Ackermann Kinematic Model

Car-like vehicle motion using Ackermann kinematic model

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Libraries:
Robotics System Toolbox / Mobile Robot Algorithms

Description

The Ackermann Kinematic Model block creates a car-like vehicle model that uses Ackermann steering. This model represents a vehicle with two axles separated by the distance, Wheel base. The state of the vehicle is defined as a four-element vector, [x y θ ψ], with an global xy-position, vehicle heading, θ, and steering angle, ψ. The vehicle heading and xy-position are defined at the center of the rear axle. Angles are specified in radians and the global positions are specified in meters. The steering input for the vehicle is given as dψ/dt, in radians per second.

Examples

Plot Ackermann Drive Vehicle in Simulink

Plot the position of an Ackermann Kinematic Model block and change the vehicle velocity and steering angular velocity in real-time.

• Open Live Script

Ports

Input

v — Vehicle speed

numeric scalar

Vehicle speed, specified in meters per second.

dψ/dt — Steering angular velocity

numeric scalar

Steering angular velocity of the vehicle, specified in radians per second.

Output

state — State of vehicle

four-element vector

Current xy-position, orientation, and steering angle, specified as [x y θ ψ], in meters and radians.

stateDot — Derivatives of state output

four-element vector

The linear and angular velocities of the vehicle, specified as a [xDot yDot thetaDot psiDot] vector in meters per second and radians per second. The linear and angular velocities are calculated by taking the time derivatives of the state output.

Parameters

Wheel base — Distance between front and rear axles

1 (default) | positive numeric scalar

The wheel base refers to the distance between the front and rear vehicle axles, specified in meters.

Vehicle speed range — Minimum and maximum vehicle speeds

[-Inf Inf] (default) | two-element vector

The wheel speed range is a two-element vector that provides the minimum and maximum vehicle wheel speeds, [MinSpeed MaxSpeed], specified in radians per second.

Maximum steering angle — Distance between front and rear axles

pi/4 (default) | positive numeric scalar

The maximum steering angle, refers to the maximum amount the vehicle can be steered to the right or left, specified in radians. The default value is pi/4.

Initial state — Initial state of vehicle

[0;0;0;0] (default) | four-element vector

The initial x-, y-position, heading angle, theta, and steering angle, psi, of the vehicle.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

• Interpreted execution — Simulate model using the MATLAB^® interpreter. For more information, see Interpreted Execution vs. Code Generation (Simulink).

• Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink^® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change.

Tunable: No

References

[1] Lynch, Kevin M., and Frank C. Park. Modern Robotics: Mechanics, Planning, and Control. 1st ed. Cambridge, MA: Cambridge University Press, 2017.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2019b