Nonlinear H∞ Control Algorithms for Autonomous
Underwater Vehicle in Diving and Steering Planes

Abstract

During the last decade, significant research has been directed on designing autonomous underwater vehicles (AUVs) for several applications including surveillance of specific
regions of a seafloor and underwater mine detection in defense applications, and scan-ning of pipelines and detection of leakages in oil/gas industries, etc. However, a number of issues arise in control of these AUVs such as control with autonomy, and commu-nication failure, etc., when underwater vehicles are deployed in underwater missions. Hence, there is a growing interest in developing control algorithms for underwater ve-hicles to address these issues. These mission control algorithms include appropriate
controllers for executing path following, trajectory tracking and point stabilization motion plans. These algorithms can be executed by designing suitable controllers for the diving and steering planes of AUVs in face of parametric uncertainties that occur in AUV dynamics (e.g. hydrodynamic coefficients and ocean currents). This thesis
focuses on designing a number of H∞ robust control algorithms for an AUV in both diving and steering planes. These robust control algorithms include designing of a
number of nonlinear H∞ control algorithms using techniques such as Taylor’s series approach, nonlinear matrix inequality (NLMI) approach and sum of square (SOS)
approach. In order to verify the efficacies of the proposed control algorithms, both simulation and experimentation were pursued. A prototype torpedo-shaped AUV is designed and developed in the laboratory. This prototype AUV is equipped with a computational module integrated with various
sensor, actuation, communication and power modules. Further, the computational unit of the developed AUV is installed with Robot Operating System (ROS) which is a software framework to integrate all the modules. The proposed nonlinear H∞ robust control algorithms are implemented using the computational unit of the prototype AUV to achieve desired diving and steering motion control objectives. The thesis first describes the development of nonlinear H∞ state feedback control algorithm using Taylor’s series approach for the diving and steering planes. In this ap-proach, the control problem is formulated as a Hamilton-Jacobi-Isaac (HJI) inequality which is obtained using dissipative theory which suggests that the input energy of a system is always greater or equal to the output energy. In this approach, the nonlinear AUV system together with the HJI inequality are transformed into Taylor’s series form with a specific order to synthesize a robust control algorithm. Then, this control
algorithm is synthesized using MATLAB/Simulink. This controller exhibits excellent tracking of the desired depths and desired yaw orientations by attenuating the distur-
bances with an improved L2 gain performance. Then, the robustness analysis of this controller is pursued to evaluate the controller performance against model uncertain-
ties. The experimental verification of the developed control algorithms is carried out in the swimming pool of National Institute of Technology Rourkela. It is observed during the controller synthesis that if the order of Taylor’s series increases, then the attenuation of disturbances also improves. However, the order of the controller struc-
ture also increases. Hence, to reduce the order of the control structure, less number of states are considered. Although this approach provides good performance during the
tracking desired depth and yaw profiles, this control algorithm is developed by considering a constant dissipative rate which yields a local solution that may not converge
to an analytical solution. In order to resolve the above issue, another nonlinear H∞ control algorithm is designed to obtain an optimal local solution that will converge to
a local analytical solution using nonlinear matrix inequality (NLMI) approach. The NLMI approach for designing the nonlinear H∞ control algorithm is used to achieve both diving and steering motion of the AUV. In this approach, the HJI inequality is transformed into state dependent LMIs which are solved to obtain the control laws for diving and steering planes of AUV. The controller is intended to track
the desired depth and yaw profiles by achieving the L2 gain performance. Similarly, the robustness of the NLMI based control algorithm is verified in presence of model
uncertainties. Also, the effectiveness of the control algorithm is verified experimentally. However, if the number of states increases, then this algorithm yields conservative
results. As discussed earlier in Taylor’s series approach, this NLMI based approach also provides a local solution for a constant dissipative rate. However, if the dissipative
rate changes, then the control law yields conservative results. Thus, it is necessary to design a control algorithm which provides a global solution for an optimized dissipative rate. Hence, a sum of square (SOS) approach is used to design a nonlinear H∞ control algorithm in order to obtain a global solution. Subsequently, an SOS based approach is used to design a nonlinear H∞ control algorithm for both steering and diving planes. Here, the HJI inequality is also con- verted into state-dependent LMIs in order to find out the solution for the nonlinear control problem. Firstly, the dynamics of diving and steering planes are transformed into an equivalent polynomial form, in which SOS decomposition technique can be easily employed. Using the SOS optimization technique, the control law is designed
for achieving the diving and steering motion of AUV by ensuring the L2 gain performance. This approach exhibits an extended stability region by transforming the quadratic Lyapunov function into a higher order Lyapunov function that results in improving the controller performance. All the developed nonlinear robust H∞ control algorithms are implemented firstly in MATLAB/Simulink and subsequently on the prototype AUV to verify their per- formances. Subsequently, the robustness analysis of all the control algorithms are performed in both diving and steering planes. From the results obtained and the as- sessment of the performances of all the developed nonlinear robust controllers, it is envisaged that the SOS based approach is desirable for real-time implementation in order to smoothly drive the AUV to achieve efficient tracking performance.