Explicit flatness-based MPC design for indoor nano-quadcopter position tracking

Abstract

Due to the nonlinearities and operational constraints of quadcopters, Model Predictive Control (MPC) encounters the requirement of high computational power. This problem may prove impractical, especially for hardware-limited setups. By removing the need for online solvers, Explicit MPC (ExMPC) stands out as a strong candidate. Yet, the formulation was usually hindered by the system's nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for quadcopter position stabilisation. With the former issue, the system is exactly linearised into a concatenation of three double integrators. For the latter, with a suitable characterisation of the new convoluted constraints, the stabilising ExMPC can be computed for each double integrator separately. The controller is validated via simulations and experiments on a nanodrone platform. The proposed scheme provides similar performance and theoretical guarantees to the up-to-date nonlinear MPC solutions but with notably less computational effort, allowing scalability in a centralised manner.