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An explicit MPC for quadrotor trajectory tracking

This paper intends to provide an explicit solution of model predictive control (MPC) for trajectory tracking of quadrotors. This kind of MPC can be designed in a conventional way where a nonlinear optimisation problem needs to be solved online. In this paper by using the differential flatness property of the quadrotor, the reference trajectory, system outputs and inputs can be represented using Bezier curves. Thus, the formulated optimisation problem can be parameterised and converted into standard quadratic programming. The resulted quadratic programming problem can be further formulated into multiparametric quadratic programming which is then solved off-line as a piecewise affine function. The involved manipulations including the reduction of the number of optimisation variables and constraints are detailed in this paper. The performance of the proposed control scheme is demonstrated in a simulation study.