# Comparison of Balance Bot design

I'm planning to build a Balance Bot and I would like to know which design should I go with. There's a vertical design such as the ArduRoller and on the other hand, there's the typical stacked type of deign. I have attached images below for both of them.

Although both of these are based on the principle of Inverted Pendulum, how do these differ from each other in terms of stability and response (assuming both the designs are of the same size)? Is the mass distribution in the vertical design better? Also, is there a difference in programming them?

A measure that can be used to describe toppling speed is the time constant of toppling $\tau$. The higher this value, the longer the duration of toppling (i.e. toppling is slower), and thus the easier it is to balance. The time constant of toppling for a simple point mass inverted pendulum is $\tau=\sqrt{L/g}$ for small toppling angles, with $L$ the length of the pendulum (defined by the distance between the hinge and the center of mass) and $g$ the gravitational acceleration. For example, a robot with a center of mass that is 4 times higher will topple approximately 2 times slower. Or, if it is not feasible to make your robot sufficiently tall, you can always send it off to another planet with lower gravity...