On the application of the Schoenberg quasi-interpolant for complexity reduction in trajectory generation

The paper extends previous work on trajectory generation for UAV (Unmanned Aerial Vehicles) using B-spline curves to parameterize an associated flat output. Typical constraints and costs (such as those involving input bounds and trajectory length) lead to nonlinear formulations in terms of the control points weighting the B-spline curve. This complexity adversely affects the computation time and conservatism of the result. To mitigate these effects we use the Schoenberg operator to provide a quasi-interpolant of the original nonlinear functions. These improvements come at the price of an approximation error which requires a tightening of the original constraints (either from a theoretical bound or via an iterative procedure). The obtained results are exemplified over a fixed wing UAV model and they can be applied for any optimization-based trajectory planning problem.