Smooth servo motions

Hi Timothy,

Thank you so much for your detailed response. This answers my questions perfectly and I really want to give it a 10 out of 3. It's so nice to have some people to break down the code for me.

After reading this, I tried to understand how the angle updates are done. Here's my understanding,

For convenience, let's call the target angle $b$ and the current angle $a$, in

diff[i - offset] = currentAng[i] - target[i - offset] * angleDataRatio;

we compute the difference as $a-b$. In the following code

for (int s = 0; s <= steps; s++) {
	for (byte i = offset; i < DOF; i++) {
		float dutyAng = (target[i - offset] * angleDataRatio + (steps == 0 ? 0 : (1 + cos(M_PI * s / steps)) / 2 * diff[i - offset]));
		calibratedPWM(i, dutyAng);
	}
}

the angle updates are done in $steps$ steps, and each update computes dutyAng as

$$

b + (1 + cos(\pi*s / steps)) / 2 * (a-b)

= (1 - cos(\pi s / steps))/2 * b + (1 + cos(\pi  s / steps))/2 * a

$$

which is a weighted average of $a$ and $b$. However, the transition from $a$ to $b$ is not equally spaced. I assume this is a trick to make the motion more life-like.

Please correct me if it's not correct or something is missing.

And thank you again, Timothy.

(PS: It would be great if the forum can add support for LaTeX)

Best,

Jiarui