Adaptive Robot Joint Control: MRAC Under Unknown Payload (2D)

A single robot-arm joint has to swing along a commanded reference trajectory, but the payload clamped in its gripper — and therefore its effective moment of inertia — can change at any moment, and the controller is never told the new value. This 2D companion implements the same model-reference adaptive control (MRAC) law as the 3D version: a Lyapunov-derived adaptation rule retunes the joint's feedback and feedforward gains online, purely from the tracking error between the arm and an ideal reference model, so the arm re-converges on the commanded motion without ever measuring the payload directly. Change the mass mid-run, switch adaptation off to see fixed gains fail on the new load, and watch θₓ and θᵣ drift — alongside a live tracking-error strip chart — to the values that cancel it out again.