Whiteboard Writing Robot Arm

I validated the kinematics by scoring the pen tip's position against the intended path at every waypoint, holding pen-down strokes to a tighter tolerance than pen-up transitions so I could use the error to diagnose the solver and tune trajectory density, rather than as a simple pass or fail gate. Most waypoints landed within about 1 cm of target, with two real outliers spiking to roughly 5 cm and 9 cm that I didn't smooth over. An early practice run writing "CAB" came out shaky and barely legible; later runs came out visibly cleaner, if still a bit wobbly, consistent with those error spikes. For the graded final test, our professor picked the word live, "DAC," and the arm wrote it legibly, still a bit shaky but clean enough that the professor asked to keep the arm afterward to show it off at an event.

The as-built arm was jittery at joints 2 and 3, and fixing it took a mechanical change and a control change together, not either alone. We added a spring at the elbow to offload gravitational torque from the motor. On the control side, I retuned both joints: joint 2 (an MX-64A with built-in PID) went from an oscillatory Kp = 32 to Kp = 205, Ki = 65, Kd = 0 for a fast response with minimal overshoot; joint 3 (an AX-12A, which uses compliance margin/slope instead of true PID) went to a compliance margin of 2 and compliance slopes of 56 clockwise / 26 counterclockwise to eliminate the same ringing.

Letters near the board's center, in line with the arm's home position, consistently came out cleaner than letters to the left or right. The cause traced to joint geometry: writing off-center forced joint 1 to rotate away from home, so the downstream joints had to reach further, which drove the same joint 2/3 jitter — worst at the board's edges, least in the middle letter.

A separate issue came from the pen mechanism: my original trajectories used upward strokes, but the spring-loaded pen compressed against the board as it wrote, and mechanical slop in the links let that compression build into upward tension that board friction held in place mid-stroke. When the arm lifted the pen at the end of an upward stroke, that tension released all at once and the pen shot upward, leaving curly artifacts in the letters. I fixed it by rewriting the trajectory planner to prefer downward strokes, which avoided building up the tension and cleaned up legibility.

Forward and inverse kinematics (product-of-exponentials, Modern Robotics library), velocity kinematics for multi-joint synchronization, trajectory planning and time-parameterization, MATLAB, Dynamixel servo control (MX-64A, AX-12A) and PID/compliance tuning, Arduino, mechanical and control co-design for vibration mitigation, quantitative trajectory-error validation, 3D-printed mechanical design, configuration-dependent error root-cause diagnosis, end-effector-aware trajectory redesign for mechanical-slop artifacts.