Drone Autopilot for a line-follower

A quadcopter holds position with nested control loops: an outer loop turns position error into a desired tilt and thrust, and an inner loop drives the attitude to that tilt. Tune the PID gains for a snappy, stable response — too little derivative and it oscillates, too much and it sluggishly drifts. Click to send a waypoint.

A PID controller drives a system to its setpoint using three terms: proportional reacts to the current error, integral eliminates steady-state offset, and derivative damps overshoot. Tuning the three gains trades off speed, overshoot, and stability — the workhorse of industrial control.

The Kalman filter fuses a motion model with noisy measurements to track a hidden state optimally. Each step it predicts, then corrects using the Kalman gain — trusting the measurement more when the model is uncertain, and vice versa. It smooths the jittery sensor (gray) into a clean estimate (cyan) that hugs the truth. The math behind GPS, radar, and spacecraft navigation.

A Rapidly-exploring Random Tree grows toward random points in free space, quickly filling the map and snaking around obstacles to connect start (blue) to goal (yellow). It is a cornerstone of motion planning for robot arms, self-driving cars, and drones — fast even in high dimensions where grid search fails.