Bicycle Kinematic Model

Compute car-like vehicle motion using bicycle kinematic model

• Library:

• Robotics System Toolbox / Mobile Robot Algorithms

• 

Description

The Bicycle Kinematic Model block creates a bicycle vehicle model to simulate simplified car-like vehicle dynamics. This model represents a vehicle with two axles defined by the length between the axles, Wheel base. The front wheel can be turned with steering angle psi. The vehicle heading theta is defined at the center of the rear axle.

Ports

Input

v — Vehicle speed

numeric scalar

Vehicle speed, specified in meters per second.

psi — Steering angle

numeric scalar

Steering angle of the vehicle, specified in radians.

Dependencies

To enable this port, set the Vehicle inputs parameter to Vehicle Speed & Steering Angle.

omega — Steering angular velocity

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 xy-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 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

Vehicle Speed & Steering Angle (default) | Vehicle Speed & Heading Angular Velocity

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• Vehicle Speed & Steering Angle — Vehicle speed in meters per second with a steering angle in radians.

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

Wheel base — 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.

Vehicle 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.

Maximum steering angle — Max turning radius

pi/4 (default) | numeric scaler

The maximum steering angle, refers to the maximum amount the vehicle can be steered to the right or left, specified in radians. The default value, pi/4 provides the vehicle with minimum turning radius, 0. This property is used to validate the user-provided state input.

Initial state — Initial pose of vehicle

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

The initial x-, y-position and orientation, theta, 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

Model Examples

Plan Path for a Bicycle 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 bicycle kinematic motion model simulates the robot motion based on those commands.

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 Simulink® Coder™.