differentialDriveKinematics

Differential-drive vehicle model

Description

differentialDriveKinematics creates a differential-drive vehicle model to simulate simplified vehicle dynamics. This model approximates a vehicle with a single fixed axle and wheels separated by a specified track width. The wheels can be driven independently. Vehicle speed and heading is defined from the axle center. 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, theta, specified in radians. To compute the time derivative states for the model, use the derivative function with input commands and the current robot state.

Creation

Syntax

kinematicModel = differentialDriveKinematics

kinematicModel = differentialDriveKinematics(Name,Value)

Description

kinematicModel = differentialDriveKinematics creates a differential drive kinematic model object with default property values.

kinematicModel = differentialDriveKinematics(Name,Value) sets properties on the object to the specified value. You can specify multiple properties in any order.

Properties

WheelRadius — Wheel radius of vehicle

0.05 (default) | positive numeric scalar

The wheel radius of the vehicle, specified in meters.

WheelSpeedRange — Range of vehicle wheel speeds

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

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

TrackWidth — Distance between wheels on axle

0.2 (default) | positive numeric scalar

The vehicle track width refers to the distance between the wheels, or the axle length, specified in meters.

VehicleInputs — Type of motion inputs for vehicle

"WheelSpeeds" (default) | character vector | string scalar

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:

• "WheelSpeeds" — Angular speeds for each of the wheels, specified in radians per second.

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

Object Functions

derivative

Time derivative of vehicle state

Examples

Plot Path of Differential-Drive Kinematic Robot

Create a Robot

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

kinematicModel = differentialDriveKinematics;
initialState = [0 0 0];

Simulate Robot Motion

Set the timespan of the simulation to 1 s with 0.05 s time steps and the input commands to 50 rad/s for the left wheel and 40 rad/s for the right wheel to result in a right turn. Simulate the motion of the robot by using the ode45 solver on the derivative function.

tspan = 0:0.05:1;
inputs = [50 40]; %Left wheel is spinning faster
[t,y] = ode45(@(t,y)derivative(kinematicModel,y,inputs),tspan,initialState);

Plot Path

figure
plot(y(:,1),y(:,2))

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 MATLAB® Coder™.

Version History

Introduced in R2019b

R2024b: Specify multiple commands and states at once

The cmds argument of the derivative object function now accepts multiple states and commands at once.