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I'm trying to find the minimal power needed to drive an omidirectional 3-wheeled robot. I already asked in Robotics Stack Exchange and they didn't respond yet.

From the equation $P=Fv$ I know I need rolling friction, as it gives $F$. There are two forces of rolling resistance, one of the whole wheel $F_t$, and one of the roller $F_n$. Rolling resistance is given by $F=\frac{fN}{R}$, where $f$ is the coefficient, $N$ is the weight and $R$ is the radius. Like this paper says, the friction increases linearly with the angle $\alpha$. However, the equation for rolling resistance doesn't want to work, as it doesn't have dependency on the angle and gives a constant. Trying to add those two vectors, $F_t$ and $F_n$, just gives a constant force.

So I could use $P=M\omega$, where $M=Nf(\alpha)$, but the wheel, while moving sideways, rolls on some virtual radius that I don't know how to get, which is needed to determine $\omega$. I think.

Could anyone help me with finding this? Any help would be appreciated.

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    $\begingroup$ look for rolling resistance values. This is dependent on wheel and surface values. Steel on steel is very low, for example. Note that theoretical friction is independent on mass of what is being moved, real-world may be different, plus you have to get the object moving. $\endgroup$
    – Tiger Guy
    Aug 7, 2023 at 17:35
  • $\begingroup$ I suggest you measure it and publish it. Make up a simple plywood platform with your wheels on it, load it up, and measure the force to drag it at constant speed. You may want to steer one of the wheels. $\endgroup$ Aug 7, 2023 at 22:52
  • $\begingroup$ A general observation: Whenever people ask for a qustions about motor sizing or tribology. Questions usually stay unanswered. There is really no answer to this particular question, because to answer it i would need to do a measurement of a real system. $\endgroup$
    – joojaa
    Aug 8, 2023 at 6:48

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I eventually got to some numbers.

Like the paper that I linked says, the friction increases linearly with the angle. So I simply multiplied $F_t$ and $F_n$ by linear scaling functions: $k_t=-\frac{\alpha}{90°}+1$ and $k_n=\frac{\alpha}{90°}$. They're valid from 0 to 90°, but you can easily extend them beyond 90°, the slope will just be negative and entire figure will form a triangle.

From there you can get the total friction force and eventually power.

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