Another project that I had in mind for a while was to experiment with robot arm path planning and inverse kinematics. If you don’t know what that is, think about how robot arms could be programmed. The simplest form would be capture and replay, in which you have a controller which which you record how you manually move the joints. The robot can then replay the movements. We humans have developed a good intuition for moving our body parts and grasping, but when it comes to formally describing what you do with the joints of your arm, it quickly becomes difficult. My younger son is in the phase of learning to grasp right now, and it’s amazing to see how the eye arm coordination evolves. The second approach would be to program it like a CNC milling machine with something like G-codes. This is a bit more general and more exact, but it’s also more difficult to do collision avoidance. And it’s complicated to calculate as most joints tend to be revolutionate. Both these approaches are only suited for repetitive tasks often found in industry automation, but completely unsuited for robots in dynamic environments. Now with inverse kinematics, you can tell the robot where the arm should move to in cartesian coordinates, and it does all the arm geometry calculations and positions the gripper to the correct position in the desired orientation. Maybe there are obstacles in between the current and the target position. To navigate around these, you also need path planning. That is usually done in configuration space. Real robots have also to care about dynamics such as inertia, but I won’t go that far.