bicycleKinematics

Bicycle vehicle model

Description

bicycleKinematics creates a bicycle vehicle model to simulate simplified car-like vehicle dynamics. This model represents a vehicle with two axles separated by a distance, WheelBase. 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. The front wheel can be turned with steering angle psi. The vehicle heading, theta, is defined at the center of the rear axle. To compute the time derivative states of the model, use the derivative function with input commands and the current robot state.

Creation

Syntax

kinematicModel = bicycleKinematics

kinematicModel = bicycleKinematics(Name,Value)

Description

kinematicModel = bicycleKinematics creates a bicycle kinematic model object with default property values.

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

Properties

WheelBase — 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.

VehicleSpeedRange — Range of vehicle speeds

[-Inf Inf] (default) | positive numeric scalar

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

MaxSteeringAngle — Maximum steering angle

pi/4 (default) | numeric scalar

The maximum steering angle, psi, refers to the maximum angle the vehicle can be steered to the right or left, specified in radians. This property is used to validate the user-provided state input.

If MaxSteeringAngle is set to pi/2, it results in a MinimumTurningRadius value of 0.

MinimumTurningRadius — Minimum vehicle turning radius

1.0000 (default) | numeric scalar

This property is read-only.

The minimum vehicle turning radius, specified as a numeric scalar, in meters. The minimum radius is computed using the wheel base and the maximum steering angle.

VehicleInputs — Type of motion inputs for vehicle

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

The VehicleInputs property specifies the format of the model input commands when using the derivative function. The property has two valid options, specified as a string or character vector:

• "VehicleSpeedSteeringAngle" — Vehicle speed and steering angle

• "VehicleSpeedHeadingRate" — Vehicle speed and heading angular velocity

Object Functions

derivative

Time derivative of vehicle state

Examples

Plot Path of Bicycle Kinematic Robot

Create a Robot

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

kinematicModel = bicycleKinematics;
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 2 m/s for the vehicle speed and pi/4 rad for the steering angle to create a left turn. Simulate the motion of the robot by using the ode45 solver on the derivative function.

tspan = 0:0.05:1;
inputs = [2 pi/4]; %Turn left
[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.

[2] Corke, Peter I. Robotics, Vision and Control: Fundamental Algorithms in MATLAB. Springer, 2011.

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.