The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups.

In this work, we approach the control problem of fully-actuated UAVs in a geometric port-Hamiltonian framework. The UAV is modeled as a floating rigid body on the special Euclidean group SE(3). A unified near-hovering motion and impedance controller is derived by the energy-balancing passivity-based control technique. A detailed analysis of the closed-loop system's behavior is presented for both the free-flight stability and contact stability of the UAV. The robustness of the control system to uncertainties is validated by several experiments, in which the UAV is controlled near its actuator limits. The experiments show the ability of the UAV to hover at its maximum allowed roll angle and apply its maximum allowed normal force to a surface, without the input saturation destabilizing the system.

This work addresses the interaction control problem of a fully actuated aerial vehicle considered as a flying end-effector. We tackle the problem using geometrically consistent variable-stiffness impedance control for safe wrench regulation using the concept of energy tanks, where both the modeling and the control are carried out in the port Hamiltonian framework. We exploit previous well-known results in the literature of ground manipulators and extend them to be applied for novel and challenging aerial physical interaction with a focus on quasi-static applications. The energy-awareness of the presented control method guarantees the stability of the aerial robot in both free-flight and in-contact scenarios together with a level of safety in the case of contact-loss with the unknown environment. Furthermore, by utilizing bond graphs we demonstrate how the closed-loop passivity can be graphically conducted. The validity of our proposed approach is shown via several experiments. We also provide several insights on how the proposed framework could be extended to a generic dynamic aerial physical interaction.