A Quaternion-based Inverse Dynamics Model for Real-time UAV Trajectory Generation

This paper presents a computationally-fast inverse dynamics model based on unit quaternion orientation representation for use in the generation of unmanned aircraft trajectories when the flight envelope may include all flight path orientations, a necessary attribute for aerobatics or unmanned air-to-air combat vehicles. The model removes the inherent singularities in Euler-angle attitude representation, is as computationally efficient as an Euler-angle point mass model, permits smooth attitude parameterization and interpolation, and has a linear orientation state equation. Implementation details are described which show that the assumptions underlying both quaternion and Euler-angle models may be maintained, and path constraints evaluated, efficiently. Examples of trajectory optimization by discretizing the model in a direct method, using derivative-free optimization and 4-dimensional optimization vectors, show feasible control vectors for O(10 2 ) trajectory evaluations, making the method and model attractive for real-time trajectory generation.