Potential field method: 20 lines of code, but stuck in a U-shaped local minimum

The potential field method dates back to the 1980s and is still in active use for factory transport robots and drone autopilot. The reason is not sophistication but extreme lightness: unlike deep learning, it needs no GPU, and a microcontroller costing a few thousand yen can recompute a path in real time.

The body walks through a numeric example to show why the method works and where it breaks. At the start, the obstacle at (5, 0) is outside the repulsion radius d_0=3.0, so the robot moves straight right. As it approaches within 0.1 of the obstacle, the repulsive gradient spikes to about 483.35, overpowering the attractive gradient of 5.1 and pushing the robot back — collision avoided. The trouble comes when the obstacle geometry creates a pocket: the forces cancel, and the robot stops at the U's entrance.

In practice, cap the maximum number of steps (for example, 1000), add random disturbance when movement becomes tiny, and treat obstacles as inflated by the robot's radius plus a safety margin — a 60cm-wide transport robot would enlarge obstacle radii by 30cm. The realistic answer, it concludes, is to combine the potential field method with something like RRT: smoothness from one, reachability from the other.