Simulating Formations of Non-holonomic Systems with Control Limits along Curvilinear Coordinates

Many games require a method for simulating formations of systems with non-trivial motion constraints, such as aircraft and boats. This paper describes a computationally efficient method for this objective, inspired by solutions in robotics, and describes how to guarantee the satisfaction of the physical constraints. The approach allows a human player to select almost an arbitrary geometric configuration for the formation and to control the aircraft as a single entity. The formation is fixed along curvilinear coordinates, defined by the curvature of the reference trajectory, resulting in naturally looking paths. Moreover, the approach supports dynamic formations and transitions from one desired shape to another. Experiments with a game engine confirm that the proposed method achieves the desired objectives.