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Presents a new motion planning system that can construct collision-free trajectories for groups of robots in dynamic environments, without global knowledge or high-bandwidth communication. The robots plan within a confined environment that consists of stationary and moving obstacles. Each robot plans independently using Kinodynamic Randomized Motion Planner techniques to construct its own trajectory that is free of collisions with moving obstacles and other robots. To resolve conflicts between robot trajectories, a new Dynamic Priority System (DPS) is introduced which gives the right of way to the robot whose local workspace is the most crowded. The kinodynamic randomized motion planner allows easy integration of the robots nonholonomic constraint into the planning so that only kinematically and dynamically consistent plans are constructed. The speed of the trajectory construction allows planning in real-time, enabling the robot to maneuver safely in a dynamic environment. To verify the planner's effectiveness, it was tested using both simulation and experiment.