Simulation 3D Four-Wheel Ground Following

R2026b

Adjust vehicle chassis pose to align with terrain geometry

Since R2026b

Libraries:
Offroad Autonomy Library / Ground Following

Description

Add-On Required: This feature requires the Robotics System Toolbox Offroad Autonomy Library add-on.

The Simulation 3D Four‑Wheel Ground Following block computes a terrain‑aligned 3D pose for a four-wheeled vehicle moving over uneven ground in an Unreal Engine^® simulation. The block determines the translation and rotation of the vehicle in an Unreal Engine scene based on the 2D pose of the rear-axle frame of the vehicle chassis and the wheel parameters. The block ensures the wheels remain in contact with the terrain surface of the scene. The output pose represents the vehicle aligned with the terrain geometry.

This figure shows the parameters of the four-wheeled vehicle.

Note

Simulating models with the Simulation 3D Four-Wheel Ground Following block requires Simulink^® 3D Animation™.

Examples

expand all

Enable Ground Following for Rigid Body Tree

This example uses:

Open Live Script

Use the exampleHelperCreateForklift helper function to create a forklift rigid body tree model. Then load the ground-following parameters, like wheelbase, track width, and wheel radius.

forklift = exampleHelperCreateForklift;
[tw,wb,rad,pose] = exampleHelperForkliftParameters(forklift);
show(forklift,Frames="off")
title("Forklift")
axis auto

Figure contains an axes object. The axes object with title Forklift, xlabel X, ylabel Y contains 63 objects of type patch.

Open the model. In the Simulation 3D Four-Wheel Ground Following block mask, specify all of ground-following parameters for the forklift.

open_system("Sim3DForkliftGroundFollowing.slx")

Run the model.

sim("Sim3DForkliftGroundFollowing.slx");

function [tw,wb,rad,pose] = exampleHelperForkliftParameters(forklift) 

homeConfig = homeConfiguration(forklift);

tformRL_RR = getTransform(forklift,homeConfig,"wheel_rr","wheel_rl");
tw = norm(tform2trvec(tformRL_RR));

tformRL_FL = getTransform(forklift,homeConfig,"wheel_fl","wheel_rl");
wb = norm(tform2trvec(tformRL_FL));

tformOrigin_RL = getTransform(forklift,homeConfig,"wheel_rl","origin");
posOrigin_RL = tform2trvec(tformOrigin_RL);
rad = posOrigin_RL(3);

pose = getTransform(forklift,homeConfig,"rear_axle","origin"); 

end

Ports

Input

expand all

X — x-coordinate of rear-axle frame in right-handed world frame
scalar

x-coordinate of the rear-axle frame in the right-handed world frame, specified as a numeric scalar, in meters.

Y — y-coordinate of rear-axle frame in right-handed world frame
scalar

y-coordinate of the rear-axle frame in the right-handed world frame, specified as a numeric scalar, in meters.

Yaw — Yaw of rear-axle frame in right-handed world frame
scalar

Yaw of the rear-axle frame in the right-handed world frame, specified as a numeric scalar. Units are in radians.

Output

expand all

Translation — Translation of actor in right-handed world frame
vector

Translation of the actor in the right-handed world frame, returned as a three-element row vector of the form [x y z]. Units are in meters.

You can specify this output translation to the input Translation port of the Simulation 3D Robot block.

Rotation — Rotation of actor in right-handed world frame
vector

Rotation of the actor in the right-handed world frame, returned as a three-element row vector representing the Euler angle sequence ZYX. Units are in radians.

You can specify this output rotation to the input Rotation port of the Simulation 3D Robot block.

Parameters

expand all

Track width — Distance between left and right wheels on rear axle
`1` (default) | positive numeric scalar

Specify the distance between the left and right wheels on the rear axle as a positive numeric scalar. Units are in meters.

Wheel base — Distance between rear and front wheels on same side
`1` (default) | positive numeric scalar

Specify the distance between the rear and front wheels on the same side as a positive numeric scalar. Units are in meters.

Wheel radius — Radius of rear wheels
`1` (default) | nonnegative numeric scalar

Specify the radius of rear wheels as a nonnegative numeric scalar. Units are in meters.

Rear-axle pose — Pose of rear-axle frame with respect to origin frame of actor
`eye(4)` (default) | 4-by-4 homogeneous transformation matrix

Specify the pose of the rear-axle frame with respect to the origin frame of the actor as a 4-by-4 homogeneous transformation matrix.

If you use the Simulation 3D Robot block to create the actor, the rear-axle pose is with respect to the base frame of the associated rigid body tree model.

Ray tracer offset — Axial offset of ray origin from wheel center
`0.05` (default) | nonnegative numeric scalar

Specify the axial distance from each wheel center to the ray-tracer origin, measured outboard along the axle axis, as a nonnegative numeric scalar. Units are in meters.

Parent actor — Name of simulation 3D actor that must follow ground
`Scene Origin` (default) | string scalar | character vector

Specify the name of the parent to which to apply ground following as either the name of a vehicle in your model or Scene Origin. The vehicle names that you can select correspond to the Name parameters of the simulation 3D vehicle blocks, such as the Simulation 3D Robot block, in your model.

Example: SimulinkVehicle1

Visualize ray tracing lines — Specify to visualize ray tracing lines
`on` (default) | `off`

Select this parameter to visualize the ray tracing lines. These ray tracers detect the ground under the vehicle for sensing the elevation of the ground in the Unreal Engine scene.

Algorithms

expand all

The block computes a ground-following pose for the rear-axle frame by estimating terrain slope from four wheel-contact elevations.

Ground Elevation Processing

The block averages the ground-contact elevations along the longitudinal and lateral axes of the vehicle. Given the four contact elevations z_FL, z_FR, z_RL, and z_RR (front-left, front-right, rear-left, and rear-right), the block computes:

${\bar{z}}_{f r o n t} = \frac{z_{F L} + z_{F R}}{2}, {\bar{z}}_{r e a r} = \frac{z_{R L} + z_{R R}}{2}$

${\bar{z}}_{l e f t} = \frac{z_{F L} + z_{R L}}{2}, {\bar{z}}_{r i g h t} = \frac{z_{F R} + z_{R R}}{2}$

These averages represent the mean terrain height along each side of the vehicle.

Orientation

The block derives the terrain pitch and roll from the elevation differences. The pitch angle α_pitch measures the terrain slope along the wheelbase L (the distance between front and rear axles):

$α_{p i t c h} = \arctan (\frac{{\bar{z}}_{r e a r} - {\bar{z}}_{f r o n t}}{L})$

The roll angle α_roll measures the terrain slope across the track width w (the lateral distance between left and right wheels):

$α_{r o l l} = \arctan (\frac{{\bar{z}}_{l e f t} - {\bar{z}}_{r i g h t}}{w})$

The yaw angle equals the rear-axle heading θ about the world Z-axis:

$α_{y a w} = θ$

The block constructs the rotation matrix R using the Z-Y-X (yaw-pitch-roll) intrinsic Euler angle convention:

$R = R_{z} (α_{y a w}) \cdot R_{y} (α_{p i t c h}) \cdot R_{x} (α_{r o l l}),$

where R_z, R_y, and R_x are elementary rotation matrices about the Z, Y, and X axes, respectively.

Position

The block then finds the position of the rear-axle frame's origin projected onto the ground:

$t = {[x, y, {\bar{z}}_{r e a r}]}^{T},$

where x and y are the rear-axle coordinates in the world frame.

Output Transformation

Finally, the block finds the rear-axle frame's ground-projected frame at T_ground:

$T_{g r o u n d} = [\begin{matrix} R & t \\ 0^{T} & 1 \end{matrix}]$

Version History

Introduced in R2026b

Simulation 3D Four-Wheel Ground Following

Description

Examples

Enable Ground Following for Rigid Body Tree

Ports

Input

X — x-coordinate of rear-axle frame in right-handed world frame scalar

Y — y-coordinate of rear-axle frame in right-handed world frame scalar

Yaw — Yaw of rear-axle frame in right-handed world frame scalar

Output

Translation — Translation of actor in right-handed world frame vector

Rotation — Rotation of actor in right-handed world frame vector

Parameters

Track width — Distance between left and right wheels on rear axle 1 (default) | positive numeric scalar

Wheel base — Distance between rear and front wheels on same side 1 (default) | positive numeric scalar

Wheel radius — Radius of rear wheels 1 (default) | nonnegative numeric scalar

Rear-axle pose — Pose of rear-axle frame with respect to origin frame of actor eye(4) (default) | 4-by-4 homogeneous transformation matrix

Ray tracer offset — Axial offset of ray origin from wheel center 0.05 (default) | nonnegative numeric scalar

Parent actor — Name of simulation 3D actor that must follow ground Scene Origin (default) | string scalar | character vector

Visualize ray tracing lines — Specify to visualize ray tracing lines on (default) | off

Algorithms

Ground Elevation Processing

Orientation

Position

Output Transformation

Version History

See Also

X — x-coordinate of rear-axle frame in right-handed world frame
scalar

Y — y-coordinate of rear-axle frame in right-handed world frame
scalar

Yaw — Yaw of rear-axle frame in right-handed world frame
scalar

Translation — Translation of actor in right-handed world frame
vector

Rotation — Rotation of actor in right-handed world frame
vector

Track width — Distance between left and right wheels on rear axle
`1` (default) | positive numeric scalar

Wheel base — Distance between rear and front wheels on same side
`1` (default) | positive numeric scalar

Wheel radius — Radius of rear wheels
`1` (default) | nonnegative numeric scalar

Rear-axle pose — Pose of rear-axle frame with respect to origin frame of actor
`eye(4)` (default) | 4-by-4 homogeneous transformation matrix

Ray tracer offset — Axial offset of ray origin from wheel center
`0.05` (default) | nonnegative numeric scalar

Parent actor — Name of simulation 3D actor that must follow ground
`Scene Origin` (default) | string scalar | character vector

Visualize ray tracing lines — Specify to visualize ray tracing lines
`on` (default) | `off`