GPS enhanced friction estimation

A vehicle and a system and method of controlling the vehicle. The system includes a sensor and a processor. The sensor obtains a first estimate of a force on a tire of the vehicle based on dynamics of the vehicle. The processor is configured to obtain a second estimate of the force on the tire using a tire model, determine an estimate of a coefficient of friction between the tire and the road from the first estimate of the force and the second estimate of the force, and control the vehicle using the estimate of the coefficient of friction.

INTRODUCTION

The subject disclosure relates to operation of an autonomous vehicle, and in particular, to a method of estimating a friction between a tire of the vehicle and a road to improve the operation of the autonomous vehicle along the road based on the friction.

An autonomous vehicle operates to navigate itself along a road given its knowledge of its environment. The autonomous vehicle can use a friction between its tires and the roadway to perform calculations for controlling the vehicle to prevent slipping, improving braking, etc. However, road conditions can vary with weather conditions and from location to location along the road. Under certain road conditions, these changes can be rapid and dramatic, thereby affecting vehicle control. Accordingly, it is desirable have an improved knowledge of road friction to control the vehicle as the road friction changes.

SUMMARY

In one exemplary embodiment, a method of controlling a vehicle is disclosed. A first estimate of a force on a tire of the vehicle is obtained based on dynamics of the vehicle. A second estimate of the force on the tire is obtained using a tire model. An estimate of a coefficient of friction between the tire and a road is determined from the first estimate of the force and the second estimate of the force. The vehicle is controlled using the estimate of the coefficient of friction.

In addition to one or more of the features described herein, the method further includes determining the estimate of the coefficient of friction by reducing a difference between the first estimate of the force and the second estimate of the force. The second estimate of the force is based on a measured slip angle of the tire. The force is at least one of a front lateral force on a front tire, a rear lateral force on a rear tire, a front longitudinal force on the front tire, and a rear longitudinal force on the rear tire. The method further includes determining a low friction condition when a metric based on a measured yaw parameter and a model-based yaw parameter is greater than a threshold value. The method further includes outputting the estimate of the coefficient of friction when at least one of: the estimate is less than one for a selected number of sample times, and the estimate is less than one when a jerk occurring at the vehicle is negative. The tire model is a non-linear tire model.

In another exemplary embodiment, a system for controlling a vehicle is disclosed. The system includes a sensor and a processor. The sensor obtains a first estimate of a force on a tire of the vehicle based on dynamics of the vehicle. The processor is configured to obtain a second estimate of the force on the tire using a tire model, determine an estimate of a coefficient of friction between the tire and a road from the first estimate of the force and the second estimate of the force, and control the vehicle using the estimate of the coefficient of friction.

In addition to one or more of the features described herein, the processor is further configured to determine the estimate of the coefficient of friction by reducing a difference between the first estimate of the force and the second estimate of the force. The second estimate of the force is based on a measured slip angle of the tire. The force is at least one of a front lateral force on a front tire, a rear lateral force on a rear tire, a front longitudinal force on the front tire, and a rear longitudinal force on the rear tire. The processor is further configured to determine a low friction condition when a metric based on a measured yaw parameter and a model-based yaw parameter is greater than a threshold value. The processor is further configured to output the estimate of the coefficient of friction when at least one of: the estimate is less than one for a selected number of sample times, and the estimate is less than one when a jerk occurring at the vehicle is negative. The tire model is a non-linear tire model.

In yet another exemplary embodiment, a vehicle is disclosed. The vehicle includes a sensor and a processor. The sensor obtains a first estimate of a force on a tire of the vehicle based on dynamics of the vehicle. The processor is configured to obtain a second estimate of the force on the tire using a tire model, determine an estimate of a coefficient of friction between the tire and a road from the first estimate of the force and the second estimate of the force, and control the vehicle using the estimate of the coefficient of friction.

In addition to one or more of the features described herein, the processor is further configured to determine the estimate of the coefficient of friction by reducing a difference between the first estimate of the force and the second estimate of the force. The second estimate of the force is based on a measured slip angle of the tire. The force is at least one of a front lateral force on a front tire, a rear lateral force on a rear tire, a front longitudinal force on the front tire, and a rear longitudinal force on the rear tire. The processor is further configured to determine a low friction condition when a metric based on a measured yaw parameter and a model-based yaw parameter is greater than a threshold value. The processor is further configured to output the estimate of the coefficient of friction when at least one of: the estimate is less than one for a selected number of sample times, and the estimate is less than one when a jerk occurring at the vehicle is negative.

DETAILED DESCRIPTION

In accordance with an exemplary embodiment,FIG.1shows an autonomous vehicle10. In an exemplary embodiment, the autonomous vehicle10is a so-called Level Four or Level Five automation system. A Level Four system indicates “high automation,” referring to the driving mode-specific performance by an automated driving system of all aspects of the dynamic driving task, even if a human driver does not respond appropriately to a request to intervene. A Level Five system indicates “full automation,” referring to the full-time performance by an automated driving system of all aspects of the dynamic driving task under all roadway and environmental conditions that can be managed by a human driver. It is to be understood that the system and methods disclosed herein can also be used with an autonomous vehicle operating at any of Levels One through Five.

The autonomous vehicle10generally includes at least a navigation system20, a propulsion system22, a transmission system24, a steering system26, a brake system28, a sensing system30, an actuator system32, and a controller34. The navigation system20determines a road-level route plan for automated driving of the autonomous vehicle10. The propulsion system22provides power for creating a motive force for the autonomous vehicle10and can, in various embodiments, include an internal combustion engine, an electric machine such as a traction motor, and/or a fuel cell propulsion system. The transmission system24is configured to transmit power from the propulsion system22to two or more wheels16of the autonomous vehicle10according to selectable speed ratios. The steering system26influences a position of the two or more wheels16. While depicted as including a steering wheel27for illustrative purposes, in some embodiments contemplated within the scope of the present disclosure, the steering system26may not include a steering wheel27. The brake system28is configured to provide braking torque to the two or more wheels16.

The sensing system30senses objects in an exterior environment of the autonomous vehicle10and determines various parameters of the objects useful in locating the position and relative velocities of various remote vehicles in the environment of the autonomous vehicle. The sensing system30can include sensors such as digital cameras, radar, Lidar, etc. The parameters of the objects are provided to the controller34for vehicle navigation.

The controller34includes a processor36and a computer readable storage device or computer-readable storage medium38. The storage medium includes programs or instructions39that, when executed by the processor36, operate the autonomous vehicle10based on sensor system outputs. The controller34builds a trajectory for the autonomous vehicle10based on the output of sensing system30. The controller34can provide the trajectory to the actuator system32to control the propulsion system22, transmission system24, steering system26, and/or brake system28in order to navigate the autonomous vehicle10with respect to the object50. The computer-readable storage medium38may further include programs or instructions39that when executed by the processor36, determines a frictional condition or a coefficient of friction between the one or more wheels16of the autonomous vehicle10and the road and uses the coefficient of friction to control the operation of the autonomous vehicle based on the coefficient of friction.

A communication system60enables communication with a remote device, such as a traffic server, an infrastructure device, a Global Positioning Satellite (GPS) system, etc. and provides data from these remote devices to the controller34. In various embodiments, the controller34uses GPS data to determine vehicle velocity and angle or orientation of the autonomous vehicle10. This information can be used to determine forces on the autonomous vehicle10and thus forces on tires of the autonomous vehicle10.

FIG.2shows a top view of a chassis200of the autonomous vehicle10. The chassis200includes a front axle202, a rear axle204and a drive shaft206connecting the front axle202to the rear axle204. The front axle202includes a left front wheel208and a right front wheel210. The rear axle204includes a left rear wheel212and a right rear wheel214. A center of gravity216can be found along the drive shaft206or in the chassis200. A front axle length ‘a’ spans a distance along the drive shaft206from the center of gravity216to the front axle202. A rear axle length ‘b’ spans a distance along the drive shaft206from the center of gravity216to the rear axle204.

A body centered coordinate system225of the chassis200is shown. The body centered coordinate system225includes a longitudinal axis (x), a lateral axis (y) and a yaw axis (z) which points out of the page. A rotation about the longitudinal axis is indicated by roll angle φ. A rotation about the lateral axis is indicated by pitch angle θ. A rotation about the yaw axis is indicated by yaw angle ψ.

Force arrows are shown to indicate forces on the tires. The right front wheel210shows a longitudinal front wheel force (Fxf) and a lateral front wheel force (Fyf). The right rear wheel214shows a longitudinal rear wheel force (Fxr) and a lateral rear wheel force (Fyr). A steering angle δ is shown at the left front wheel208. The steering angle δ is an angle between the longitudinal axis and the direction in which the tire is pointing. A slip angle is an angle between the direction in which the tire is pointing and the actual direction in which the tire is travelling.

FIG.3shows a flow diagram300for controlling the autonomous vehicle10using the method disclosed herein. The autonomous vehicle10includes various modules operating on the processor36of the autonomous vehicle10, including a vehicle operation module302for changing a state of the autonomous vehicle10(i.e., via acceleration, deceleration, braking, turning, etc.), an integrated control system304that provides instructions or signals to the vehicle operation module302and a driver input306that provides driver's instructions to the vehicle operation module302. In other embodiments, the modules disclosed herein can be operated on separate processors or circuitry. The vehicle operation module302changes the state of the autonomous vehicle10based on the data from the integrated control system304and from driver input306. The autonomous vehicle10also includes a vehicle state estimation module308operating at the processor36that evaluates the change in the state of the autonomous vehicle10and generates parameters that can be used at the integrated control system for subsequent instructions to the autonomous vehicle10. In various embodiments, the vehicle state estimation module308determines a coefficient of friction between a tire of the autonomous vehicle10and the road based on the current state of the vehicle or current dynamics of the vehicle. The integrated control system304uses the coefficient of friction in determining the control signals that are sent to the vehicle operation module302.

FIG.4shows a flowchart400of a method for estimating a coefficient of friction between the vehicle and the road, as performed in the vehicle state estimation module308ofFIG.3. The method begins at box402, in which data is obtained of various dynamic parameters of the vehicle. In an embodiment, the data is obtained using a sensor such as an Inertial Measurement Unit (IMU) and can include parameters such as forces, accelerations, angular rates, orientation, speeds, etc. on the vehicle using sensors such as accelerometers, gyroscopes, magnetometers, etc. These measurements can be made along three degrees of freedom or 6 degrees of freedom, in various embodiments. In box402, the coefficient of friction is initially set at μ=1.

In box404, the dynamic parameters are used to determine whether the vehicle is experiencing a low coefficient of friction. A flag is set when the vehicle is experiencing this low coefficient of friction. The flag can be set when a difference between measured parameters and a model-based estimate of the parameters exceeds a selected threshold. In an embodiment, the parameters include a yaw rate of the vehicle and a time-derivate of the yaw rate. In another embodiment, the parameters include a rotation rate of a wheel and a time-derivate of the rotation rate.

The flag is set to ‘Flag=0’ when a difference between measured parameters and a model-based estimate of the parameters is less than the threshold (i.e., when a high friction state is detected). If the high friction state is detected, the method loops back to box402to obtain further measurements. The flag is set to ‘Flag=1’ when the difference between measured parameters and the model-based estimate is greater than or equal to the threshold (i.e., when a low friction state is detected). If the low friction state is detected, the method continues to box406.

In box406, a dynamic estimate of force on the tire is made using the dynamic parameter measurements. Also, an estimate is made of slip angle for the tire using the dynamic parameter measurements.

In box408, an estimate for the coefficient of friction is determined. The estimate is determined from the dynamic estimate of force obtained in box406and a model-based estimate of force. The model-based estimate of force is based in part of the slip angle obtained in box406. In various embodiments, the value that is determined for the coefficient of friction is the value that reduces, minimizes, or substantially minimizes a difference between the dynamic estimate of force and the model-based estimate of force. In an embodiment, this value can be determined using any suitable optimization method applied to a cost function based on a difference between the dynamic estimate of force and the model-based estimate of force.

In box410, the low friction estimate is obtained and provided to a selection criterion in box412. In box412, an algorithm is used to determine the actual coefficient of friction at the tires, which can be represented either by a high friction coefficient (e.g., μn=1, where n is an iteration index) or by the low friction coefficient estimated in box410. The algorithm applies a criterion to avoid jumping excessively between the high friction coefficient and the efficient low coefficient, as explained herein. When the high friction coefficient is used, the method returns to box402(with μn+1=1). When the low friction coefficient is used, the method returns to box410(with μn+1=μn).

FIG.5shows a flowchart500for a method of determining a low-friction condition, as performed in box404. The low-friction condition is determined by comparing measured yaw parameters to predicted or model-based yaw parameters. In box502, a lateral slip of the front wheel is determined. If the lateral slip is less than or equal to a slip threshold, the method loops back to box502. If the lateral slip is greater than the slip threshold, the method proceeds to box504. In box504, a deviation is determined between measured yaw parameters and the model-based yaw parameter. In one embodiment, a non-linear bicycle model is used to compute the model-based yaw parameters, as shown in Eqs. (1) and (2):
M{dot over (V)}y=M{dot over (ψ)}Vx+Fyf(αf)cos(δ)+Fyf(αr)−Mgcos(θ)sin(φ)  Eq. (1)
Iz{umlaut over (ψ)}=aFyf(αf)−bFyf(αr)  Eq. (2)
where M is the mass of the vehicle, Vxis the longitudinal velocity of the vehicle, {dot over (V)}yis the time-derivative of the lateral velocity of the vehicle, is {dot over (ψ)} is the yaw rate, {umlaut over (ψ)} is the time-derivative of the yaw rate or the yaw angular acceleration, αfis the slip angle of the front tires, αris the slip angle of the rear tires and g is the gravitational constant. It is to be understood that other models can also be used to determine the yaw rate parameters, in various embodiments.

The non-linear bicycle model of Eqs. (1) and (2) receives input in the form of the steering angle δ and assumes a coefficient of friction of μ=1. The output of the non-linear bicycle model is a lateral velocity Vy, the model-based yaw rate {dot over (ψ)}band the model-based time-derivative of the yaw {dot over (ψ)}b(or model-based yaw acceleration). A measured yaw rate {dot over (ψ)} (or measured yaw angular velocity) and measured time-derivative of the yaw rate {umlaut over (ψ)} (or measured yaw acceleration) are obtained at the vehicle using, for example, the Inertial Measurement Unit (IMU). A metric m between these values is computed as shown in Eq. (3):
m=√{square root over (({dot over (ψ)}b−{dot over (ψ)})2−({umlaut over (ψ)}b−{umlaut over (ψ)})2)}  Eq. (3)

In box506, the metric is compared to a yaw deviation threshold. When the metric is greater than the yaw deviation threshold and the absolute value of the slip angle is greater than one, then the method proceed to box508in which the flag is set to 1 (“FLAG=1”) to indicate a low friction condition. Returning to box506, when the metric is less or equal to the yaw deviation threshold, then the method proceeds to box510in which the flag is set to 0 (“FLAG=0”) to indicate a high friction condition.

FIG.6shows a phase plot600for yaw parameters for a low-friction road, such as an icy road. Yaw rate is shown along the x-axis and the differential yaw rate is shown along the y-axis. The phase plot includes a first curve602representative of measured yaw rate and measured differential yaw rate (time-derivative of the yaw rate). A second curve604represents yaw rate and differential yaw rate that is determined from a model, such as the non-linear bicycle model. It is evident fromFIG.6that there are many occasions at which the first curve602and the second curve604deviate from each other by a considerable amount due to the ice on the road.

FIG.7shows a phase plot700for yaw rate and differential yaw rate for a high-friction road. Yaw rate is shown along the x-axis and the differential yaw rate is shown along the y-axis. A first curve702is representative of measured yaw rate and measured differential yaw rate. A second curve704represents yaw rate and differential yaw rate that is determined from the model. The first curve702and the second curve704remain very close to each other throughout and rarely deviate from each other by an amount that exceeds a selected yaw deviation threshold.

For the phase plots ofFIGS.6and7, the metric of Eq. (3) can be used to determines a deviation between the first curves (602,702) and the second curves (604,704) and compares the deviation to a yaw deviation threshold. When the deviation is greater than the yaw deviation threshold, a flag is set (i.e., “FLAG=1”) to indicate that a low-friction condition is being experienced. When the deviation is less than the yaw deviation threshold, a flag is removed (i.e., “FLAG=0”) to indicate that a high-friction condition is being experienced.

The process of estimating the forces on the wheel performed in box406is discussed with respect to Eqs. (4)-(5). The lateral force {circumflex over (F)}yfon the front wheel (e.g., left front wheel208or right front wheel210) can be determined from the lateral acceleration, yaw rate and steering angle, as shown in Eq. (4):
{circumflex over (F)}yf=(bMAy+Iz{umlaut over (ψ)})/((a+b)cos δ)  (4)
where M is the mass of the vehicle, Ayis the measured lateral acceleration of the vehicle, Izis the moment of inertia of the vehicle about the z axis, {dot over (ψ)} is the measured yaw rate, and δ is the steering angle. The lateral acceleration and steering angle can be determined from vehicle sensors. Similarly, the lateral force {circumflex over (F)}yron the rear wheel is determined using Eq. (5):
{circumflex over (F)}yr=(aMAy−Iz{umlaut over (ψ)})/(a+b)  (5)

The slip angle is a difference between a direction of the movement of wheel and a direction in which the wheel is pointed. An estimate of slip angle {circumflex over (α)}ffor the front tire can be obtained using Eq. (6):
{circumflex over (α)}f=δf−{circumflex over (V)}y/Vx−a{dot over (ψ)}/Vx(6)
where δfis the steering angle of the front tire, {circumflex over (V)}yis an estimate of the lateral velocity of the vehicle, Vxis the measured forward velocity of the vehicle, and {dot over (ψ)} is the yaw rate. Similarly, an estimate of slip angle {circumflex over (α)}rfor rear tire can be obtained using Eq. (7):
{circumflex over (α)}r=δr−{circumflex over (V)}y/Vx+b{dot over (ψ)}/Vx(7)
where δris the steering angle of the rear tire. Using a model of tire forces, the lateral force on the front tire is given by Eq. (8):

Fyf(αf)=cf⁢tanh⁡(1μ⁢df⁢αf)(8)
where cfand dfare model coefficients. Similarly, a lateral force on the rear tire is given by Eq. (9):

FIG.8shows a graph800of model-based lateral forces on a tire. The slip angle is shown in radians (rad) along the x-axis and the force is shown in Newtons (N) along the y-axis. Curve802represents the lateral forces on the tire for a high coefficient of frication (e.g., μ=1) and curve804represents the lateral forces on the tire for a low coefficient of friction (e.g., μ=0.2).

Eq. (10) shows an optimization method for locating an estimate {circumflex over (μ)}fof the coefficient of friction at the front wheel.

μˆf=arg⁢minμ⁢❘"\[LeftBracketingBar]"Fˆyf-cf⁢tanh⁡(1μ⁢df⁢α^f)❘"\[RightBracketingBar]"(10)
The optimization method of Eq. (10) locates a value of the coefficient of friction that reduces or minimizes a difference between the measured lateral tire force of Eq. (4) and the modeled the lateral tire force of Eq. (8). Similarly, Eq. (11) shows an optimization method for locating an estimate {circumflex over (μ)}rof the coefficient of friction at the rear wheel.

A similar estimate of coefficient of friction can be determined using longitudinal forces. A longitudinal slip ratio can be determined using Eq. (13):
σ=(Rω−Vx)/max(Rω,Vx)  (13)
where R is the radius of the wheel, ω is the rotation rate or rotational velocity of the wheel and Vxis the longitudinal velocity of the vehicle. A nonlinear longitudinal model can be used to determine the rotational velocity ω of the wheel. The nonlinear longitudinal model receives a torque T on the vehicle as input and assumes a coefficient of friction μ=1. The model outputs a model rotational velocity ωband time-derivative of rotational velocity {dot over (ω)}b. These parameters can be compared to corresponding measurements of rotational velocity ω and time-derivative of rotational velocity {dot over (ω)}. A metric can be used to determine the deviation between the modeled parameters and measured parameters, as shown in Eq. (14):
m=√{square root over ((ωb−ω)2−({dot over (ω)}b−{dot over (ω)})2)}  (14)
The metric m can be compared to a rotational velocity deviation threshold to determine when the wheel is in a low friction condition, using the same methods disclosed herein with respect to the yaw parameters. Once the metric is determined to be greater than the rotational velocity deviation threshold, the longitudinal forces on the tires can be used to determine coefficient of friction.

The dynamic longitudinal forces on the wheel are given in Eq. (15):
{circumflex over (F)}x=(T−Iw{dot over (ω)})/R(15)
where T is a rotational torque on the wheel, Iwis the rotational inertia of the wheel and R is the radius of the wheel. A model of the longitudinal force on a front tire is given by Eq. (16):

Fx⁢f(σf)=cf⁢tanh⁡(1μ⁢df⁢σf)(16)
A model of the longitudinal force on a rear tire is given by Eq. (17):

Fyr(σr)=cr⁢tanh⁡(1μ⁢dr⁢σr)(17)
The coefficient of friction can be determined by minimizing a difference between the modeled longitudinal force and the measured longitudinal force, as shown in Eq. (18):

μˆf=arg⁢minμ⁢❘"\[LeftBracketingBar]"Fˆx-cf⁢tanh⁡(1μ⁢df⁢σˆf)❘"\[RightBracketingBar]"(18)
Eq. (18) can be applied to both front and rear tires separately.

FIG.9shows a chart900illustrating operation of an optimization method for lateral forces. Force is shown in Newtons (N) along the y-axis and time is shown in seconds (sec) along the x-axis. Curve902shows a predicted force for a coefficient of friction of μ=1 between the tire and the road. Curve904shows a predicted force for a coefficient of friction of μ=0.8. Curve906shows a predicted force for a coefficient of friction of μ=0.6. Curve908shows a predicted force for a coefficient of friction of μ=0.4. Curve910shows a predicted force for a coefficient of friction of μ=0.2. Curve912shows the measured forces on the tire. The predicted force for μ=0.2 (curve910) best matches with the measured forces (curve912).

FIG.10shows a flow chart1000for a method of preventing excessive flips between low and high coefficient of friction estimations. At each iteration of the flowchart400ofFIG.4, the criterion is checked to see if the output coefficient of friction is to be changed (i.e., in box412). The criterion is used to move between outputting a high coefficient of friction1002and a low coefficient of friction1004. When the method is currently outputting a high coefficient of friction and the estimate generated using the steps disclosed herein (e.g., via any of Eqs. (10), (11), (12) and (18)) meets a first set of conditions, then the method switches to outputting an estimate of the low coefficient of friction. The first set of conditions includes either the estimate being less than 1 for a selected number of sample time or the estimate being less than 1 while a lateral jerk on the vehicle is negative. The selected number of sample times can be a tunable parameter. A sample time is a time interval in which the measurement can calculations of friction are performed. The measurements and calculations can be performed several times per second, for example.

Similarly, when the method currently is outputting a low coefficient of friction and the estimate generated used the steps disclosed herein meets a second set of conditions, then the method switches to outputting the high coefficient of friction. The second set of conditions includes either the estimate being equal to 1 for a selected number of sample times or the estimate being equal to 1 while a lateral jerk on the vehicle is positive.