Dynamic Modeling of AWD CARΒΆ

I am fascinated by Bond-Graphs and how capable they are, They are a graph representation of dynamics/kinematics and they work for electrical, mechanical and even chemical systems.

if you are familiar with mass-spring-damper system dynamics, this is how a bond graph for that system looks like,

../_images/bond-spring.png

very simple right? one connection node in the middle and four other elements.

I used similar techniques to extract a detailed model for an all wheel drive car, the graph looks like

../_images/bond-car.png

and lateral and longitudinal friction models can be drawn as (based on stribeck friction model)

../_images/bond-tire.png

and eventually you can use a software package to convert the graph to analytical equations (I used 20Sim). one could simpy write a solver themselves.

../_images/bond-ode.png

Runnig some simulations of this ODE gives reasonable trajectories for the vehicle. Here is a simulation of one equilibrium point on the equilibrium manifold

../_images/bond-equi.png

You can find a c++ implementation of mentione ODE here