Gaussian Process Model Predictive Control of An Unmanned Quadrotor

The Model Predictive Control (MPC) trajectory tracking problem of an unmanned quadrotor with input and output constraints is addressed. In this article, the dynamic models of the quadrotor are obtained purely from operational data in the form of probabilistic Gaussian Process (GP) models. This is different from conventional models obtained through Newtonian analysis. A hierarchical control scheme is used to handle the trajectory tracking problem with the translational subsystem in the outer loop and the rotational subsystem in the inner loop. Constrained GP based MPC are formulated separately for both subsystems. The resulting MPC problems are typically nonlinear and non-convex. We derived 15 a GP based local dynamical model that allows these optimization problems to be relaxed to convex ones which can be efficiently solved with a simple active-set algorithm. The performance of the proposed approach is compared with an existing unconstrained Nonlinear Model Predictive Control (NMPC). Simulation results show that the two approaches exhibit similar trajectory tracking performance. However, our approach has the advantage of incorporating constraints on the control inputs. In addition, our approach only requires 20% of the computational time for NMPC.Comment: arXiv admin note: text overlap with arXiv:1612.0121

A survey on fractional order control techniques for unmanned aerial and ground vehicles

In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade

Gaussian process based model predictive control : a thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering, School of Engineering and Advanced Technology, Massey University, New Zealand

The performance of using Model Predictive Control (MPC) techniques is highly dependent on a model that is able to accurately represent the dynamical system. The datadriven modelling techniques are usually used as an alternative approach to obtain such a model when first principle techniques are not applicable. However, it is not easy to assess the quality of learnt models when using the traditional data-driven models, such as Artificial Neural Network (ANN) and Fuzzy Model (FM). This issue is addressed in this thesis by using probabilistic Gaussian Process (GP) models. One key issue of using the GP models is accurately learning the hyperparameters. The Conjugate Gradient (CG) algorithms are conventionally used in the problem of maximizing the Log-Likelihood (LL) function to obtain these hyperparameters. In this thesis, we proposed a hybrid Particle Swarm Optimization (PSO) algorithm to cope with the problem of learning hyperparameters. In addition, we also explored using the Mean Squared Error (MSE) of outputs as the fitness function in the optimization problem. This will provide us a quality indication of intermediate solutions. The GP based MPC approaches for unknown systems have been studied in the past decade. However, most of them are not generally formulated. In addition, the optimization solutions in existing GP based MPC algorithms are not clearly given or are computationally demanding. In this thesis, we first study the use of GP based MPC approaches in the unconstrained problems. Compared to the existing works, the proposed approach is generally formulated and the corresponding optimization problem is eff- ciently solved by using the analytical gradients of GP models w.r.t. outputs and control inputs. The GPMPC1 and GPMPC2 algorithms are subsequently proposed to handle the general constrained problems. In addition, through using the proposed basic and extended GP based local dynamical models, the constrained MPC problem is effectively solved in the GPMPC1 and GPMPC2 algorithms. The proposed algorithms are verified in the trajectory tracking problem of the quadrotor. The issue of closed-loop stability in the proposed GPMPC algorithm is addressed by means of the terminal cost and constraint technique in this thesis. The stability guaranteed GPMPC algorithm is subsequently proposed for the constrained problem. By using the extended GP based local dynamical model, the corresponding MPC problem is effectively solved

Data-Driven MPC for Quadrotors

Aerodynamic forces render accurate high-speed trajectory tracking with quadrotors extremely challenging. These complex aerodynamic effects become a significant disturbance at high speeds, introducing large positional tracking errors, and are extremely difficult to model. To fly at high speeds, feedback control must be able to account for these aerodynamic effects in real-time. This necessitates a modelling procedure that is both accurate and efficient to evaluate. Therefore, we present an approach to model aerodynamic effects using Gaussian Processes, which we incorporate into a Model Predictive Controller to achieve efficient and precise real-time feedback control, leading to up to 70% reduction in trajectory tracking error at high speeds. We verify our method by extensive comparison to a state-of-the-art linear drag model in synthetic and real-world experiments at speeds of up to 14m/s and accelerations beyond 4g.Comment: 8 page

MIMO PID Controller Tuning Method for Quadrotor Based on LQR/LQG Theory

In this work, a new pre-tuning multivariable PID (Proportional Integral Derivative) controllers method for quadrotors is put forward. A procedure based on LQR/LQG (Linear Quadratic Regulator/Gaussian) theory is proposed for attitude and altitude control, which suposes a considerable simplification of the design problem due to only one pretuning parameter being used. With the aim to analyze the performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, together with sensors drift/bias properties and noise characteristics of low-cost commercial sensors typically used in this type of applications are considered. In order to estimate the state vector and compensate bias/drift effects in the measures, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robustness analysis of the control system is carried out by employing numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show the proposed controller design method for multivariable PID controller is robust with respect to: (a) parametric uncertainty in the plant model, (b) disturbances acting at the plant input, (c) sensors measurement and estimation errors