some small value below the threshold.

It may be desirable to quickly reduce the target shaft slip λT, <NUM> when wheel speeds start to diverge, and to more slowly bring the target shaft slip λT, <NUM> back towards the nominal shaft slip λ<NUM>, <NUM> once the wheel speeds start to converge again. For instance, the target shaft slip may be iteratively updated using a step-length, as <MAT> where k is an iteration index. The magnitude of w determines the bandwidth constraint. A large w allows for rapid convergence, and vice versa. The magnitude of w may be selected as a function of the rate of change in the wheel speed difference, i.e., if <MAT> then wheel speed difference is increasing and w is then selected larger compared to the case where <MAT>.

To summarize, according to some aspects, the target shaft slip λT, <NUM> is adapted S34 according to a bandwidth constraint, where the bandwidth constraint is smaller for a decreasing target shaft slip λT, <NUM> compared to an increasing target shaft slip λT, <NUM>.

The target shaft slip λT, <NUM> is optionally also adapted S35 such that neither of the speed ω<NUM> of the left wheel and the speed ω<NUM> of the right wheel exceeds a wheel slip limit configured in dependence of the nominal shaft slip λ<NUM>, <NUM>. This can be realized in a number of different ways. For instance, with reference to <FIG>, in case one of the wheel slips <NUM>, <NUM> exceeds a pre-determined slip limit of, say <NUM>, then the shaft speed ω<NUM> is reduced until both wheels show wheel slips below the configured wheel slip threshold. This implies that the nominal shaft slip λ<NUM>, <NUM> is reduced down to a target shaft slip λT < λ<NUM> at which both wheels operate below the slip limit.

The methods disclosed herein optionally also comprise triggering S5 a service brake intervention procedure in case the magnitude of the difference between the speed ω<NUM> of the left wheel and the speed ω<NUM> of the right wheel exceeds a split-µ condition threshold. Thus, the herein proposed methods may be used as a complement to existing traction control systems which apply service brakes <NUM>, <NUM> to transfer propulsion power away from a fast slipping wheel to the not-so fast slipping wheel. Such traction control methods are known and will therefore not be discussed in more detail herein. Related to this, <CIT> discloses a method for controlling motion of a heavy-duty vehicle, where the vehicle comprises an open differential driven axle, and where the vehicle wheel forces are controlled based on a wheel slip target, i.e., a wheel slip limit. <CIT> discloses monitoring of a difference in wheel speeds over the driven axle, and reduces wheel slip if the difference in wheel speeds increases, such that neither of the wheel slips exceed the initial target slip value. However, <CIT> does not relate to control of shaft slip.

According to some aspects of the disclosed methods, a relationship between nominal shaft slip λ<NUM>, <NUM> and desired wheel force Fx is given by an inverse tyre model <NUM>, as discussed above in connection to <FIG>. The method then comprises initially obtaining S12 this inverse tyre model. The model may be pre-configured as a software update of the ECU <NUM>, or obtained from the remote server <NUM>.

<FIG> schematically illustrates, in terms of a number of functional units, the components of a control unit <NUM> according to embodiments of the discussions herein, such as any of the VUCs <NUM>, <NUM>. This control unit <NUM> may be comprised in the articulated vehicle <NUM>. Processing circuitry <NUM> 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 <NUM>. The processing circuitry <NUM> may further be provided as at least one application specific integrated circuit ASIC, or field programmable gate array FPGA.

Thus, there is also disclosed herein a control unit <NUM> arranged to control propulsion of a heavy-duty vehicle <NUM>, where the heavy-duty vehicle <NUM> comprises a differential drive arrangement <NUM> arranged in connection to a drive axle <NUM> with a left wheel <NUM> and a right wheel <NUM>, the control unit comprising processing circuitry <NUM> configured to.

Claim 1:
A method for controlling propulsion of a heavy-duty vehicle (<NUM>), where the heavy-duty vehicle (<NUM>) comprises a differential drive arrangement (<NUM>) arranged in connection to a drive axle (<NUM>) with a left wheel (<NUM>) and a right wheel (<NUM>), the method comprising
determining (S1) a nominal shaft slip (λ<NUM>, <NUM>) corresponding to a desired wheel force (Fx) to be generated by the drive axle wheels (<NUM>, <NUM>), wherein the nominal shaft slip is indicative of a difference between a current vehicle velocity (vx) and a vehicle velocity corresponding to the shaft speed (ω<NUM>),
determining (S2) a difference between a speed (ω<NUM>) of the left wheel and a speed (ω<NUM>) of the right wheel,
adjusting (S3) the nominal shaft slip (λ<NUM>, <NUM>) in dependence of a magnitude of the wheel speed difference to a target shaft slip (λT, <NUM>),
wherein the target shaft slip (λT, <NUM>) is smaller than the nominal wheel slip (λ<NUM>, <NUM>) by an amount (<NUM>) determined as a function of the magnitude of the wheel speed difference, and controlling (S4) the shaft speed (ω<NUM>) based on the target shaft slip (λT, <NUM>).