CARBC – Model of tractor with two-axle trailer

Block SymbolLicensing group: MODEL

Function Description
The CARBC block simulates the kinematics of an articulated vehicle consisting of a tractor with a two-axle trailer, as shown in the figure below. The model is designed for testing control algorithms, especially during reversing and maneuvering in confined spaces. Its main application is in the development of driver assistance systems and in the research into stabilization and tracking controllers.

The model’s inputs are the forward speed of the front wheels u1 and the angular velocity of the front wheels u2. A negative value of u1 corresponds to reversing. The input signal R1 is used to reset the system to its initial state.

Model parameters represent the physical properties of the vehicle, i.e., the lengths of individual parts (wheelbase, drawbar, trailer), the initial state of the system, and the limits of wheel rotation. The parameter description corresponds to the notation in the figure above.

The model outputs the current position of the tractor’s rear axle x0, y0, its orientation theta0 relative to the x-axis in space, the steering angle of the front wheels phi0, the hitch angle between the tractor and the drawbar phi1, and the total articulation angle between the tractor and the flatbed truck phiT. The output E indicates an error condition or the exceeding of limit values.

Thanks to these outputs, the block is suitable for simulating and testing the following scenarios:

design and verification of stabilization controllers for reversing,
simulation of dynamics without regulation for instability research,
testing of tracking algorithms following the desired angle of rotation.

This block does not propagate the signal quality. More information can be found in the 1.4 section.

Input

u1	Longitudinal velocity of front wheels [m/s]	Double (F64)
u2	Steering angular velocity of front wheels [rad]	Double (F64)
R1	Block reset	Bool

Parameter

d0	Wheelbase of the tractor unit [m] $↓$ 0.0	Double (F64)
d1	Length of drawbar [m] $↓$ 0.0	Double (F64)
d2	Length of trailer [m] $↓$ 0.0	Double (F64)
a0	Distance from rear axle of tractor to hitch point [m] $↓$ 0.0	Double (F64)
b0	Offset of front axle of trailer [m] $↓$ 0.0	Double (F64)
phi0l	Steering angle lower limit [rad] $↓$ 0.0	Double (F64)
phi0h	Steering angle upper limit [rad] $↓$ 0.0	Double (F64)
x0_0	Initial X position of rear axle [m] $↓$ 0.0	Double (F64)
y0_0	Initial Y position of rear axle [m] $↓$ 0.0	Double (F64)
theta0_0	Initial orientation angle of rear axle in x-axis [rad] $↓$ 0.0	Double (F64)
phi0_0	Initial front wheels steering angle [rad] $↓$ 0.0	Double (F64)
phi1_0	Initial hitch angle (tractor to drawbar) [rad] $↓$ 0.0	Double (F64)
phiT_0	Initial angle between tractor and rear axle [rad] $↓$ 0.0	Double (F64)

Output

x0	Current X position of rear axle [m]	Double (F64)
y0	Current Y position of rear axle [m]	Double (F64)
theta0	Current orientation of rear axle in x-axis [rad]	Double (F64)
phi0	Current front wheels steering angle [rad]	Double (F64)
phi1	Current hitch angle (tractor to drawbar) [rad]	Double (F64)
phiT	Current tractor-trailer angle [rad]	Double (F64)
E	Error indicator	Bool

[Back to top] [Up] [Next]