Mobile Robot Navigation for a surgical robot

A differential-drive robot steers by spinning its two wheels at different speeds — like a tank. Equal speeds go straight, a difference curves the path, and opposite speeds spin in place. Its forward speed is the average of the wheels and its turn rate is their difference over the wheelbase.

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.

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.