[NalNezumi]

Cool project! Since the arm seems to be a 2 DoF arm in a 2D application, you don't really need numerical optimization but can get the analytical solution to the inverse kinematics problem. Otherwise using previous joint states as initial guess for the optimization is good so that you don't get weird "swings" in the arm (rarely happen in 2D)

[nomel]

To put it simply: there's only one solution for each 2d position, if you force the mid joint to always be on one side (and that preferred side can be allowed to switch, to minimize accelerations of the lower arm).

[robertleoj]

That's true - using numerical optimization was just the simplest/fastest way to get it working :P