Brian covered the more electrical side of things; because of the question about our control loops, I’ll explain a few of the general ideas here, but I have to go off to a concert soon, so I don’t have much time to get into the details.
Basically, for all of our control loops, we use a state-space representation of our various systems (since motors are so very conveniently linear and time-invariant) using feedback from our encoders. This relies on an equation:
dx/dt = Ax + Bu
Where x is the current state of the motor/system (angle and angular velocity), u is the voltage(s) applied to the motor (we have multiple motors in the drivetrain and claw). A and B are constants which have to do with the physical characteristics of the system. This entire system can be discretized into:
x[k + 1] = A_discrete * x[k] + B_discrete * u[k]
Using this state-space representation and using the a controller where u = K(R - x) where R is the goal state and K is a constant matrix which we can adjust to tune the poles of the system. There is also an observer for taking in sensor feedback.
In the claw, by carefully choosing a u such that the two inputs control separation of the two claw halves and position of the bottom half separately (so u isn’t actually the two voltages applied to the motors... it is just a simple transform away
), we can then place certain constraints on K such that certain values in the matrix must be zero. This allows us to control separation of the claws and position of the bottom half of the claw independently.
In order to deal with the caps on voltage (we only have plus or minus 12 volts available to us in a match; realistically, less), we create constraints in a 2-dimensional space where the two dimensions are the top and bottom claw voltages. We then transform these (linear) constraints into a space where we have separation and position of the claw as the two dimensions. If our controller is asking for voltages outside of the realistic range, we then find the best point in this space to prioritize reducing separation error such that, if the claws open or close a bit, they quickly go back to normal and don’t drop the ball. This is also used in our drivetrain to ensure constant-radius turns. More details will be forthcoming. That was the 15 minutes of writing explanation.
Edit: I wasn't very clear, but everything in here is a matrix.