ZinZam

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Physics

This page details some of the physics that govern a wheelchair type micromouse that is suitable for designing a controller. The physics detailed isn't exact, that's what the controller is for, to take care of any error! These equations were used to formulate the controller for my team's micromouse core trio, and worked very well.

There are two types of movement a mouse can make. Translation, and rotation. This requires two models to be formulated, one for translational movement, and another for rotational movement.

let $\dot{x}_{l}$ = left wheel tangential velocity
let $\dot{x}_{r}$ = right wheel tangential velocity
let $\dot{x}_{m}$ = micromouse translational velocity
let $\dot{\theta}_{m}$ = micromouse rotational velocity
let $r_{m}$ = micromouse turning circle radius

$\dot{x}_{m} = f(\dot{x}_{l}, \dot{x}_{r})$
$\dot{x}_{m} = \frac{\dot{x}_{l} + \dot{x}_{r}}{2}$
$\dot{\theta}_{m} = K_{r} \cdot r_{m}\cdot(\dot{x}_{l} - \dot{x}_{r})$

Tyres

The keyword for any wheel-surface interface is traction. A high tractive allows you to use a high tractive effort (torque). However if you apply a torque higher than the adhesion conditions will allow, you will get wheel slip (bad).

$F_{m} = m\cdot a < \mu\cdot m\cdot g$
$\Rightarrow a < \mu\cdot g$

Mass cancels out and doesn't matter in this simplistic model.

Last Modified: August 30, 2008 with 5 page views.

This page is licensed under the following license: GNU Free Document License

ZinZam

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Physics

Tyres