Differential Drive Kinematic Model

Compute vehicle motion using differential drive kinematic model

Since R2019b

• 

Libraries:
Robotics System Toolbox / Mobile Robot Algorithms

Description

The Differential Drive Kinematic Model block 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 Track width. Each of the wheels can be driven independently using speed inputs, dϕL/dt and dϕR/dt, for the left and right wheels respectively. Vehicle speed and heading is defined from the axle center.

Examples

Plan Path for a Differential Drive Robot in Simulink

Demonstrates how to execute an obstacle-free path between two locations on a given map in Simulink®. The path is generated using a probabilistic road map (PRM) planning algorithm (mobileRobotPRM). Control commands for navigating this path are generated using the Pure Pursuit controller block. A differential drive kinematic motion model simulates the robot motion based on those commands.

Open Live Script

Ports

Input

dϕ_L/dt — Left wheel speed

numeric scalar

Left wheel speed of the vehicle, specified in radians per second.

Dependencies

To enable this port, set the Vehicle inputs parameter to Wheel Speeds.

dϕ_R/dt — Right wheel speed

numeric scalar

Right wheel speed of the vehicle, specified in radians per second.

Dependencies

To enable this port, set the Vehicle inputs parameter to Wheel Speeds.

v — Vehicle speed

numeric scalar

Vehicle speed, specified in meters per second.

Dependencies

To enable this port, set the Vehicle inputs parameter to Vehicle Speed & Heading Angular Velocity.

ɷ — Angular velocity of vehicle

numeric scalar

Angular velocity of the vehicle, specified in radians per second. A positive value steers the vehicle left and negative values steer the vehicle right.

Dependencies

To enable this port, set the Vehicle inputs parameter to Vehicle Speed & Heading Angular Velocity.

Output

state — Pose of vehicle

three-element vector

Current position and orientation of the vehicle, specified as a [x y theta] vector in meters and radians.

stateDot — Derivatives of state output

three-element vector

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

Parameters

Vehicle inputs — Type of speed and directional inputs for vehicle

Wheel Speeds (default) | Vehicle Speed & Heading Angular Velocity

The format of the model input commands

• Wheel Speeds — Angular speeds of the two wheels in radians per second.

• Vehicle Speed & Heading Angular Velocity — Vehicle speed in meters per second with a heading angular velocity in radians per second.

Wheel radius — Wheel radius of vehicle

0.05 (default) | positive numeric scalar

The radius of the wheels on the vehicle, specified in meters.

Wheel 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.

Track width — Track length of vehicle from wheel to wheel

0.2 (default) | numeric scalar

Length of the track from the left wheel to right wheel, specified in meters.

Initial state — Initial pose of the vehicle

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

The initial xy-position and orientation, θ, 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 Simulation Modes (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