Learning model predictive control – with application to quadcopter trajectory tracking

Abstract: In this work, we develop a learning model predictive controller (LMPC) for energy-optimal tracking of periodic trajectories for a quadcopter. The main advantage of this controller is that it is “reference-free”. Moreover, the controller is able to improve its performance over iterations by incorporating learning from the previous iterations. The proposed learning model predictive controller aims to learn the “best” energy-optimal trajectory over time by learning a terminal constraint set and a terminal cost from the history data of previous iterations. We have shown how to recursively construct terminal constraint set and terminal cost as a convex hull and a convex piece-wise linear approximation of state and input trajectories of previous iterations respectively. These steps allow us to formulate the on-line planning problem for the controller as a convex optimization program, thereby avoiding the complex combinatorial optimization problems that alternative formulations in the literature need to solve. The data-driven terminal constraint set and terminal cost not only ensure recursive feasibility, and stability of LMPC but also guarantee non-decreasing performance of LMPC at each iteration. Our LMPC formulation includes a linear time-varying system dynamics which is also learnt from stored state and input trajectories of previous iterations.

To show the performance of LMPC, a quadcopter trajectory learning problem in the vertical plane is simulated in MATLAB/SIMULINK. This particular trajectory learning problem involves non-convex state constraints, which makes the resulting optimal control problem difficult to solve. A tangent cut method is implemented to approximate the non-convex constraints by convex ones, which allows the optimal control problem to be solved by efficient convex optimization solvers. Simulation results illustrate the effectiveness of the proposed control strategy.