Nonlinear and Hybrid Feedback Control of Marine Vehicles and Multirotors

Abstract

This thesis presents new results and solutions for prioritized control of robotic systems and hybrid feedback control of marine and aerial vehicles. We introduce a novel task-priority framework for redundant robotic systems based on a hierarchy of control Lyapunov function (CLF) and control barrier function (CBF) based quadratic programs. The proposed method guarantees strict priority among different groups of tasks such as safety-related, operational and optimization tasks. Subsequently, we present a prioritized control scheme for safety-critical control of autonomous surface vehicles in the presence of unknown ocean currents. The stabilization objective is formulated as a maneuvering problem and integral action is introduced in the CLFs to counteract the effect of unknown irrotational ocean currents. Moreover, ocean current estimates are constructed for robust control barrier function design, and analytic conditions under which the estimates guarantee safety are derived. The use of hybrid feedback is motivated by its ability to employ logic variables together with a properly defined switching mechanism to overcome inherent topological obstructions to global asymptotic stability. These topological obstructions are associated with the rotational degrees of freedom of marine and aerial vehicles. We introduce a hybrid proportional-derivative (PD) control law with a hysteretic switching mechanism for left-invariant systems whose configuration space can be identified with a matrix Lie group. This baseline hybrid PD control law has global asymptotic stability properties when the model parameters are known. Although full state measurements are usually assumed throughout the thesis, we develop an output-feedback variant of the baseline PD control law which only requires measurements of the configuration. Moreover, we augment the PD control law with integral action to obtain two slightly different hybrid proportional-integral-derivative (PID) control laws that both achieve global asymptotic tracking in the presence of unknown and constant disturbances. The aforementioned hybrid control laws are designed using the notion of a synergistic function, also known as a synergistic potential function. Synergistic Lyapunov function and feedback (SLFF) pairs generalize the notion of a synergistic function.We propose a generalization of SLFF pairs, which allows the logic variable in traditional synergistic control, denoted the synergy variable, to change during flows. Moreover, we introduce synergy gaps relative to components of product sets, enabling us to define jump conditions in the form of synergy gaps for different components of the synergy variable. We demonstrate how the proposed generalization can be employed for synergistic maneuvering control of a marine surface vehicle with discrete path dynamics. In the subsequent chapter, we introduce hysteretic control Lyapunov functions (HCLFs). A family of HCLFs consists of local control Lyapunov functions defined on open domains, and include finite collections of open and closed sets that cover the state-space, implicitly defining a hysteresis-based switching mechanism. We have highlighted the connection between HCLFs and synergistic Lyapunov functions and feedbacks. Specifically, we have shown that HCLFs generalize the concept of synergistic control Lyapunov functions (SCLFs), and that an SCLF family together with a collection of continuous control laws synthesized from the SCLF family constitute an SLFF pair. Furthermore, given an HCLF family, we derive sufficient conditions for the existence of globally asymptotically stabilizing control laws. Moreover, we provide a constructive design procedure for synthesis of optimization-based feedback laws under mild conditions on the objective functions. Then, we design a sliding-surface type adaptive hybrid control law for marine vehicles for global asymptotic tracking in the presence of parametric modeling errors. This control law is derived from a set of potential functions and a hysteretic switching mechanism. The assumptions on the potential functions and the hysteretic switching mechanism are less restrictive than the conditions for synergistic control. In contrast to e.g. backstepping-based control approaches, the switching mechanism remains independent of the vehicle velocities in this approach, which enables estimation of the inertial parameters. Moreover, we experimentally validate the proposed control scheme for surface and underwater vehicles. Finally, we synthesize a tuning function-based adaptive hybrid control law which achieves global asymptotic position and heading tracking for multirotors in the presence of unknown and constant disturbances in both the translational and rotational dynamics. The use of tuning functions results in a minimal number of parameter estimates, and ensures global convergence of the disturbance estimates to their true values.