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Unicycle vehicle model


unicycleKinematics creates a unicycle vehicle model to simulate simplified car-like vehicle dynamics. The state of the vehicle is defined as a three-element vector, [x y theta], with a global xy-position, specified in meters, and a vehicle heading angle, theta, specified in radians. This model approximates a unicycle vehicle with a given wheel radius, WheelRadius, that can spin in place according to a heading angle, theta. To compute the time derivative states for the model, use the derivative function with input commands and the current robot state.




kinematicModel = unicycleKinematics creates a unicycle kinematic model object with default property values.

kinematicModel = unicycleKinematics(Name,Value) sets additional properties to the specified values. You can specify multiple properties in any order.


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The wheel radius of the vehicle, specified in meters.

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

The VehicleInputs property specifies the format of the model input commands when using the derivative function. Options are specified as one of the following strings:

  • "WheelSpeedHeadingRate" — Wheel speed and heading angular velocity, specified in radians per second.

  • "VehicleSpeedHeadingRate" — Vehicle speed and heading angular velocity, specified in radians per second.

Object Functions

derivativeTime derivative of vehicle state


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Create a Robot

Define a robot and set the initial starting position and orientation.

kinematicModel = unicycleKinematics;
initialState = [0 0 0];

Simulate Robot Motion

Set the timespan of the simulation to 1 s with 0.05 s timesteps and the input commands to 10 m/s and left turn. Simulate the motion of the robot by using the ode45 solver on the derivative function.

tspan = 0:0.05:1;
inputs = [10 1]; %Constant speed and turning left
[t,y] = ode45(@(t,y)derivative(kinematicModel,y,inputs),tspan,initialState);

Plot path


Figure contains an axes. The axes contains an object of type line.


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

Extended Capabilities

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Introduced in R2019b