Bicycle vehicle model
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
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
function with input commands and the current robot state.
a bicycle kinematic model object with default property values.
kinematicModel = bicycleKinematics
sets additional properties to the specified values. You can specify multiple properties
in any order.
kinematicModel = bicycleKinematics(Name,Value)
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. A value of
pi/2 provides the vehicle with a minimum turning radius of 0. This
property is used to validate the user-provided state input.
MinimumTurningRadius— Minimum vehicle turning radius
1.0000(default) | numeric scalar
This read-only property returns the minimum vehicle turning radius 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
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
"VehicleSpeedHeadingRate" — Vehicle speed and heading angular
|Time derivative of vehicle state|
Create a Robot
Define a robot and set the initial starting position and orientation.
kinematicModel = bicycleKinematics; initialState = [0 0 0];
Simulate Robot Motion
tspan = 0:0.05:1; inputs = [2 pi/4]; %Turn left [t,y] = ode45(@(t,y)derivative(kinematicModel,y,inputs),tspan,initialState);
 Lynch, Kevin M., and Frank C. Park. Modern Robotics: Mechanics, Planning, and Control 1st ed. Cambridge, MA: Cambridge University Press, 2017.
 Corke, Peter I. Robotics, Vision and Control: Fundamental Algorithms in MATLAB. Springer, 2011.