Cycling for Computer Scientists

Simulation of bicycle (self-)stability

Introduction

In this project we examine the self-stability of a bicycle by numerically simulating the dynamics of a bicycle. The math is based on the paper "Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review" by J. P. Meijaard et al (2007). The paper is available here.

Additionally, to simulating the bicycle on its own, we also model a rider controlling the bicycle via the steering angle to keep it upright.

Usage

To use the project, create a virtual environment and install the required packages:

python -m venv venv
source venv/bin/activate
pip install -r requirements.txt

Run the simulation and store the results

python bicycler simulate --output FILENAME

For additional parameters like model parameters, simulation settings and rider control, see the help message:

python bicycler simulate --help

Play a simulation result

python bicycler visualize -i FILENAME

... or simulate and immediately play the result

python bicycler simulate --show -o show

Add any parameters just like in the simulate command.

Evaluation

The behavior of the simulation is evaluated by comparing the results to the analytical results presented in the paper. Below are the parameters used in the evaluation:

// inverted-prendulum-like fall
python bicycler simulate --show -o show -t 0.01 -s 1600 -v 4.

// low speed weave mode
python bicycler simulate --show -o show -t 0.01 -s 1600 -v 4.2

// riderless stable mode
python bicycler simulate --show -o show -t 0.005 -s 1500 -v 4.35

// capsize mode
python bicycler simulate --show -o show -t 0.01 -s 2000 -v 10

Furthermore we show that the rider control can stabilize the bicycle at otherwise installable speeds:

// stability at high speed with rider control
python bicycler simulate --show -o show -t 0.01 -s 500 -v 10 -c pid

// stability with high initial lean
python bicycler simulate --show -o show -t 0.005 -s 1000 -v 20 -c pid --roll 20