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Constant Radius Maneuver

This reference application represents a full vehicle dynamics model undergoing a constant radius test maneuver. For information about similar maneuvers, see standards SAE J266_199601[4] and ISO 4138:2012[5]. You can create your own versions, establishing a framework to test that your vehicle meets the design requirements under normal and extreme driving conditions. Use this reference application in ride and handling studies and chassis controls development to characterize the steering and lateral vehicle dynamics.

You can configure the reference application for open-loop and closed-loop tests:

  • Open-loop — Maintain the target velocity and steering wheel angle to determine the lateral acceleration, side-slip characteristics, and steering angles for specific accelerations and subsequent test maneuvers. For the open-loop test, set the Reference Generator block Maneuver parameter to Increasing Steer.

  • Closed-loop — Use the predictive driver to maintain a prespecified turn radius at different velocities for drivability and handling performance studies. For the closed-loop test, set the Reference Generator block Maneuver parameter to Constant radius.

To create and open a working copy of the constant radius reference application, enter

This table summarizes the blocks and subsystems in the reference application. Some subsystems contain variants.

Reference Application ElementDescriptionVariants

Reference Generator block

Sets the parameters that configure the maneuver and 3D visualization environment. By default, the block is set for the constant radius maneuver with the 3D simulation engine environment disabled.

For the minimum 3D visualization environment hardware requirements, see 3D Visualization Engine Requirements and Limitations.

To enable 3D visualization, on the 3D Engine tab, select Enabled.

Driver Commands

Implements the driver model that the reference application uses to generate acceleration, braking, gear, and steering commands.

By default, Driver Commands subsystem variant is the Predictive Driver block.


Implements wind and road forces.


Implements controllers for engine control units (ECUs), transmissions, anti-lock braking systems (ABS), and active differentials.

Passenger Vehicle

Implements the:

  • Body, suspension, and wheels

  • Engine

  • Steering, transmission, driveline, and brakes


Provides the vehicle trajectory and driver response

To override the default variant, on the Modeling tab, in the Design section, click the drop-down. In the General section, select Variant Manager. In the Variant Manager, navigate to the variant that you want to use. Right-click and select Override using this Choice.

Reference Generator

The Reference Generator block sets the parameters that configure the maneuver and 3D simulation environment. By default, the block is set for the constant radius maneuver with the 3D simulation engine environment disabled.

Use the Maneuver parameter to specify the type of maneuver. You can specify the double lane change, swept sine, sine with dwell, and slowly increasing maneuvers.

If you select the Use maneuver-specific driver, initial position, and scene parameter, the reference application sets the driver, initial position, and scene for the maneuver that you specified.

For more information, see Reference Generator.

Driver Commands

The Driver Commands block implements the driver model that the reference application uses to generate acceleration, braking, gear, and steering commands. By default, if you select the Reference Generator block parameter Use maneuver-specific driver, initial position, and scene, the reference application selects the driver for the maneuver that you specified.

Vehicle Command Mode Setting


Longitudinal Driver

Longitudinal Driver block — Longitudinal speed-tracking controller. Based on reference and feedback velocities, the block generates normalized acceleration and braking commands that can vary from 0 through 1. Use the block to model the dynamic response of a driver or to generate the commands necessary to track a longitudinal drive cycle.

Predictive Driver

Predictive Driver block — 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.

Open Loop

Implements an open-loop system so that you can configure the reference application for constant or signal-based steering, acceleration, braking, and gear command input.


The Environment subsystem generates the wind and ground forces. The reference application has these environment variants.


Ground Feedback

3D Engine

Uses Vehicle Terrain Sensor block to implement ray tracing in 3D environment

Constant (default)

Implements a constant friction value


The Controllers subsystem generates engine torque, transmission gear, brake pressure, and differential pressure commands.


The ECU controller generates the engine torque command. The controller prevents over-revving the engine by limiting the engine torque command to the value specified by model workspace variable EngRevLim. By default, the value is 7000 rpm. If the differential torque command exceeds the limited engine torque command, the ECU sets the engine torque command to the commanded differential torque.

Transmission Control

The Transmission Controller subsystem generates the transmission gear command. The controller includes these variants.


Transmission Controller

Implements a transmission control module (TCM) that uses Stateflow® logic to generate the gear command based on the vehicle acceleration, wheel speed, and engine speed.

Driver - No Clutch

Open loop transmission control. The controller sets the gear command to the gear request.

PRNDL Controller (default)

Implements a transmission control module (TCM) that uses Stateflow logic to generate the gear command based on the vehicle acceleration, brake command, wheel speed, engine speed, and gear request.


Implements a paddle controller that uses the vehicle acceleration and engine speed to generate the gear command.

Brake Pressure Control

The Brake Controller subsystem implements a Brake Pressure Control subsystem to generate the brake pressure command. The Brake Pressure Control subsystem has these variants.


Bang Bang ABS

Implements an anti-lock braking system (ABS) feedback controller that switches between two states to regulate wheel slip. The bang-bang control minimizes the error between the actual slip and desired slip. For the desired slip, the controller uses the slip value at which the mu-slip curve reaches a peak value. This desired slip value is optimal for minimum braking distance.

Open Loop (default)

Open loop brake control. The controller sets the brake pressure command to a reference brake pressure based on the brake command.

Five-State ABS

Five-state ABS control when you simulate the maneuver.1,2,3 The five-state ABS controller uses logic-switching based on wheel deceleration and vehicle acceleration to control the braking pressure at each wheel.

Consider using five-state ABS control to prevent wheel lock-up, decrease braking distance, or maintain yaw stability during the maneuver. The default ABS parameters are set to work on roads that have a constant friction coefficient scaling factor of 0.6.

Active Differential Control

The Active Differential Control subsystem generates the differential pressure command. To calculate the command, the subsystem has these variants.


Rear Diff Controller

Implements a controller that generates the differential pressure command based on the:

  • Steer angle

  • Vehicle pitch, yaw, and roll

  • Brake command

  • Wheel speed

  • Gear

  • Vehicle acceleration

No Control (default)

Does not implement a controller. Sets the differential pressure command to 0.

Passenger Vehicle

The Passenger Vehicle subsystem has an engine, controllers, and a vehicle body with four wheels. Specifically, the vehicle contains these subsystems.

Body, Suspension, Wheels SubsystemVariantDescription



Vehicle with four wheels:

  • Vehicle body has three degrees-of-freedom (DOFs) — Longitudinal, lateral, and yaw

  • Each wheel has one DOF — Rolling


PassVeh14DOF (default)

Vehicle with four wheels.

  • Vehicle body has six DOFs — Longitudinal, lateral, vertical and pitch, yaw, and roll

  • Each wheel has two DOFs — Vertical and rolling

Engine SubsystemVariantDescription

Mapped Engine

SiMappedEngine (default)

Mapped spark-ignition (SI) engine

Steering, Transmission, Driveline, and Brakes Subsystem


Driveline Ideal Fixed Gear

Driveline model

All Wheel Drive

Configure the driveline for all-wheel, front-wheel, rear-wheel, or rear-wheel active differential drive and specify the type of torque coupling.

Front Wheel Drive

Rear Wheel Drive

Rear Wheel Drive Active Differential (default)


Ideal (default)

Implements an ideal fixed gear transmission.

Brake Hydraulics


Implements the heuristic response of a hydraulic system when the controller applies a brake command to a cylinder. Includes front and rear wheel bias coefficients. The subsystem converts the applied pressure to a cylinder spool position. To generate the brake pressure, the spool applies a flow downstream to the cylinders.


When you run the simulation, the Visualization subsystem provides driver, vehicle, and response information. The reference application logs vehicle signals during the maneuver, including steering, vehicle and engine speed, and lateral acceleration. You can use the Simulation Data Inspector to import the logged signals and examine the data.

Image of Visualization subsystem


Driver Commands

Driver commands:

  • Handwheel angle

  • Acceleration command

  • Brake command

Vehicle Response

Vehicle response:

  • Engine speed

  • Vehicle speed

  • Lateral acceleration

Steer, Velocity, Lat Accel Scope block

  • SteerAngle — Steering angle versus time

  • <xdot> — Longitudinal vehicle velocity versus time

  • <ay> — Lateral acceleration versus time

Vehicle XY Plotter

Vehicle longitudinal versus lateral distance

ISO 15037-1:2006 block

Display ISO standard measurement signals in the Simulation Data Inspector, including steering wheel angle and torque, longitudinal and lateral velocity, and sideslip angle

If you enable 3D visualization on the Reference Generator block 3D Engine tab by selecting Enabled, you can view the vehicle response in the AutoVrtlEnv window.

To smoothly change the camera views, use these key commands.

KeyCamera View


Back left

Image showing key commands and corresponding camera view

 View Animated GIF




Back right








Front left




Front right



For additional camera controls, use these key commands.

KeyCamera Control

Cycle the view between all vehicles in the scene.

 View Animated GIF

Mouse scroll wheel

Control the camera distance from the vehicle.

 View Animated GIF


Toggle a camera lag effect on or off. When you enable the lag effect, the camera view includes:

  • Position lag, based on the vehicle translational acceleration

  • Rotation lag, based on the vehicle rotational velocity

This lag enables improved visualization of overall vehicle acceleration and rotation.

 View Animated GIF


Toggle the free camera mode on or off. When you enable the free camera mode, you can use the mouse to change the pitch and yaw of the camera. This mode enables you to orbit the camera around the vehicle.

 View Animated GIF


[1] Pasillas-Lépine, William. "Hybrid modeling and limit cycle analysis for a class of five-phase anti-lock brake algorithms." Vehicle System Dynamics 44, no. 2 (2006): 173-188.

[2] Gerard, Mathieu, William Pasillas-Lépine, Edwin De Vries, and Michel Verhaegen. "Improvements to a five-phase ABS algorithm for experimental validation." Vehicle System Dynamics 50, no. 10 (2012): 1585-1611.

[3] Bosch, R. "Bosch Automotive Handbook." 10th ed. Warrendale, PA: SAE International, 2018.

[4] J266_199601. Steady-State Directional Control Test Procedures for Passenger Cars and Light Trucks. Warrendale, PA: SAE International, 1996.

[5] ISO 4138:2012. Passenger cars — Steady-state circular driving behaviour — Open-loop test methods. Geneva: ISO, 2012.

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