A Chebyshev Pseudospectral Method-based Model Predictive Control of UAVs for Trajectory Tracking and Collision Avoidance

In this paper, we address the Unmanned Aerial Vehicle trajectory (UAV) tracking and obstacle avoidance problem, by proposing a novel Chebyshev pseudospectral method-based Model Predictive Control (MPC) formulation that is real-time implementable. In this formulation, a continuous-time integral form of the quadratic tracking error cost function is considered and its exact solution is obtained by the Clenshaw-Curtis quadrature rule. The state and control histories are approximated by Lagrange interpolating polynomials, with their coefficients as decision variables. These polynomials are proven to yield smooth control histories, unlike piecewise constant control inputs in the standard MPC. The collocation method is used to satisfy the dynamics and avoid computationally expensive numerical integration. This also allows us for a longer prediction horizon with the same number of decision variables without affecting the computational speed. The MPC is designed by considering the translational dynamics for determining acceleration inputs, which are subsequently used by the low-level controller to obtain desired thrust, orientation, and angular speeds. The performance of the proposed MPC is validated by indoor experiments.SUPPLEMENTARY MATERIALVideo: https://youtu.be/eBeCuGa7B3E