RVO2

RVO2 is a real-time, decentralized collision avoidance framework for multiple agents moving in a shared two-dimensional workspace. It builds on the concept of reciprocal velocity obstacles to compute collision-free motions for teams of agents that act autonomously or under external control. RVO2 is widely used in robotics, crowd simulation, and computer animation where scalable, responsive navigation is required.

In RVO2, each agent is modeled as a circle with position p_i, velocity v_i, and radius r_i. Each agent also has a preferred velocity v_pref_i and a maximum speed. For every pair of agents (i, j), a velocity obstacle VO_ij is defined as the set of velocities for i that would cause a collision with j within a chosen time horizon tau if j maintains its current velocity v_j. The reciprocal aspect means that both agents share responsibility for avoidance; the new velocity for i is chosen to avoid all VO_ij while remaining as close as possible to v_pref_i.

Computation proceeds at each time step by solving an optimization problem: minimize ||v_i - v_pref_i||^2 subject to |v_i| <= v_max_i and v_i not lying in VO_ij for all j ≠ i. The resulting velocity v_i is then used to update the agent’s position. The approach typically runs in real time for moderate agent counts, with computational complexity that grows with the number of agents.

Implementation and extensions: The RVO2 library provides an open-source, widely used C++ implementation with language bindings for other environments. It supports two-dimensional simulations with dynamic and static obstacles and is employed in robotics, video games, and crowd modeling. RVO2 has inspired related methods such as ORCA, which offers alternative constraint formulations. Limitations include assumptions of circular agents, 2D motion, and purely local, velocity-based avoidance without global path planning, which can yield suboptimal behavior in dense or complex environments.