Same rule. Different walls.
Compare open ground with a corridor. Look at the paths and the contribution of the walls.
02 / Motion · Beginner
Artificial
Potential Fields.
Can local decisions find a way through?
Three agents share a destination.
Each combines a command toward the goal with commands away from nearby surfaces.
01 / Add4.8 m/s
Goal contribution. Peer pushes cancel.
02 / Limit1 m/s
The speed cap limits the command.
03 / Move2 cm
A2 moves toward the goal in 0.02 s.
Walls are outside repulsion range. Arrows are schematic velocity contributions, not physical forces.
A browser simulation of planar motion. The 3D drones show the same disk model; there is no flight physics or live execution.
Before you begin
If the commands cancel,
what happens next?
A route may exist even when the local rule cannot find it. Predict what the agents will do inside a U-shaped trap.
Explore the four questionsMethod & assumptionsReactive local rule · known map · exact nearby peer sensing
Synchronous 0.02 s steps · no message network
- Algorithm / variant
- Artificial Potential Fields
Quadratic goal attraction plus finite-range inverse-clearance repulsion, adapted to velocity commands.
- Decision architecture
- Decentralized · reactive
Each agent uses its own position, a preloaded goal/map, and nearby peer positions. No shared route planner.
- Update timing
- Synchronous · discrete time
All commands read the previous state. Position advances by velocity × 0.02 s.
- Sensing / communication
- Ideal local peer sensing
Peers within 0.7 m surface clearance are sensed exactly. The static obstacle map is known. No message network is modeled.
Execution: one browser simulation of planar kinematics. The 3D view places detailed quadrotors at a fixed 0.65 m display height above the same x/y footprint. Extruded capsule walls match the map. There is no vertical escape, acceleration limit or flight physics.
01 / Try it
PausedA direction at every step.
Goal attraction Wall repulsion Agent separation Capped velocity
Select an agent to inspect its decision. Arrows are capped for legibility; the table gives exact velocity components. Map distances are in metres.
Simulated time0.00 sStep 0 / 2,000
Inside goal region0 / 3All three required for success
Farthest from goal8.02 mCentre distance; goal radius 0.8 m
Minimum clearance0.36 mSwept surfaces over the entire run
The experiment is paused. Predict, then advance one model step.
Watch the distance
Maximum centre distance · mProgress toward the goal
Dashed line: the 0.8 m goal radius. Near-zero speed alone does not establish arrival.
Look inside
Agent A1’s decision
The controller receives its own position, the goal, the known map and nearby peer positions. Arrival, clearance and stall are evaluator measurements.
| Agent | x | y | Goal distance | Path travelled | Inside goal? |
|---|
02 / Follow a question
Arrive. Stall. Collide.
What makes the difference?
Change one condition. Inspect how the outcome changes.
A way out. No plan to find it.
The U opens to the left; the goal is on the right. Can local contributions guide the agents back out and around?
What keeps agents apart?
Turn off agent separation on open ground. Do their disks touch before reaching the goal?
The wall is still there.
Turn off wall repulsion in the U. Compare the outcome with the trapped run: does moving forward solve the problem?
Guided cases load the reference gains, then apply only the stated change. Each starts paused. Diagrams are schematics, not recorded trajectories.
Compare measured reference runs Arrival · stall · collision
Computed with this model and a maximum budget of 2,000 steps. Each run stops at its first evaluated outcome. Results do not change your current run.
| Experiment | Outcome | Step | Time | Inside goal | Min. clearance |
|---|
03 / Go deeper
Add directions.
Take a small step.
The goal points one way; nearby surfaces point away. Each agent adds these velocity contributions, caps the speed, then moves for 0.02 s.
One agent, one step
At the start, A2 is at (−4, 0). The goal contribution is (4.8, 0) m/s. Peer contributions cancel and the walls are out of range.
1 m/s × 0.02 s = 2 cm
After the speed cap, A2 reaches (−3.98, 0) in one step.
Read the rule, assumptions & source
ugoal = kgoal (g − p)
urep = η (1/d − 1/d₀) n / d² if 0 < d < d₀
v = limit(ugoal + ∑ uwall + ∑ upeer, 1 m/s)
p[k + 1] = p[k] + 0.02 v[k]
urep = η (1/d − 1/d₀) n / d² if 0 < d < d₀
v = limit(ugoal + ∑ uwall + ∑ upeer, 1 m/s)
p[k + 1] = p[k] + 0.02 v[k]
- p, g · metres
- The agent position and goal centre.
- d, d₀ · metres
- Surface clearance and influence distance: 1 m for walls, 0.7 m for peers. Repulsion is zero beyond d₀.
- n
- A unit vector pointing away from the wall or neighboring disk.
- kgoal, η
- Attraction gain in s⁻¹; repulsion gains in m⁴/s for this velocity formulation.
What counts as success?
All three agent centres must be within 0.8 m of the goal centre, with no swept contact. Agents are disks of radius 0.12 m; wall segments have radius 0.10 m. Contact stops the run as a collision.
What counts as stalled?
For 100 consecutive updates, all speeds stay below 0.005 m/s and the maximum goal distance changes by less than 0.01 m, with arrival still incomplete. This measured criterion is not a proof that every small perturbation must stay trapped.
Primary method source: Oussama Khatib (1986), Real-Time Obstacle Avoidance for Manipulators and Mobile Robots ↗. This page implements the stated velocity-controller adaptation, with no global path search or guarantee of collision avoidance or arrival.
These are velocity commands, not physical forces. Local avoidance gives no general guarantee of arrival or collision avoidance. A stopped agent has not necessarily reached its goal.
Keep the thread
Moving locally.
Planning ahead.
Explore how A* searches a known map before the agent moves, in a separate grid-based experiment.