Nonlinear Control of Quadcopters via Approximate Dynamic Programming
For quadcopter control, this work demonstrates the feasibility of ADP in continuous state/input spaces, though the approach is incremental as it combines existing techniques.
This paper applies Approximate Dynamic Programming (ADP) to the continuous, nonlinear dynamics of a quadcopter, using polynomial approximations and sum-of-squares programming to compute value functions. The method is validated in simulations and experiments, showing competitive performance against a linear time-varying MPC, and a combined approach leverages short-horizon MPC with ADP terminal cost.
While Approximate Dynamic Programming has successfully been used in many applications involving discrete states and inputs such as playing the games of Tetris or chess, it has not been used in many continuous state and input space applications. In this paper, we combine Approximate Dynamic Programming techniques and apply them to the continuous, non-linear and high dimensional dynamics of a quadcopter vehicle. We use a polynomial approximation of the dynamics and sum-of-squares programming techniques to compute a family of polynomial value function approximations for different tuning parameters. The resulting approximations to the optimal value function are combined in a point-wise maximum approach, which is used to compute the online policy. The success of the method is demonstrated in both simulations and experiments on a quadcopter. The control performance is compared to a linear time-varying Model Predictive Controller. The two methods are then combined to keep the computational benefits of a short horizon MPC and the long term performance benefits of the Approximate Dynamic Programming value function as the terminal cost.