Efficient Convolution-Based Representation of Smooth Reference Trajectories for Urban Air Mobility

Accurate trajectory-following control using dynamic inversion controllers requires suitable parameterizations of reference trajectories, such as energy-minimal flight paths generated with optimal control methods. These trajectory representations must enable efficient onboard storage and real-time evaluation while ensuring sufficient accuracy and smoothness to provide the required feedforward commands. We explore trajectory parameterizations based on the convolution of a piecewise low-order polynomial with an infinitely smooth kernel. These combine efficient storage with unlimited differentiability and allow for simple and efficient evaluation using numerical quadrature. To construct such parameterizations from given trajectories, we formulate quadratic programs that account for additional, mission-specific constraints. A numerical example demonstrates the parameterization of an approach and vertical landing trajectory based on optimal control results; we show that the convolution-based approach yields competitive results compared to a piecewise polynomial parameterization, with significant storage savings.