Velocity Obstacle Formulations, Reciprocal Collision Avoidance (ORCA) & Jitter Bounds

Non-blocking multi-agent collision avoidance running in deterministic execution time regardless of local robot density.

Reciprocal Velocity Obstacle Half-Plane Projections

Each robot assumes neighboring agents will share equal responsibility for collision avoidance. By solving a 2D linear program over half-plane constraints, ORCA guarantees collision-free velocity selection in under 200 microseconds.

Kinematic Acceleration Bound Clamping

Unlike theoretical ORCA formulations that assume instant velocity changes, RealtimeSwarm clips velocity targets against physical wheel torque and motor current limits, preventing motor stall or wheel slip.

Deterministic linear programming solver executing in <200 microseconds
Guaranteed collision-free trajectories for dozens of converging robots
Kinematic acceleration and torque constraints clamped into feasible space
Elimination of oscillatory reciprocal deadlock maneuvers

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