# Nonlinear Control of Quadcopters via Approximate Dynamic Programming

## TL;DR

This paper introduces a novel application of Approximate Dynamic Programming to control a quadcopter's nonlinear, high-dimensional dynamics, demonstrating improved performance over traditional MPC in simulations and experiments.

## Contribution

It develops a polynomial approximation and sum-of-squares approach for continuous nonlinear control, integrating ADP with MPC for enhanced quadcopter performance.

## Key findings

- ADP-based control outperforms linear MPC in simulations
- The combined ADP-MPC method improves long-term control performance
- Experimental validation confirms the effectiveness of the proposed approach

## Abstract

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.