The potential field method steers a robot by pretending the goal pulls it like gravity and obstacles push it away like magnets — a fast, intuitive way to react to obstacles in real time, with one famous failure mode.
Imagine the goal is downhill and every obstacle is a hill. The robot simply rolls downhill toward the goal while being pushed away from obstacles. That combined "slope" is the potential field, and following it gives smooth, reactive motion.
Sometimes a robot doesn't need a full plan — it needs to react to whatever's in front of it, right now. The potential field method gives it a beautifully simple instinct for that.
The idea
Treat navigation like a landscape of hills and valleys:
The goal creates an attractive field — the robot is pulled toward it, like a ball rolling downhill.
Each obstacle creates a repulsive field — a hill that pushes the robot away, stronger the closer it gets.
Add the two together and the robot simply follows the negative gradient (the downhill direction) of the combined field. The result is smooth, real-time obstacle avoidance with almost no computation.
Two forces combine into one motion
At every instant the robot just adds the attractive and repulsive vectors and steps along the result — no global map or search needed.
The famous flaw: local minima
Because it only looks at the local slope, the method can trap the robot in a local minimum — a spot where the pull toward the goal and the push from obstacles cancel out, but you're not at the goal. A robot heading into a U-shaped obstacle stalls at the mouth, unable to see that backing out would help. This is the defining weakness, and it's why pure potential fields aren't used for global planning.
How it's used in practice
Modern systems keep the reactive elegance but fix the trap: they use potential fields as a local obstacle-avoidance layer beneath a global planner like A* that guarantees the robot eventually escapes, or they use improved variants (navigation functions, harmonic fields) that are provably minima-free. The idea also lives on in the dynamic window approach and in swarm and formation control.
Why it matters
The potential field method is the cleanest introduction to reactive navigation — and its local-minimum problem is one of the most instructive failure modes in all of robotics, teaching exactly why local and global planning must work together.
