Predictive Driver

Predictive driver controller to track longitudinal speed and lateral path

Libraries:
Vehicle Dynamics Blockset / Vehicle Scenarios / Driver

Description

The Predictive Driver block implements a controller that generates normalized steering, acceleration, and braking commands to track longitudinal velocity and a lateral reference displacement. The normalized commands can vary between -1 to 1. The controller uses a single-track (bicycle) model for optimal single-point preview control.

Configurations

External Actions

Use the External Actions parameters to create input ports for signals that you can use to simulate standard test maneuvers. The block uses this priority order for the input commands: disable (highest), hold, override.

This table summarizes the external action parameters.

Goal	External Action Parameter	Input Ports	Data Type
Override the accelerator command with an input acceleration command.	Accelerator override	`EnablAccelOvr`	`Boolean`
	Accelerator override	`AccelOvrCmd`	`double`
Hold the acceleration command at the current value.	Accelerator hold	`AccelHld`	`Boolean`
Disable the acceleration command.	Accelerator disable	`AccelZero`	`Boolean`
Override the decelerator command with an input deceleration command.	Decelerator override	`EnablDecelOvr`	`Boolean`
	Decelerator override	`DecelOvrCmd`	`double`
Hold the decelerator command at current value.	Decelerator hold	`DecelHld`	`Boolean`
Disable the decelerator command.	Decelerator disable	`DecelZero`	`Boolean`
Override the steering command with an input steering command.	Steering override	`EnblSteerOvr`	`Boolean`
	Steering override	`SteerOvrCmd`	`double`
Hold the steering command at the current value.	Steering hold	`SteerHld`	`Boolean`
Disable the steering command.	Steering disable	`SteerZero`	`Boolean`

Controllers

Use the Longitudinal control type, cntrlType parameter to specify one of these control options.

Setting	Block Implementation
`PI`	Proportional-integral (PI) control with tracking windup and feed-forward gains.
`Scheduled PI`	PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.
`Predictive`	Optimal single-point preview (look ahead) control model developed by C. C. MacAdam^{1, 2, 3}. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block: Represents the dynamics as a linear single track (bicycle) vehicle Minimizes the previewed error signal at a single point T* seconds ahead in time Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Setting

Block Implementation

PI

Proportional-integral (PI) control with tracking windup and feed-forward gains.

Scheduled PI

PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.

Predictive

Optimal single-point preview (look ahead) control model developed by C. C. MacAdam^{1, 2, 3}. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block:

Represents the dynamics as a linear single track (bicycle) vehicle
Minimizes the previewed error signal at a single point T* seconds ahead in time
Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Use the Lateral control type, controlTypeLat parameter to specify the type of lateral control. The table specifies the block implementation.

Setting

Block Implementation

Predictive (default)

Stanley

Controller that uses the Stanley⁴ method to minimize the position error and the angle error of the current pose with respect to the reference pose.

On the Reference Control pane, use the:

Vector input for poses parameter to input the to specify the input.

Setting	Implementation
`off` (default)	Block uses the longitudinal, lateral, and yaw reference (`LongRef`, `LatRef`, `LatRef`) input ports and the feedback (`LongFdbk`, `LatFdbk`, `LatFdbk`) input ports for the reference and feedback pose.
`on`	Block uses input ports, `RefPose` and `CurrPose`, for the reference and feedback pose, respectively.

Include dynamics parameter to specify the type of model for the controller to use.

Setting	Implementation
`off` (default)	Controller uses a kinematic bicycle model that is suitable for path following in low-speed environments such as parking lots, where inertial effects are minimal.
`on`	Controller uses a dynamic bicycle model that is suitable for path following in high-speed environments such as highways, where inertial effects are more pronounced.

Shift

Use the Shift type, ShftType parameter to specify one of these shift options.

Setting	Block Implementation
`None`	No transmission. Block outputs a constant gear of 1. Use this setting to minimize the number of parameters you need to generate acceleration and braking commands to track forward vehicle motion. This setting does not allow reverse vehicle motion.
`Reverse, Neutral, Drive`	Block uses a Stateflow^® chart to model reverse, neutral, and drive gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using simple reverse, neutral, and drive gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses the initial gear and time required to shift to shift the vehicle up into drive or down into reverse or neutral. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
`Scheduled`	Block uses a Stateflow chart to model reverse, neutral, park, and N-speed gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, park, and N-speed gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses these parameters to determine the: Initial gear Upshift and downshift accelerator pedal positions Upshift and downshift velocity Timing for shifting and engaging forward and reverse from neutral For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
`External`	Block uses the input gear, vehicle state, and velocity feedback to generate acceleration and braking commands to track forward and reverse vehicle motion. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.

Units

Use the and Longitudinal velocity units, velUnits and Angular units, angUnits parameter to specify the units for the input and output ports.

Gear Signal

Use the Output gear signal parameter to create the GearCmd output port. The GearCmd signal contains the integer value of the commanded vehicle gear.

Gear	Integer
Park	`80`
Reverse	`-1`
Neutral	`0`
Drive	`1`
Gear	`Gear number`

Output Handwheel Angle

Use the Output handwheel angle parameter to specify the units for the steering ports.

Setting	Block Implementation	Port
`off` (default)	Commanded steer angle, normalized from -1 through 1. The block uses the tire wheel angle saturation limit Tire wheel angle limit, theta parameter to normalize the command.	`SteerCmd` — Output
`off` (default)	Overrides the steering command with an input steering command normalized from -1 through 1.	`SteerOvrCmd` — Input
`on`	Commanded steer angle, in units specified by Angular units, angUnits.	`SteerCmd` — Output
`on`	Overrides the steering command with an input steering command, in units specified by Angular units, angUnits.	`SteerOvrCmd` — Input

Controller: PI Speed-Tracking

If you set the control type to PI or Scheduled PI, the block implements proportional-integral (PI) control with tracking windup and feedforward gains. For the Scheduled PI configuration, the block uses feed forward gains that are a function of vehicle velocity.

To calculate the speed control output, the block uses these equations.

Setting	Equation
`PI`	$y = \frac{K_{f f}}{v_{n o m}} v_{r e f} + \frac{K_{p} e_{r e f}}{v_{n o m}} + \int (\frac{K_{i} e_{r e f}}{v_{n o m}} + K_{a w} e_{o u t}) d t + K_{g} θ$
`Scheduled PI`	$y = \frac{K_{f f} (v)}{v_{n o m}} v_{r e f} + \frac{K_{p} (v) e_{r e f}}{v_{n o m}} + \int (\frac{K_{i} (v) e_{r e f}}{v_{n o m}} + K_{a w} e_{o u t}) d t + K_{g} (v) θ$

Setting

Equation

PI

$y = \frac{K_{f f}}{v_{n o m}} v_{r e f} + \frac{K_{p} e_{r e f}}{v_{n o m}} + \int (\frac{K_{i} e_{r e f}}{v_{n o m}} + K_{a w} e_{o u t}) d t + K_{g} θ$

Scheduled PI

$y = \frac{K_{f f} (v)}{v_{n o m}} v_{r e f} + \frac{K_{p} (v) e_{r e f}}{v_{n o m}} + \int (\frac{K_{i} (v) e_{r e f}}{v_{n o m}} + K_{a w} e_{o u t}) d t + K_{g} (v) θ$

$\begin{array}{l} where: \\ e_{r e f} = v_{r e f} - v \\ e_{o u t} = y_{s a t} - y \\ y_{s a t} = {\begin{matrix} - 1 & y < - 1 \\ y & - 1 \leq y \leq 1 \\ 1 & 1 < y \end{matrix} \end{array}$

The velocity error low-pass filter uses this transfer function.

$H (s) = \frac{1}{τ_{e r r} s + 1} for τ_{e r r} > 0$

To calculate the acceleration and braking commands, the block uses these equations.

$\begin{array}{l} y_{a c c} = {\begin{matrix} 0 & y_{s a t} < 0 \\ y_{s a t} & 0 \leq y_{s a t} \leq 1 \\ 1 & 1 < y_{s a t} \end{matrix} \\ y_{d e c} = {\begin{matrix} 0 & y_{s a t} > 0 \\ - y_{s a t} & - 1 \leq y_{s a t} \leq 0 \\ 1 & y_{s a t} < - 1 \end{matrix} \end{array}$

The equations use these variables.

v_nom	Nominal vehicle speed
K_p	Proportional gain
K_i	Integral gain
K_aw	Anti-windup gain
K_ff	Velocity feedforward gain
K_g	Grade angle feedforward gain
θ	Grade angle
τ_err	Error filter time constant
y	Nominal control output magnitude
y_sat	Saturated control output magnitude
e_ref	Velocity error
e_out	Difference between saturated and nominal control outputs
y_acc	Acceleration signal
y_dec	Braking signal
v	Velocity feedback signal
v_ref	Reference velocity signal

Controller: Predictive Speed-Tracking

If you set the Longitudinal control type, cntrlType or Lateral control type, cntrlType to Predictive, the block implements an optimal single-point preview (look ahead) control model developed by C. C. MacAdam^{1, 2, 3}. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block:

Represents the dynamics as a linear single track (bicycle) vehicle
Minimizes the previewed error signal at a single point T* seconds ahead in time
Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Vehicle Dynamics

For lateral and yaw motion, the block implements these linear dynamic equations.

$\begin{array}{l} x_{1} = U \\ {\dot{x}}_{1} = x_{2} = \frac{K_{p t}}{m} + v r - g sin (γ) + F_{r} x_{1} \\ \dot{y} = v + U ψ \\ \dot{v} = [- \frac{2 (C_{α F} + C_{α R})}{m U}] v + [\frac{2 (b C_{α R} - a C_{α F})}{m U} - U] r + (\frac{2 C_{α F}}{m}) δ_{F} \\ \dot{r} = [\frac{2 (b C_{α R} - a C_{α F})}{I U}] v + [- \frac{2 (a^{2} C_{α F} + b^{2} C_{α R})}{I U}] r + (\frac{2 a C_{α F}}{I}) δ_{F} \\ \dot{ψ} = r \end{array}$

In matrix notation:

$\begin{array}{l} \dot{x} = F x + g u \\ where: \\ x = [\begin{matrix} \begin{matrix} x_{1} \\ x_{2} \\ y \\ v \\ r \end{matrix} \\ ψ \end{matrix}] \\ F = [\begin{matrix} 0 & 1 & 0 & 0 & 0 & 0 \\ \frac{F_{r}}{m} & 0 & 0 & 0 & v & 0 \\ 0 & 0 & 0 & 1 & 0 & U \\ 0 & 0 & 0 & - \frac{2 (C_{α F} + C_{α R})}{m U} & \frac{2 (b C_{α R} - a C_{α F})}{m U} - U & 0 \\ 0 & 0 & 0 & \frac{2 (b C_{α R} - a C_{α F})}{I U} & - \frac{2 (a^{2} C_{α F} + b^{2} C_{α R})}{I U} & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \end{matrix}] \\ g = [\begin{matrix} \begin{matrix} 0 & 0 \\ \frac{K_{p t}}{m} & 0 \\ 0 & 0 \\ 0 & \frac{2 C_{α F}}{m} \\ 0 & \frac{2 a C_{α F}}{I} \\ 0 & 0 \end{matrix} \end{matrix}] \\ u = [\begin{matrix} \begin{matrix} \bar{u} \\ δ_{F} \end{matrix} \end{matrix}] \\ \bar{u} = u - \frac{m^{2}}{K_{p t}} g sin (γ) \end{array}$

The single-point model assumes a minimum previewed error signal at a single point T* seconds ahead in time. a* is the driver ability to predict the future vehicle response based on the current steering control input. b* is the driver ability to predict the future vehicle response based on the current vehicle state. The block uses these equations.

$\begin{array}{l} a^{*} = (T^{*}) m^{T} [I + \sum_{n = 1}^{\infty} \frac{F^{n} {(T^{*})}^{n}}{(n + 1)!}] g \\ b^{*} = m^{T} [I + \sum_{n = 1}^{\infty} \frac{F^{n} {(T^{*})}^{n}}{n!}] \\ m^{T} = [\begin{matrix} 1 & 1 & 1 & 0 & 0 & 0 \end{matrix}] \end{array}$

The equations use these variables.

a, b	Forward and rearward tire location, respectively
m	Vehicle mass
I	Vehicle rotational inertia
C_ɑF	Front tire cornering coefficient
C_ɑR	Rear tire cornering coefficient
a, b	Driver prediction scalar and vector gain, respectively
x	Predicted vehicle state vector
v	Lateral velocity
r	Yaw rate
Ψ	Front wheel heading angle
y	Lateral displacement
F	System matrix
δ, δ_F	Steer angle and front axle steer angle, respectively
γ	Grade angle
g	Control coefficient vector
U	Forward (longitudinal) vehicle velocity
T*	Preview time window
ƒ(t+T)*	Previewed path input T* seconds ahead
u	Tractive force
*m^T*	Constant observer vector; provides vehicle lateral position
a_r	Static rolling and driveline resistance
b_r	Linear rolling and driveline resistance
c_r	Aerodynamic rolling and driveline resistance
F_r	Rolling resistance

Optimization

The single-point model implemented by the block finds the steering command that minimizes a local performance index, J, over the current preview interval, (t, t+T).

$J = \frac{1}{T} \int_{t}^{t + T} {[f (η) - y (η)]}^{2} d η$

To minimize J with respect to the steering command, this condition must be met.

$\frac{d J}{d u} = 0$

You can express the optimal control solution in terms of a current non-optimal and corresponding nonzero preview output error T* seconds ahead^{1, 2, 3}.

$u^{o} (t) = u (t) + \frac{e (t + T^{*})}{a^{*}}$

The block uses the preview distance and vehicle longitudinal velocity to determine the preview time window.

$T^{*} = \frac{L}{U}$

The equations use these variables.

T*	Preview time window
ƒ(t+T)*	Previewed path input T* sec ahead
y(t+T)*	Previewed plant output T* sec ahead
e(t+T)*	Previewed error signal T* sec ahead
u(t), u^o(t)	Steer angle and optimal steer angle, respectively
L	Preview distance
J	Performance index
U	Forward (longitudinal) vehicle velocity

Driver Lag

The single-point model implemented by the block introduces a driver lag. The driver lag accounts for the delay when the driver is tracking tasks. Specifically, it is the transport delay deriving from perceptual and neuromuscular mechanisms. To calculate the driver transport delay, the block implements this equation.

$H (s) = e^{- s τ}$

The equations use these variables.

τ	Driver transport delay
y(t+T)*	Previewed plant output T* sec ahead
e(t+T)*	Previewed error signal T* sec ahead
u(t), u^o(t)	Steer angle and optimal steer angle, respectively
J	Performance index

Controller: Stanley Lateral Path-Tracking

If you set Lateral control type, controlTypeLat to Stanley, the block implements the Stanley method⁴. To compute the steering angle command, the Stanley controller minimizes the position error and the angle error of the current pose with respect to the reference pose. The driving direction of the vehicle determines these error values.

To compute the steering angle command, the controller minimizes the position error and the angle error of the current pose with respect to the reference pose.

The position error is the lateral distance from the vehicle center-of-gravity (CG) to the reference point on the path.
The angle error is the angle of the vehicle with respect to reference path.

Examples

Double Lane Change Reference Application

Simulate a full vehicle dynamics model undergoing a double lane change maneuver standard ISO 3888-2. Use for vehicle dynamics ride and handling analysis and chassis controls development, including yaw stability and lateral acceleration limits.

Open Script

Ports

Input

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VelRef — Reference vehicle velocity
`scalar`

Reference velocity, v_ref, in units specified by Longitudinal velocity units, velUnits.

LongRef — Longitudinal displacement reference
`scalar`

Longitudinal center of mass (CM) displacement reference, in the inertial reference frame, in m.

Dependencies

To enable this port:

Set Lateral control type, controlTypeLat to Stanley.
Clear Vector input for poses.

LatRef — Lateral displacement reference
`scalar`

Lateral center of mass (CM) displacement reference, in the inertial reference frame, in m.

Dependencies

To enable this port, do one of these:

Set Lateral control type, controlTypeLat to Stanley and clear Vector input for poses.
Set Lateral control type, controlTypeLat to Predictive.

YawRef — Yaw angle reference
`scalar`

Vehicle yaw angle, Ψ_o, in the inertial reference frame, in units specified by Angular units, angUnits.

Dependencies

To enable this port:

Set Lateral control type, controlTypeLat to Stanley
Clear Vector input for poses

EnblSteerOvr — Enable steering command override
`scalar`

Enable steering command override.

Dependencies

To enable this port, select Steering override.

Data Types: Boolean

SteerOvrCmd — Steering override command
`scalar`

Steering override command.

Use the Output handwheel angle parameter to specify the units for the steering ports.

Setting	Block Implementation	Port
`off` (default)	Commanded steer angle, normalized from -1 through 1. The block uses the tire wheel angle saturation limit Tire wheel angle limit, theta parameter to normalize the command.	`SteerCmd` — Output
`off` (default)	Overrides the steering command with an input steering command normalized from -1 through 1.	`SteerOvrCmd` — Input
`on`	Commanded steer angle, in units specified by Angular units, angUnits.	`SteerCmd` — Output
`on`	Overrides the steering command with an input steering command, in units specified by Angular units, angUnits.	`SteerOvrCmd` — Input

Dependencies

To enable this port, select Steering override.

Data Types: double

SteerHld — Steering hold
`scalar`

Boolean signal that holds the steering command at the current value.

Dependencies

To enable this port, select Steering hold.

Data Types: Boolean

SteerZero — Disable steering command
`scalar`

Disable steering command.

Dependencies

To enable this port, select Steering disable.

Data Types: Boolean

EnblAccelOvr — Enable acceleration command override
`scalar`

Enable acceleration command override.

Dependencies

To enable this port, select Acceleration override.

Data Types: Boolean

AccelOvrCmd — Acceleration override command
`scalar`

Acceleration override command, normalized from 0 through 1.

Dependencies

To enable this port, select Acceleration override.

Data Types: double

AccelHld — Acceleration hold
`scalar`

Boolean signal that holds the acceleration command at the current value.

Dependencies

To enable this port, select Acceleration hold.

Data Types: Boolean

AccelZero — Disable acceleration command
`scalar`

Disable acceleration command.

Dependencies

To enable this port, select Acceleration disable.

Data Types: Boolean

EnblDecelOvr — Enable deceleration command override
`scalar`

Enable deceleration command override.

Dependencies

To enable this port, select Deceleration override.

Data Types: Boolean

DecelOvrCmd — Deceleration override command
`scalar`

Deceleration override command, normalized from 0 through 1.

Dependencies

To enable this port, select Deceleration override.

Data Types: double

DecelHld — Deceleration hold
`scalar`

Boolean signal that holds the deceleration command at the current value.

Dependencies

To enable this port, select Deceleration hold.

Data Types: Boolean

DecelZero — Disable deceleration command
`scalar`

Disable deceleration command.

Dependencies

To enable this port, select Deceleration disable.

Data Types: Boolean

ExtGear — Gear
`scalar`

Gear	Integer
Park	`80`
Reverse	`-1`
Neutral	`0`
Drive	`1`
Gear	`Gear number`

Dependencies

To enable this port, set Shift type, shftType to External.

Grade — Road grade angle
`scalar`

Road grade angle, γ, in deg.

Curvature — Path curvature
scalar

Path curvature defined as the rate of change of the tangent angle with respect to the arc length of the path, Κ, in 1/m.

Dependencies

To enable this port:

Set Lateral control type, controlTypeLat to Stanley.
Select Include dynamics.

RefPose — Reference pose
[X_ref, Y_ref, φ_ref] vector

Reference pose, specified as an [X_ref, Y_ref, φ_ref] vector. X_ref and Y_ref are in meters, and φ_ref are in units specified by Angular units, angUnits.

X_ref and Y_ref specify the reference point to steer the vehicle toward.

φ_ref specifies the orientation angle of the path at this reference point and is positive in the clockwise direction.

The reference point is the point on the path that is closest to the vehicle CG. You can use the either the Z-up or Z-down vehicle coordinate system, as long you use the same coordinate system (Z-up or Z-down) for block inputs and parameters.

Figure indicating location of x, y, and psi on vehicle path

Dependencies

To enable this port:

Set Lateral control type, controlTypeLat to Stanley.
Select Vector input for poses.

Data Types: single | double

VelFdbk — Longitudinal vehicle velocity
`scalar`

Longitudinal vehicle velocity, U, in the vehicle-fixed frame, in units specified by Longitudinal velocity units, velUnits.

CurrPose — Current pose
[X_curr, Y_curr, φ_curr] vector

Current pose of the vehicle, specified as an [X_curr, Y_curr, φ_curr] vector. X_curr and Y_curr are in meters, and φ_curr is in units specified by Angular units, angUnits.

X_curr and Y_curr specify the location of the vehicle, which is defined as the vehicle CG.

φ_curr specifies the orientation angle of the vehicle location at (X_curr, Y_curr) and is positive in the clockwise direction.

You can use the either the Z-up or Z-down vehicle coordinate system, as long you use the same coordinate system (Z-up or Z-down) for block inputs and parameters.

Figure indicating location of x, y, and psi on vehicle path

Dependencies

To enable this port:

Set Lateral control type, controlTypeLat to Stanley.
Select Vector input for poses.

Data Types: single | double

LatFdbk — Lateral displacement
`scalar`

Lateral CM displacement, y_o, in the inertial reference frame, in m.

Dependencies

To enable this port, do either of these:

Set Lateral control type, controlTypeLat to Stanley and clear Vector input for poses.
Set Lateral control type, controlTypeLat to Predictive.

LatVelFdbk — Lateral vehicle velocity
`scalar`

Lateral vehicle velocity, v_o , in the vehicle-fixed frame, in m/s.

Dependencies

To enable this port, Set Lateral control type, controlTypeLat to Predictive.

YawFdbk — Vehicle yaw angle
`scalar`

Vehicle yaw angle, Ψ_o, in the inertial reference frame, in units specified by Angular units, angUnits.

Dependencies

To enable this port, do either of these:

Set Lateral control type, controlTypeLat to Stanley and clear Vector input for poses.
Set Lateral control type, controlTypeLat to Predictive.

YawVelFdbk — Yaw rate
`scalar`

Yaw rate, r_o, in the vehicle-fixed frame, in units specified by Angular units, angUnits per sec.

Dependencies

To enable this port, Set Lateral control type, controlTypeLat to Predictive.

Output

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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Variable	Description
`Steer`			δ_F	Commanded steer angle, normalized from 0 through 1
`Accel`			y_acc	Commanded vehicle acceleration, normalized from 0 through 1
`Decel`			y_dec	Commanded vehicle deceleration, normalized from 0 through 1
`Gear`				Integer value of commanded gear
`Clutch`				Clutch command
`Err`	`LatErr`	`Err`	e_ref	Difference in reference vehicle position and vehicle position.
		`ErrSqrSum`	$\int_{0}^{t} e_{r e f}^{2} d t$	Integrated square of error.
		`ErrMax`	$\max (e_{r e f} (t))$	Maximum error during simulation.
		`ErrMin`	$\min (e_{r e f} (t))$	Minimum error during simulation.
	`LngErr`	`Err`	e_ref	Difference in reference vehicle speed and vehicle speed
		`ErrSqrSum`	$\int_{0}^{t} e_{r e f}^{2} d t$	Integrated square of error
		`ErrMax`	$\max (e_{r e f} (t))$	Maximum error during simulation
		`ErrMin`	$\min (e_{r e f} (t))$	Minimum error during simulation
`ExtActions`	`EnblSteerOvr`			Override the steering command with an input deceleration command
	`SteerOvrCmd`			Input steering override command
	`SteerHld`			Hold the steering command at the current value
	`SteerZero`			Disable the steering command
	`EnblAccelOvr`			Override the accelerator command with an input acceleration command
	`AccelOvrCmd`			Input accelerator override command
	`AccelHld`			Hold the acceleration command at the current value
	`AccelZero`			Disable the acceleration command
	`EnblDecelOvr`			Override the decelerator command with an input deceleration command
	`DecelOvrCmd`			Input deceleration override command
	`DecelHld`			Hold the decelerator command at current value
	`DecelZero`			Disable the decelerator command

SteerCmd — Steer angle command
`scalar`

Commanded steer angle, δ_F.

Use the Output handwheel angle parameter to specify the units for the steering ports.

Setting	Block Implementation	Port
`off` (default)	Commanded steer angle, normalized from -1 through 1. The block uses the tire wheel angle saturation limit Tire wheel angle limit, theta parameter to normalize the command.	`SteerCmd` — Output
`off` (default)	Overrides the steering command with an input steering command normalized from -1 through 1.	`SteerOvrCmd` — Input
`on`	Commanded steer angle, in units specified by Angular units, angUnits.	`SteerCmd` — Output
`on`	Overrides the steering command with an input steering command, in units specified by Angular units, angUnits.	`SteerOvrCmd` — Input

AccelCmd — Commanded vehicle acceleration
`scalar`

Commanded vehicle acceleration, y_acc, normalized from 0 through 1.

DecelCmd — Commanded vehicle deceleration
`scalar`

Commanded vehicle deceleration, y_dec, normalized from 0 through 1.

GearCmd — Commanded vehicle gear
`scalar`

Integer value of commanded vehicle gear.

Gear	Integer
Park	`80`
Reverse	`-1`
Neutral	`0`
Drive	`1`
Gear	`Gear number`

Dependencies

To enable this port, select Output gear signal.

Parameters

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Configuration

External Actions

Accelerator override — Override acceleration command
`off` (default) | `on`

Select to override the acceleration command with an input acceleration command.

Dependencies

Selecting this parameter creates the EnblAccelOvr and AccelOvrCmd input ports.

Accelerator hold — Hold acceleration command
`off` (default) | `on`

Select to hold the acceleration command.

Dependencies

Selecting this parameter creates the AccelHld input port.

Accelerator disable — Disable acceleration command
`off` (default) | `on`

Select to disable the acceleration command.

Dependencies

Selecting this parameter creates the AccelZero input port.

Decelerator override — Override deceleration command
`off` (default) | `on`

Select to override the deceleration command with an input deceleration command.

Dependencies

Selecting this parameter creates the EnblDecelOvr and DecelOvrCmd input ports.

Decelerator hold — Hold deceleration command
`off` (default) | `on`

Select to hold the deceleration command.

Dependencies

Selecting this parameter creates the DecelHld input port.

Decelerator disable — Disable deceleration command
`off` (default) | `on`

Select to disable the deceleration command.

Dependencies

Selecting this parameter creates the DecelZero input port.

Steering override — Override steering command
`off` (default) | `on`

Select to override the steering command with an input steering command.

Dependencies

Selecting this parameter creates the EnblSteerOvr and SteerOvrCmd input ports.

Steering hold — Hold steering command
`off` (default) | `on`

Select to hold the steering command.

Dependencies

Selecting this parameter creates the SteerHld input port.

Steering disable — Disable steering command
`off` (default) | `on`

Select to disable the steering command.

Dependencies

Selecting this parameter creates the SteerZero input port.

Control and Shift

Longitudinal control type, cntrlType — Longitudinal control
`PI` (default) | `Scheduled PI` | `Predictive`

Type of longitudinal control.

Setting	Block Implementation
`PI`	Proportional-integral (PI) control with tracking windup and feed-forward gains.
`Scheduled PI`	PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.
`Predictive`	Optimal single-point preview (look ahead) control model developed by C. C. MacAdam^{1, 2, 3}. The model represents driver steering control behavior during path-following and obstacle avoidance maneuvers. Drivers preview (look ahead) to follow a predefined path. To implement the MacAdam model, the block: Represents the dynamics as a linear single track (bicycle) vehicle Minimizes the previewed error signal at a single point T* seconds ahead in time Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Setting

Block Implementation

PI

Proportional-integral (PI) control with tracking windup and feed-forward gains.

Scheduled PI

PI control with tracking windup and feed-forward gains that are a function of vehicle velocity.

Predictive

Represents the dynamics as a linear single track (bicycle) vehicle
Minimizes the previewed error signal at a single point T* seconds ahead in time
Accounts for the driver lag deriving from perceptual and neuromuscular mechanisms

Lateral control type, controlTypeLat — Controller
`Predictive` (default) | `Stanley`

Use the Lateral control type, controlTypeLat parameter to specify the type of lateral control. The table specifies the block implementation.

Setting

Block Implementation

Predictive (default)

Stanley

Controller that uses the Stanley⁴ method to minimize the position error and the angle error of the current pose with respect to the reference pose.

On the Reference Control pane, use the:

Vector input for poses parameter to input the to specify the input.

Setting	Implementation
`off` (default)	Block uses the longitudinal, lateral, and yaw reference (`LongRef`, `LatRef`, `LatRef`) input ports and the feedback (`LongFdbk`, `LatFdbk`, `LatFdbk`) input ports for the reference and feedback pose.
`on`	Block uses input ports, `RefPose` and `CurrPose`, for the reference and feedback pose, respectively.

Include dynamics parameter to specify the type of model for the controller to use.

Setting	Implementation
`off` (default)	Controller uses a kinematic bicycle model that is suitable for path following in low-speed environments such as parking lots, where inertial effects are minimal.
`on`	Controller uses a dynamic bicycle model that is suitable for path following in high-speed environments such as highways, where inertial effects are more pronounced.

Shift type, shftType — Shift type
`None` (default) | `Reverse, Neutral, Drive` | `Scheduled` | `External`

Shift type.

Setting	Block Implementation
`None`	No transmission. Block outputs a constant gear of 1. Use this setting to minimize the number of parameters you need to generate acceleration and braking commands to track forward vehicle motion. This setting does not allow reverse vehicle motion.
`Reverse, Neutral, Drive`	Block uses a Stateflow chart to model reverse, neutral, and drive gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using simple reverse, neutral, and drive gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses the initial gear and time required to shift to shift the vehicle up into drive or down into reverse or neutral. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
`Scheduled`	Block uses a Stateflow chart to model reverse, neutral, park, and N-speed gear shift scheduling. Use this setting to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, park, and N-speed gear shift scheduling. Depending on the vehicle state and vehicle velocity feedback, the block uses these parameters to determine the: Initial gear Upshift and downshift accelerator pedal positions Upshift and downshift velocity Timing for shifting and engaging forward and reverse from neutral For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.
`External`	Block uses the input gear, vehicle state, and velocity feedback to generate acceleration and braking commands to track forward and reverse vehicle motion. For neutral gears, the block uses braking commands to control the vehicle speed. For reverse gears, the block uses an acceleration command to generate torque and a brake command to reduce vehicle speed.

Longitudinal velocity units, velUnits — Velocity units
`m/s` (default)

Vehicle velocity reference and feedback units.

Dependencies

If you set Longitudinal control type, CntrlType control type to Scheduled or Scheduled PI, the block uses the Longitudinal velocity units, velUnits for the Nominal speed, vnom parameter dimension.

If you set Shift Type, shftType to Scheduled, the block uses the Longitudinal velocity units, velUnits for these parameter dimensions:

Upshift velocity data table, upShftTbl
Downshift velocity data table, dwnShftTbl

Angular units, angUnits — Input and output port angular units
`rad` (default) | `deg`

Input and output port angular units.

Output gear signal — Create `GearCmd` output port
`off` (default) | `on`

Specify to create output port GearCmd.

Output handwheel angle — Steering port units in rad
`off` (default) | `on`

Use the Output handwheel angle parameter to specify the units for the steering ports.

Setting	Block Implementation	Port
`off` (default)	Commanded steer angle, normalized from -1 through 1. The block uses the tire wheel angle saturation limit Tire wheel angle limit, theta parameter to normalize the command.	`SteerCmd` — Output
`off` (default)	Overrides the steering command with an input steering command normalized from -1 through 1.	`SteerOvrCmd` — Input
`on`	Commanded steer angle, in units specified by Angular units, angUnits.	`SteerCmd` — Output
`on`	Overrides the steering command with an input steering command, in units specified by Angular units, angUnits.	`SteerOvrCmd` — Input

Dependencies

To create the SteerOvrCmd input port, select Steering override.

Reference Control

Longitudinal

Proportional gain, Kp — Gain
`10` (default) | `scalar`

Proportional gain, K_p, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Integral gain, Ki — Gain
`5` (default) | `scalar`

Proportional gain, K_i, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Velocity feed-forward, Kff — Gain
`.1` (default) | `scalar`

Velocity feed-forward gain, K_ff, dimensionless.

Dependencies

To create this parameter, set Control type to PI.

Grade angle feed-forward, Kg — Gain
`0` (default) | `scalar`

Grade angle feed-forward gain, K_g, in 1/deg.

Dependencies

To create this parameter, set Control type to PI.

Velocity gain breakpoints, VehVelVec — Breakpoints
`[0 100]` (default) | `vector`

Velocity gain breakpoints, VehVelVec, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Velocity feed-forward gain values, KffVec — Gain
`[.1 .1]` (default) | `vector`

Velocity feed-forward gain values, KffVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Proportional gain values, KpVec — Gain
`[10 10]` (default) | `vector`

Proportional gain values, KpVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Integral gain values, KiVec — Gain
`[5 5]` (default) | `vector`

Integral gain values, KiVec, as a function of vehicle velocity, dimensionless.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Grade angle feed-forward values, KgVec — Grade gain
`[0 0]` (default) | `vector`

Grade angle feed-forward values, KgVec, as a function of vehicle velocity, in 1/deg.

Dependencies

To create this parameter, set Control type to Scheduled PI.

Nominal speed, vnom — Nominal vehicle speed
`5` (default) | `scalar`

Nominal vehicle speed, v_nom, in units specified by the Reference and feedback units, velUnits parameter. The block uses the nominal speed to normalize the controller gains.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Anti-windup, Kaw — Gain
`1` (default) | `scalar`

Anti-windup gain, K_aw, dimensionless.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Error filter time constant, tauerr — Filter
`.01` (default) | `scalar`

Error filter time constant, τ_err, in s. To disable the filter, enter 0.

Dependencies

To create this parameter, set Control type to PI or Scheduled PI.

Predictive

Driver response time, tau — Response time
`0.1` (default) | `scalar`

Driver response time, τ, in s.

Dependencies

To enable this parameter, Set Longitudinal control type, cntrlType or Lateral control type, controlTypeLat to Predictive.

Preview distance, L — Distance
`3` (default) | `scalar`

Driver preview distance, L, in m. Used to determine the preview time window, T^*.

Dependencies

To enable this parameter, Set Longitudinal control type, cntrlType or Lateral control type, controlTypeLat to Predictive.

Effective vehicle total tractive force, Kpt — Tractive force
`3000` (default) | `scalar`

Effective vehicle total tractive force, K_pt, in N.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Rolling resistance coefficient, aR — Resistance
`200` (default) | `scalar`

Static rolling and driveline resistance coefficient, a_R, in N. Block uses the parameter to estimate the constant acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Rolling and driveline resistance coefficient, bR — Resistance
`2.5` (default) | `scalar`

Rolling and driveline resistance coefficient, b_R, in N·s/m. Block uses the parameter to estimate the linear velocity-dependent acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Aerodynamic drag coefficient, cR — Drag
`.5` (default) | `scalar`

Aerodynamic drag coefficient, c_R, in N·s^2/m^2. Block uses the parameter to estimate the quadratic velocity-dependent acceleration or braking effort.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Gravitational constant, g — Gravitational constant
`9.81` (default) | `scalar`

Gravitational constant, g, in m/s^2.

Dependencies

To create this parameter, set Longitudinal control type, cntrlType to Predictive.

Stanley

Vector input for poses — Select to create `RefPose` and `CurrPose` input ports
`off` (default) | `on`

Select this parameter to create the RefPose and CurrPose input ports.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley.

Include dynamics — Select to include dynamics
`off` (default) | `on`

The controller computes this command using the Stanley method, whose control law is based on both a kinematic and dynamic bicycle model. To change between models, use this parameter.

Setting	Implementation
`off`	Controller uses a kinematic bicycle model that is suitable for path following in low-speed environments such as parking lots, where inertial effects are minimal.
`on`	Controller uses a dynamic bicycle model that is suitable for path following in high-speed environments such as highways, where inertial effects are more pronounced.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley.

Position gain of forward motion, PositionGainF — Position gain of vehicle in forward motion
`2.5` (default) | positive real scalar

Position gain of the vehicle when it is in forward motion, specified as a positive scalar. This value determines how much the position error affects the steering angle. Typical values are in the range [1, 5]. Increase this value to increase the magnitude of the steering angle.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley.

Position gain of reverse motion, PositionGainR — Position gain of vehicle in reverse motion
`2.5` (default) | positive real scalar

Position gain of the vehicle when it is in reverse motion, specified as a positive scalar. This value determines how much the position error affects the steering angle. Typical values are in the range [1, 5]. Increase this value to increase the magnitude of the steering angle.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley.

Yaw rate feedback gain, YawRateGain — Yaw rate feedback gain
`.2` (default) | nonnegative real scalar

Yaw rate feedback gain, specified as a nonnegative real scalar. This value determines how much weight is given to the current yaw rate of the vehicle when the block computes the steering angle command.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley and select Include dynamics.

Steering angle feedback gain, DelayGain — Steering angle feedback gain
`.2` (default) | nonnegative real scalar

Steering angle feedback gain, specified as a nonnegative real scalar. This value determines how much the difference between the current steering angle command, SteerCmd, and the current steering angle, CurrSteer, affects the next steering angle command.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Stanley and select Include dynamics.

Vehicle Parameters

Forward location of tire, a — Along vehicle longitudinal axis
`1.41` (default) | `scalar`

Forward location of tire, a, in m. Distance from vehicle cg to forward tire location, along vehicle longitudinal axis.

Rearward location of tire, b — Along vehicle longitudinal axis
`1.41` (default) | `scalar`

Rearward location of tire, b, in m. Absolute value of distance from vehicle cg to rearward tire location, along vehicle longitudinal axis.

Vehicle mass, m — Mass
`2016` (default) | `scalar`

Vehicle mass, m, in kg.

Dependencies

To enable this port, do either of these:

Set Lateral control type, controlTypeLat to Stanley and select Include dynamics.
Set Lateral control type, controlTypeLat to Predictive.

Front tire cornering coefficient, Cy_f — Coefficient
`25266` (default) | `scalar`

Cornering stiffness coefficient, C_αF , in N/rad.

Dependencies

To enable this port, do either of these:

Set Lateral control type, controlTypeLat to Stanley and select Include dynamics.
Set Lateral control type, controlTypeLat to Predictive.

Rear tire cornering coefficient, Cy_r — Coefficient
`70933` (default) | `scalar`

Cornering stiffness coefficient, C_αR , in N/rad.

Dependencies

To enable this port, set Lateral control type, controlTypeLat to Predictive.

Vehicle rotational inertia, I — Inertia about yaw axis
`4013` (default) | `scalar`

Vehicle rotational inertia, I, about the vehicle yaw axis, in N·m·s^2.

Dependencies

To enable this parameter, Set Lateral control type, controlTypeLat to Predictive.

Nominal steering ratio, Ksteer — Steering ratio
`18` (default) | `scalar`

Steering ratio, K_steer. The value has no dimension.

Dependencies

To enable this parameter, select Output handwheel angle.

Tire wheel angle limit, theta — Angle limit
`45*pi/180` (default) | `scalar`

Tire wheel angle limit, θ, in rad.

Shift

Reverse, Neutral, Drive

Initial gear, GearInit — Initial gear
`0` (default) | `scalar`

Integer value of the initial gear. The block uses the initial gear to generate acceleration and braking commands to track forward and reverse vehicle motion.

Gear	Integer
Park	`80`
Reverse	`-1`
Neutral	`0`
Drive	`1`
Gear	`Gear number`

Dependencies

To create this parameter, set Shift type, shftType to Reverse, Neutral, Drive or Scheduled. If you specify Reverse, Neutral, Drive, the Initial Gear, GearInit parameter value can be only -1, 0, or 1.

Time required to shift, tShift — Time
`.1` (default) | `scalar`

Time required to shift, tShift, in s. The block uses the time required to shift to generate acceleration and braking commands to track forward and reverse vehicle motion using reverse, neutral, and drive gear shift scheduling.

Dependencies

To create this parameter, set Shift type, shftType to Reverse, Neutral, Drive.

Scheduled

Initial gear, GearInit — Initial gear
`0` (default) | `scalar`

Integer value of the initial gear. The block uses the initial gear to generate acceleration and braking commands to track forward and reverse vehicle motion.

Gear	Integer
Park	`80`
Reverse	`-1`
Neutral	`0`
Drive	`1`
Gear	`Gear number`

Dependencies

Up and down shift accelerator pedal positions, pdlVec — Pedal position breakpoints
`[0.1 0.4 0.5 0.9]` (default) | `[1-by-m] vector`

Pedal position breakpoints for lookup tables when calculating upshift and downshift velocities, dimensionless. Vector dimensions are 1 by the number of pedal position breakpoints, m.