Robot Crowd Navigation 2D — Reciprocal Collision Avoidance

An event-security robot patrols the perimeter of a crowded plaza, viewed from directly above, while dozens of pedestrians wander between their own goals. Every agent — robot included — resolves collisions with the same reciprocal velocity-obstacle (ORCA) math used by real crowd-navigating robots and multi-agent path planners: nearby pairs compute a minimal avoidance vector, split responsibility for it, and iteratively project their preferred velocity onto the resulting half-plane constraints. Tune the crowd density, the robot's patrol speed, how far it senses neighbors, how much of the avoidance burden it takes on versus leaving to pedestrians, and its avoidance time horizon, then watch the live speed, nearest-neighbor distance, active-constraint and near-miss readouts respond in real time. Drag the plaza to pan and scroll to zoom; toggle velocity vectors and the robot's active constraint lines to see the linear-programming solve happen frame by frame.