Simulate lane-keeping assistance using adaptive model predictive controller - Simulink

Library:
Model Predictive Control Toolbox / Automated Driving

Ports

Input

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`Curvature`— Road curvature
scalar

Road curvature, specified as1/R, whereRis the radius of the curve in meters.

The road curvature is:

Positive when the road curves toward the positive Y axis of the global coordinate system.
Negative when the road curves toward the negative Y axis of the global coordinate system.
Zero for a straight road.

的controller models the road curvature as a measured disturbance with previewing. You can specify the curvature as a:

Scalar signal — Specify the curvature for the current control interval. The controller uses this curvature value across the prediction horizon.
Vector signal with length less than or equal to thePrediction Horizon——指定当前和预测的曲率价值es across the prediction horizon. If the length of the vector is less than the prediction horizon, then the controller uses the final curvature value in the vector for the remainder of the prediction horizon.

`Longitudinal velocity`— Ego vehicle velocity
nonnegative scalar

Ego vehicle velocity in m/s.

`Lateral deviation`— Ego vehicle lateral deviation
scalar

Ego vehicle lateral deviation in meters from the centerline of the lane.

`Relative yaw angle`— Angle from lane centerline
scalar

Ego vehicle longitudinal axis angle in radians from the centerline of the lane.

`Minimum steering angle`— Minimum front steering angle
scalar

Minimum front steering angle constraint in radians. Use this input port when the minimum steering angle varies at run time.

Dependencies

To enable this port, selectUse external sourcefor theMinimum steering angleparameter.

`Maximum steering angle`— Maximum front steering angle
scalar

Maximum front steering angle constraint in radians. Use this input port when the maximum steering angle varies at run time.

Dependencies

To enable this port, selectUse external sourcefor theMaximum steering angleparameter.

`Enable optimization`— Controller optimization enable signal
scalar

Controller optimization enable signal. When this signal is:

Nonzero, the controller performs optimization calculations and generates aSteering anglecontrol signal.
Zero, the controller does not perform optimization calculations. In this case, theSteering angleoutput signal remains at the value it had when the optimization was disabled. The controller continues to update its internal state estimates.

Dependencies

To enable this port, select theUse external signal to enable or disable optimizationparameter.

`External control signal`— Steering angle applied to ego vehicle
scalar

Actual steering angle in radians applied to the ego vehicle. The controller uses this signal to estimate the ego vehicle model states. Use this input port when the control signal applied to the ego vehicle does not match the optimal control signal computed by the model predictive controller. This mismatch can occur when, for example:

TheLane Keeping Assist Systemis not the active controller. Maintaining an accurate state estimate when the controller is not active prevents bumps in the control signal when the controller becomes active.
The steering actuator fails and does not provide the correct control signal to the ego vehicle.

Dependencies

To enable this port, select theUse external control signal for bumpless transfer between PFC and other controllersparameter.

`Vehicle dynamics matrix A`— State matrix of ego vehicle predictive model
square matrix

State matrix of ego vehicle predictive model. The number of rows in the state matrix corresponds to the number of states in the predictive model. This matrix must be square.

The ego vehicle predictive model defined byVehicle dynamics matrix A,Vehicle dynamics matrix B, andVehicle dynamics matrix Cmust be minimal.

Dependencies

To enable this port, select theUse vehicle modelparameter.

`Vehicle dynamics matrix B`— Input-to-state matrix of ego vehicle predictive model
column vector

Input-to-state matrix of ego vehicle predictive model. The number of rows in this signal must match the number of rows inVehicle dynamics matrix A.

The ego vehicle predictive model defined byVehicle dynamics matrix A,Vehicle dynamics matrix B, andVehicle dynamics matrix Cmust be minimal.

Dependencies

To enable this port, select theUse vehicle modelparameter.

`Vehicle dynamics matrix C`— State-to-output matrix of ego vehicle predictive model
matrix with two rows

State-to-output matrix of ego vehicle predictive model. The number of columns in this signal must match the number of rows inVehicle dynamics matrix A.

The ego vehicle predictive model defined byVehicle dynamics matrix A,Vehicle dynamics matrix B, andVehicle dynamics matrix Cmust be minimal.

Dependencies

To enable this port, select theUse vehicle modelparameter.

Output

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`Steering angle`— Front steering angle control signal
scalar

Front steering angle control signal in radians generated by the controller. The front steering angle is the angle of the front tires from the longitudinal axis of the vehicle. The steering angle is positive towards the positive lateral axis of the ego vehicle.

Parameters

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Parameters Tab

Ego Vehicle

`使用车辆参数s`— Define ego vehicle model using vehicle properties
`on`(default) |`off`

Select this parameter to define the ego vehicle model used by the MPC controller by specifying properties of the ego vehicle. The ego vehicle model is the linear model from the front steering angle to the lateral velocity and yaw angle rate. For more information, see自我车辆预测模型.

定义车辆模型,specify the following block parameters:

Total mass
Yaw moment of inertia
Longitudinal distance from center of gravity to front tires
Longitudinal distance from center of gravity to rear tires
Cornering stiffness of front tires
Cornering stiffness of rear tires

For more information on the ego vehicle model, see自我车辆预测模型.

Selecting this parameter clears theUse vehicle modelparameter.

Programmatic Use

Block Parameter:ModelType

Type:string, character vector

Default:"Use vehicle parameters"

`Use vehicle model`— Define ego vehicle model using state-space matrices
`off`(default) |`on`

Select this parameter to define the state-space matrices of the ego vehicle model used by the MPC controller. This model is the linear model from the front steering angle in radians to the lateral velocity in meters per second and yaw angle rate in radians per second. For more information on the ego vehicle model, see自我车辆预测模型.

To define the initial internal model, specify theA,B, andCstate-space matrices. The internal model must be a minimal realization with no direct feedthrough, and the dimensions ofA,B, andCmust be consistent.

Typically, the ego vehicle steering model is velocity-dependent, and therefore, it varies over time. To update the internal model at run time, use theVehicle dynamics A,Vehicle dynamics B, andVehicle dynamics Cinput ports.

Selecting this parameter clears the使用车辆参数sparameter.

Programmatic Use

Block Parameter:ModelType

Type:string, character vector

Default:"Use vehicle parameters"

`Total mass`— Ego vehicle mass
`1575`(default) | positive scalar

Ego vehicle mass in kg.

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:VehicleMass

Type:string, character vector

Default:"1575"

`Yaw moment of inertia`— Moment of inertia about the ego vehicle vertical axis
`2875`(default) | positive scalar

Moment of inertia about the ego vehicle vertical axis in Kg·m².

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:VehicleYawInertia

Type:string, character vector

Default:"2875"

`Longitudinal distance from center of gravity to front tires`— Distance from the ego vehicle center of mass to its front tires
`1.2`(default) | positive scalar

Distance from the ego vehicle center of mass to its front tires in meters, measured along the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:LengthToFront

Type:string, character vector

Default:"1.2"

`Longitudinal distance from center of gravity to rear tires`— Distance from the ego vehicle center of mass to its rear tires
`1.6`(default) | positive scalar

Distance from the ego vehicle center of mass to its rear tires in meters, measured along the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:LengthToRear

Type:string, character vector

Default:"1.6"

`Cornering stiffness of front tires`— Front tire stiffness
`19000`(default) | positive scalar

Front tire stiffness in N/rad, defined as the relationship between the side force on the front tires and the angle of the tires to the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:FrontTireStiffness

Type:string, character vector

Default:"19000"

`Cornering stiffness of rear tires`— Rear tire stiffness
`33000`(default) | positive scalar

Rear tire stiffness in N/rad, defined as the relationship between the side force on the rear tires and the angle of the tires to the longitudinal axis of the vehicle.

Dependencies

To enable this parameter, select the使用车辆参数sparameter.

Programmatic Use

Block Parameter:RearTireStiffness

Type:string, character vector

Default:"33000"

`A`— Initial state matrix of ego vehicle predictive model
square matrix

Initial state matrix of ego vehicle predictive model. The number of rows in the state matrix corresponds to the number of states in the predictive model. This matrix must be square.

The initial ego vehicle predictive model defined byA,B, andCmust be minimal.

Typically, the ego vehicle model varies over time. To update the state matrix at run time, use theVehicle dynamics Ainput port.

Dependencies

To enable this parameter, select theUse vehicle modelparameter.

Programmatic Use

Block Parameter:EgoModelMatrixA

Type:string, character vector

Default:"[-4.4021 ,-12.4603;1.3913,-5.1868]"

`B`— Initial input-to-state matrix of ego vehicle predictive model
column vector

Initial input-to-state matrix of ego vehicle predictive model. The number of rows in this parameter must match the number of rows inA.

The initial ego vehicle predictive model defined byA,B, andCmust be minimal.

Typically, the ego vehicle model varies over time. To update the input-to-state matrix at run time, use theVehicle dynamics Binput port.

Dependencies

To enable this parameter, select theUse vehicle modelparameter.

Programmatic Use

Block Parameter:EgoModelMatrixB

Type:string, character vector

Default:"[24.1270;15.8609]"

`C`— Initial state-to-output matrix of ego vehicle predictive model
matrix with two rows

Initial state-to-output matrix of ego vehicle predictive model. The number of columns in this parameter must match the number of rows inA.

The initial ego vehicle predictive model defined byA,B, andCmust be minimal.

Typically, the ego vehicle model varies over time. To update the state-to-output matrix at run time, use theVehicle dynamics Cinput port.

Dependencies

To enable this parameter, select theUse vehicle modelparameter.

Programmatic Use

Block Parameter:EgoModelMatrixC

Type:string, character vector

Default:"[1,0;0,1]"

`Initial longitudinal velocity`— Initial velocity of the ego vehicle
`15`(default) | positive scalar

Initial velocity of the ego vehicle model when the lane-keeping assist is enabled in m/s. This velocity can differ from the actual ego vehicle initial velocity.

Note

A very small initial velocity, for exampleeps, can produce a nonminimal realization for the controller plant model, causing an error. To prevent this error, set the initial velocity to a larger value, for example1e-3.

Programmatic Use

Block Parameter:InitialLongVel

Type:string, character vector

Default:"15"

`Transport lag between model inputs and outputs`— Total transport lag in ego vehicle model
`0`(default) | nonnegative scalar

Total transport lag,τ, in the ego vehicle model in seconds. This lag includes actuator, sensor, and communication lags. For each input-output channel, the transport lag is approximated by:

$\frac{1}{τ s + 1}$

Programmatic Use

Block Parameter:TransportLag

Type:string, character vector

Default:"0"

Lane Keeping Controller Constraints

`Minimum steering angle`— Minimum front steering angle
`-0.26`(default) | scalar between`-pi/2`and`pi/2`

Minimum front steering angle constraint in radians.

If the minimum steering angle varies over time, add theMinimum steering angleinput port to the block by selectingUse external source.

Dependencies

This parameter must be less than theMaximum steering angleparameter.

Programmatic Use

Block Parameter:MinSteering

Type:string, character vector

Default:"-0.26"

`Maximum steering angle`— Maximum front steering angle
`0.26`(default) | scalar between`-pi/2`and`pi/2`

Maximum front steering angle constraint in radians.

If the maximum steering angle varies over time, add theMaximum steering angleinput port to the block by selectingUse external source.

Dependencies

This parameter must be greater than theMinimum steering angleparameter.

Programmatic Use

Block Parameter:MaxSteering

Type:string, character vector

Default:“0.26”

Model Predictive Controller Settings

`Sample time`— Controller sample time
`0.1`(default) | positive scalar

Controller sample time in seconds.

Programmatic Use

Block Parameter:Ts

Type:string, character vector

Default:"0.1"

`Prediction horizon`— Controller prediction horizon
`10`(default) | positive integer

控制器预测地平线的步骤。的controller prediction time is the product of the sample time and the prediction horizon.

Programmatic Use

Block Parameter:PredictionHorizon

Type:string, character vector

Default:"30"

`Controller behavior`— Closed-loop controller performance
`0.5`(default) | scalar between`0`and`1`

Closed-loop controller performance. The default parameter value provides a balanced controller design. Specifying a:

Smaller value produces a more robust controller with smoother control actions.
Larger value produces a more aggressive controller with a faster response time.

When you modify this parameter, the change is applied to the controller immediately.

Programmatic Use

Block Parameter:ControllerBehavior

Type:string, character vector

Default:"0.5"

Block Tab

`Use suboptimal solution`— Apply suboptimal solution after specified number of iterations
`off`(default) |`on`

Configure the controller to apply a suboptimal solution after a specified maximum number of iterations, which guarantees the worst-case execution time for your controller.

For more information, seeSuboptimal QP Solution.

Dependencies

After selecting this parameter, specify theMaximum iteration numberparameter.

Programmatic Use

Block Parameter:suboptimal

Type:string, character vector

Default:"off"

`Maximum iteration number`— Maximum optimization iterations
`10`(default) | positive integer

Maximum number of controller optimization iterations.

Dependencies

To enable this parameter, select theUse suboptimal solutionparameter.

Programmatic Use

Block Parameter:maxiter

Type:string, character vector

Default:"10"

`Use external signal to enable or disable optimization`— Add port for enabling optimization
`off`(default) |`on`

To add theEnable optimizationinput port to the block, select this parameter.

Programmatic Use

Block Parameter:optmode

Type:string, character vector

Default:"off"

`Use external signal for bumpless transfer between LKA and other controllers`— Add external control signal input port
`off`(default) |`on`

To add theExternal control signalinput port to the block, select this parameter.

Programmatic Use

Block Parameter:trackmode

Type:string, character vector

Default:"off"

`Create LKA subsystem`— Create custom controller
button

Generate a custom LKA subsystem, which you can modify for your application. The controller configuration data for the custom controller is exported to the MATLAB^®workspace as a structure.

You can modify the custom controller subsystem to:

Modify default MPC settings or use advanced MPC features.
Modify the default controller initial conditions.

Model Examples

Lane Keeping Assist System Using Model Predictive Control

Design an MPC controller that keeps an ego vehicle traveling along the center of a straight or curved road by adjusting the front steering angle.

Lane Keeping Assist with Lane Detection

Design an MPC-based lane-keeping assist system that uses lane detection and road curvature previewing from the Automated Driving Toolbox™.

Algorithms

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自我车辆预测模型

The default ego vehicle predictive model is the following state-space model:

$\begin{array}{l} A = [\begin{matrix} - 2 (C_{F} + C_{R}) / m / V_{X} & - V_{X} - 2 (C_{F} L_{F} - C_{R} L_{R}) / m / V_{X} \\ - 2 (C_{F} L_{F} - C_{R} L_{R}) / I_{Z} / V_{X} & - 2 (C_{F} L_{F}^{2} + C_{R} L_{R}^{2}) / I_{Z} / V_{X} \end{matrix}] \\ B = 2 C_{F} [\begin{matrix} 1 / m \\ L_{F} / I_{Z} \end{matrix}] \\ C = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] \\ D = [\begin{matrix} 0 \\ 0 \end{matrix}] \end{array}$

Here:

V_Xis the longitudinal velocity of the car. At the start of the simulation, this velocity is equal to theInitial condition for longitudinal velocityparameter. At run time, this velocity is equal to theLongitudinal velocityinput signal.
mis theTotal massparameter.
I_Zis theYaw moment of inertiaparameter.
L_Fis theLongitudinal distance from center of gravity to front tiresparameter.
L_Ris theLongitudinal distance from center of gravity to rear tiresparameter.
C_Fis theCornering stiffness of front tiresparameter.
C_Ris theCornering stiffness of rear tiresparameter.

The input to this model is the steering angle in radians, and the outputs are the lateral velocity in meters per second and yaw angle rate in radians per second.

To define a different ego vehicle predictive model, select theUse vehicle modelparameter, and specify the initial state-space model. Then, specify the run-time values of the state-space matrices using theVehicle dynamics A,Vehicle dynamics B, andVehicle dynamics Cinput signals.

的controller creates its internal predictive model by augmenting the ego vehicle dynamic model. The augmented model includes the road curvature as a measured disturbance input signal.

Initial Conditions

By default, the model predictive controller assumes the following initial conditions for the ego vehicle:

Longitudinal velocity is equal to theInitial longitudinal velocityparameter.
Lateral velocity is zero.
Steering angle is zero.
Yaw angle rate is zero.

If the initial conditions in your model do not match these conditions, theSteering angleoutput can exhibit an initial bump at the start of the simulation.

To modify the controller initial conditions to match your simulation, create a custom lane-keeping control system by, on theBlocktab, clickingCreate LKA subsystem.

Lane Keeping Assist System

Description

Ports

Input

Curvature— Road curvaturescalar

Longitudinal velocity— Ego vehicle velocitynonnegative scalar

Lateral deviation— Ego vehicle lateral deviationscalar

Relative yaw angle— Angle from lane centerlinescalar

Minimum steering angle— Minimum front steering anglescalar

Dependencies

Maximum steering angle— Maximum front steering anglescalar

Dependencies

Enable optimization— Controller optimization enable signalscalar

Dependencies

External control signal— Steering angle applied to ego vehiclescalar

Dependencies

Vehicle dynamics matrix A— State matrix of ego vehicle predictive modelsquare matrix

Dependencies

Vehicle dynamics matrix B— Input-to-state matrix of ego vehicle predictive modelcolumn vector

Dependencies

Vehicle dynamics matrix C— State-to-output matrix of ego vehicle predictive modelmatrix with two rows

Dependencies

Output

Steering angle— Front steering angle control signalscalar

Parameters

Parameters Tab

使用车辆参数s— Define ego vehicle model using vehicle propertieson(default) |off

Programmatic Use

Use vehicle model— Define ego vehicle model using state-space matricesoff(default) |on

Programmatic Use

Total mass— Ego vehicle mass1575(default) | positive scalar

Dependencies

Programmatic Use

Yaw moment of inertia— Moment of inertia about the ego vehicle vertical axis2875(default) | positive scalar

Dependencies

Programmatic Use

Longitudinal distance from center of gravity to front tires— Distance from the ego vehicle center of mass to its front tires1.2(default) | positive scalar

Dependencies

Programmatic Use

Longitudinal distance from center of gravity to rear tires— Distance from the ego vehicle center of mass to its rear tires1.6(default) | positive scalar

Dependencies

Programmatic Use

Cornering stiffness of front tires— Front tire stiffness19000(default) | positive scalar

Dependencies

Programmatic Use

Cornering stiffness of rear tires— Rear tire stiffness33000(default) | positive scalar

Dependencies

Programmatic Use

A— Initial state matrix of ego vehicle predictive modelsquare matrix

Dependencies

Programmatic Use

B— Initial input-to-state matrix of ego vehicle predictive modelcolumn vector

Dependencies

Programmatic Use

C— Initial state-to-output matrix of ego vehicle predictive modelmatrix with two rows

Dependencies

Programmatic Use

Initial longitudinal velocity— Initial velocity of the ego vehicle15(default) | positive scalar

Programmatic Use

Transport lag between model inputs and outputs— Total transport lag in ego vehicle model0(default) | nonnegative scalar

Programmatic Use

Minimum steering angle— Minimum front steering angle-0.26(default) | scalar between-pi/2andpi/2

Dependencies

Programmatic Use

Maximum steering angle— Maximum front steering angle0.26(default) | scalar between-pi/2andpi/2

Dependencies

Programmatic Use

Sample time— Controller sample time0.1(default) | positive scalar

Programmatic Use

Prediction horizon— Controller prediction horizon10(default) | positive integer

Programmatic Use

Controller behavior— Closed-loop controller performance0.5(default) | scalar between0and1

Programmatic Use

Block Tab

Use suboptimal solution— Apply suboptimal solution after specified number of iterationsoff(default) |on

Dependencies

Programmatic Use

Maximum iteration number— Maximum optimization iterations10(default) | positive integer

Dependencies

Programmatic Use

`Curvature`— Road curvature
scalar

`Longitudinal velocity`— Ego vehicle velocity
nonnegative scalar

`Lateral deviation`— Ego vehicle lateral deviation
scalar

`Relative yaw angle`— Angle from lane centerline
scalar

`Minimum steering angle`— Minimum front steering angle
scalar

`Maximum steering angle`— Maximum front steering angle
scalar

`Enable optimization`— Controller optimization enable signal
scalar

`External control signal`— Steering angle applied to ego vehicle
scalar

`Vehicle dynamics matrix A`— State matrix of ego vehicle predictive model
square matrix

`Vehicle dynamics matrix B`— Input-to-state matrix of ego vehicle predictive model
column vector

`Vehicle dynamics matrix C`— State-to-output matrix of ego vehicle predictive model
matrix with two rows

`Steering angle`— Front steering angle control signal
scalar

`使用车辆参数s`— Define ego vehicle model using vehicle properties
`on`(default) |`off`

`Use vehicle model`— Define ego vehicle model using state-space matrices
`off`(default) |`on`

`Total mass`— Ego vehicle mass
`1575`(default) | positive scalar

`Yaw moment of inertia`— Moment of inertia about the ego vehicle vertical axis
`2875`(default) | positive scalar

`Longitudinal distance from center of gravity to front tires`— Distance from the ego vehicle center of mass to its front tires
`1.2`(default) | positive scalar

`Longitudinal distance from center of gravity to rear tires`— Distance from the ego vehicle center of mass to its rear tires
`1.6`(default) | positive scalar

`Cornering stiffness of front tires`— Front tire stiffness
`19000`(default) | positive scalar

`Cornering stiffness of rear tires`— Rear tire stiffness
`33000`(default) | positive scalar

`A`— Initial state matrix of ego vehicle predictive model
square matrix

`B`— Initial input-to-state matrix of ego vehicle predictive model
column vector

`C`— Initial state-to-output matrix of ego vehicle predictive model
matrix with two rows

`Initial longitudinal velocity`— Initial velocity of the ego vehicle
`15`(default) | positive scalar

`Transport lag between model inputs and outputs`— Total transport lag in ego vehicle model
`0`(default) | nonnegative scalar

`Minimum steering angle`— Minimum front steering angle
`-0.26`(default) | scalar between`-pi/2`and`pi/2`

`Maximum steering angle`— Maximum front steering angle
`0.26`(default) | scalar between`-pi/2`and`pi/2`

`Sample time`— Controller sample time
`0.1`(default) | positive scalar

`Prediction horizon`— Controller prediction horizon
`10`(default) | positive integer

`Controller behavior`— Closed-loop controller performance
`0.5`(default) | scalar between`0`and`1`

`Use suboptimal solution`— Apply suboptimal solution after specified number of iterations
`off`(default) |`on`

`Maximum iteration number`— Maximum optimization iterations
`10`(default) | positive integer

`Use external signal to enable or disable optimization`— Add port for enabling optimization
`off`(default) |`on`

`Use external signal for bumpless transfer between LKA and other controllers`— Add external control signal input port
`off`(default) |`on`

`Create LKA subsystem`— Create custom controller
button

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