Gaussian processes for online system identification and control of a quadrotor

Abstract: The aim of this master thesis was to develop adaptive control for a quadrotor using Gaussian process regression (GP). Online regression with GPs can provide many benefits as it is a flexible non-linear regression model that can provide uncertainty measures of the estimate. However, online GP regression may also gives rise to problems. Because of the high numerical complexity of GPs, sparse approximations are necessary. To this end, the algorithm Sparse Online Gaussian Processes (SOGP) was used. Adaptive control, however, requires the ability to estimate time-varying functions which SOGP does not provide any obvious solution to. To provide time-varying estimations, a Kalman filter interpretation of the update equations in SOGP was used. This addition to the classical SOGP algorithm provided good adaption to non-stationary disturbances at the same time as it was lowering the numerical complexity compared to previously proposed algorithms for nonstationary regression with SOGP. Further, the developed time-varying SOGP regression can provide valuable estimates even under the lack of persistence of excitation, which can be a great advantage in adaptive control. The SOGP algorithm was applied to estimate a model error between a nominal model of the quadrotor and the observed dynamics. The estimated model error could then be used in model-based controllers to improve performance under uncertainties in the dynamics. Two strategies were tested: Model Reference Control and Model Predictive Control. Through these two control strategies, modeled uncertainties in the form of flap- and drag-induced effects, as well as parametric uncertainties, could be estimated online for better flight control. The performance of the proposed controllers was showed through simulations. Even if it was the aim of the thesis no real-time experiments were performed due to lack of time.