The navigation of multiple mobile robots or virtual agents through environments containing static and dynamic obstacles to specified goal locations is an important problem in mobile robotics, many video games, and simulated environments. Moreover, technological advances in mobile robot hardware and video games consoles have allowed increasing numbers of mobile robots or virtual agents to navigate shared environments simultaneously. However, coordinating the navigation of large groups of mobile robots or virtual agents remains a difficult task. Kinematic and dynamic constraints and the effects of sensor and actuator uncertainty exaggerate the challenge of navigating multiple physical mobile robots, and video games players demand plausible motion and an ever increasing visual fidelity of virtual agents without sacrificing frame rate.;We present new methods for navigating multiple mobile robots or virtual agents through shared environments, each using formulations based on velocity obstacles. These include algorithms that allow navigation through environments in two-dimensional or three-dimensional workspaces containing both static and dynamic obstacles without collisions or oscillations. Each mobile robot or virtual agent senses its surroundings and acts independently, without central coordination or inter-communication with its neighbors, implicitly assuming the neighbors use the same navigation strategy based on the notion of reciprocity. We use the position, velocity, and physical extent of neighboring mobile robots or virtual agents to compute their future trajectories to avoid collisions locally and show that, in principle, it is possible to theoretically guarantee that the motion of each mobile robot or virtual agent is smooth. Moreover, we demonstrate direct, collision-free, and oscillation-free navigation in experiments using physical iRobot Create mobile robots, simulations of multiple differential-drive robots or simple-airplanes, and video games levels containing hundreds of virtual agents.
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