Geometric-Dynamic Trajectory: A Quaternion Pythagorean Hodograph Curves Approach

You are here: Homepage > Search

Geometric-Dynamic Trajectory: A Quaternion Pythagorean Hodograph Curves Approach

Otto, Gustav / van Schoor, George / Uren, Kenneth R.

Trajectory generation remains one of the primary challenges in achieving true autonomy, especially in relation to universal applicability needed for coordination as well as scalability of both the environment and number of obstacles. Geometric-dynamic approaches offer a universal solution to trajectory generation that is both intuitive and computationally efficient. In this paper, an extension of Bézier spline-based techniques is presented that exploits the quaternion structure of a Pythagorean hodograph curve to include the orientation of the vehicle in a four-dimensional trajectory specification. The trajectory is constructed to achieve $G^{2}$ continuity and paired with a timing law that ensures $C^{2}$ continuity. Various kinodynamic evaluation parameters are derived and presented for use in trajectory optimization, and the technique is demonstrated on a high-fidelity nonlinear model of an F16 jet. The segmented nature of this approach allows for the efficient scaling of the algorithm to large environments with long and complex trajectories, which combined with efficient spatial separation computations allow for environments with multiple obstacles or trajectories. The focus of this paper is on the method used to represent the trajectory rather than the optimization algorithm that finally exploits this structure to generate the optimal trajectory.