Robotics by the Numbers: Wheel Encoders, Odometry, Two-Link Arm Kinematics, Motor Gearing & PID Control Steps

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Turn Pip's wheel size and encoder resolution into a distance per tick, then convert six logged runs from ticks into metres and average speed.
• Turn eight steps of left and right wheel distances into heading changes and track where Pip thinks it is with a COS/SIN step table that starts from a known pose.
• Turn a 0.4 % wheel-size error into a heading drift per leg, find the real heading of each leg of a planned 2 m square and see how far from the start Pip really ends.
• Calculate where the elbow and the tool of Pip's two-link arm end up for six poses, from the shoulder and elbow angles with COS, SIN and RADIANS.
• Check whether a target is inside the arm's reach, measure how far each of 16 angle candidates misses it and pick the best shoulder angle with SMALL and INDEX/MATCH.
• Compare four fictional motor-and-gearbox options for Pip: wheel speed and top speed from the gear ratio, the torque at the wheel after gearbox losses and the torque each wheel needs to climb a 15° ramp.
• Replay 1.1 seconds of Pip's speed log and recompute the PID controller row by row: error, running integral, derivative and the output that the three gains make of them.
• Read the peak speed of each gain set from the logged step responses, turn it into overshoot, work out the battery runtime from the average current and chart the three responses against each other.