Energy-Efficient Trajectory Planning with B-Splines and the Schoenberg Quasi-Interpolant

Few studies address the challenge of minimizing energy consumption during trajectory generation, particularly in the context of multicopter dynamics, characterized by strong non-linearity. This paper introduces a novel approach by formulating energy consumption as a function of $\mathbf{B}$-splines control points, enabling comprehensive optimization of total energy expenditure throughout the trajectory. To mitigate the complexity of representation, we leverage the Schoenberg quasi-interpolant, which not only facilitates the solution of the optimization problem but also effectively reduces computational overhead. The approach is validated through two distinct scenarios: a conventional trajectory used in precision agriculture, and a scenario involving more aggressive maneuvers.