Time-Constrained Position-Based Dynamics for Crowd Simulation

Precise temporal coordination in crowd simulation—ensuring agents arrive at targets in a specific order or at set intervals—remains a challenge for real-time applications. While existing force-based methods can handle timing, they often suffer from instability at large time steps. his paper addresses the problem of enforcing strict arrival-time constraints within a stable, multi-agent simulation. We propose a novel Position-Based Dynamics (PBD) framework that incorporates arrival-order and fixed-time-gap constraints via an adaptive interpolation scheme. By adjusting individual agent speeds based on distance-to-target and predicted arrival times, our method coordinates collective behavior without compromising the underlying geometric stability of PBD. Experimental results demonstrate that the proposed algorithm maintains real-time performance for up to 1,000 agents while effectively minimizing constraint violations even in high-density, unpredictable environments.