A Python description of the Kinematic Bicycle Model with an animated example.

Last update: Dec 23, 2022

Overview

Kinematic Bicycle Model

Abstract

A python library for the Kinematic Bicycle model. The Kinematic Bicycle is a compromise between the non-linear and linear bicycle models for high-speed integration of the library with little configuration.

At initialisation
:param wheelbase:       (float) vehicle's wheelbase [m]
:param max_steer:       (float) vehicle's steering limits [rad]
:param dt:              (float) discrete time period [s]
:param c_r:             (float) vehicle's coefficient of resistance 
:param c_a:             (float) vehicle's aerodynamic coefficient

At every time step  
:param x:               (float) vehicle's x-coordinate [m]
:param y:               (float) vehicle's y-coordinate [m]
:param yaw:             (float) vehicle's heading [rad]
:param velocity:        (float) vehicle's velocity in the x-axis [m/s]
:param throttle:        (float) vehicle's accleration [m/s^2]
:param delta:           (float) vehicle's steering angle [rad]

:return x:              (float) vehicle's x-coordinate [m]
:return y:              (float) vehicle's y-coordinate [m]
:return yaw:            (float) vehicle's heading [rad]
:return velocity:       (float) vehicle's velocity in the x-axis [m/s]
:return delta:          (float) vehicle's steering angle [rad]
:return omega:          (float) vehicle's angular velocity [rad/s]

Advantages

The model allows the vehicle to come to rest without passing the model a negative acceleration; similar to the non-linear bicycle.
This lightweight model is able to accurately represent a vehicle with no slip or tire stiffness.

Limitations

Just like with all other bicycle models, this model is a discrete model and loses its accuracy when the time step is set too large or the vehicle is made to travel at unreasonably high speeds. Usually, the FPS of the simulation should be set to the highest possible value for the greatest accuracy. However, for rendering high-quality GIFs, 50 FPS is found to be most optimal.

Requirements

pip install numpy

Demo

Install the requirements

pip install -r requirements.txt

Play the animation

python animation.py

Concept

To simplify the equations, we perform all calculations from the rear axle.

Comments

Animation not running and getting warning instead

When I try to run the animation, I am getting the following warning message that halts the animation:

UserWarning: Animation was deleted without rendering anything. This is most likely not intended. To prevent deletion, assign the Animation to a variable, e.g.anim, that exists until you have outputted the Animation usingplt.show()oranim.save(). warnings.warn(

So I assigned the variable anim for function FuncAnimation and uncommented anim.save('animation.gif', writer='imagemagick', fps=50). With this change, I see the a full white plot screen and the following on the console:

Not sure what is it that I need to do to remedy this. Your help will be highly appreciated. Thanks in advance.

opened by enter802 6
not subscriptable

File "animate.py", line 9, in from libs.car_description import Description KinematicBicycleModel-main\libs\car_description.py", line 5, in class Description: KinematicBicycleModel-main\libs\car_description.py", line 80, in Description def plot_car(self, x: float, y: float, yaw: float, steer: float) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray]: TypeError: 'type' object is not subscriptable
good first issue

opened by myildirimm 4
Plot both map and camera tracks car at the same time?

Is there a way to plot animation of both original map plot and camera tracking car plot at the same time for better visualization? I'm pretty new to matplot in python. Thanks for sharing your implementation anyways!

opened by namKolorfuL 2
Wrong calculation for low FPS

For lower FPS values the results of the calculations are wrong.

For fps = 50 everything works just fine, but I wanted to simulate fps = 1 (to see where the vehicle will be every 1 second) but the algorithm crash.

I found that for dt >= 0.073 the algorithm crash... Is there any way to use the code for higher dts?
good first issue

opened by rhalaly 1
Pure Pursuit implementation (exists?)

Hi W!

I'm looking to evaluate the pure-pursuit algorithm in your simulator. Do you have already an implementation? If not, I'd be happy to propose my solution and to hear recommendations. Specially on making the lookahead distance dynamic, maybe speed dependant as proposed here: [taken from https://www.coursera.org/learn/intro-self-driving-cars]

cheers!

opened by IonyM-BWR 1

Owner

Winston H.

I have no idea what I am doing.

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