# Inverse Kinematics

A project log for Fluffbug

Cheap four-legged insect robot

While I'm working on re-doing the PCB to incorporate all the recent changes, we can talk about the hard part: programming. Obviously, without a program the robot is useless, and if you want the robot to do anything, most of the work is going to be writing the program for it. This is why I'm trying to make this part as hassle-free as possible, switching to a high-level language like Python, and using a variant of it, CircuitPython, that makes it especially easy to modify any code, by exposing it as an USB drive. Another thing I can do so simplify things is to provide libraries that handle the low-level details, and expose a higher-level interface to the user's code.

One of the details I can handle is Inverse Kinematics — that is, translating between the desired positions of the robot's legs, to actual angles the servos need to move to. This is a little bit simpler with the eight servo configuration than it was with the twelve servos of Tote, but it's still a little bit of tricky trigonometry.

Let's look at a side view of the robot:

We can see that each leg forms several triangles: a right-angle triangle formed by the coordinates of the tip of the leg, that lets us calculate a part of the angle of the first servo and the distance of he tip of the leg from the first servo, and the triangle ABC, which we then know all the dimensions of, and which gives us the remaining angles.

So basically we need the Pythagorean Theorem, and then the Law of Cosines. In code, it looks like this:

```        leg_length2 = x * x + y * y
leg_length = math.sqrt(leg_length2)

hip_leg_angle = math.acos(
(FEMUR2 + leg_length2 - TIBIA2) /
(2 * FEMUR * leg_length)
)
knee_angle = PI2 - math.acos(
(FEMUR2 + TIBIA2 - leg_length2) /
(2 * FEMUR * TIBIA)
)
hip_base_angle = math.atan2(y, x)
self.angles(hip_base_angle - hip_leg_angle, knee_angle)```

We can add some error checking for out-of-reach points, some convenience code that lets us move by increments and flips the y coordinate, and we have a working leg.