Spacecraft formation flying in the port-Hamiltonian framework

Distributed formation control of networked mechanical systems

“…Hence, the position of each agent i is denoted by q i (t) = [x i , y i , z i ] ∈ R 3 in the local coordinates, known as the Hill frame. For further details on the model, we refer the reader to Javanmardi et al (2020). Moreover, we set the leader and follower spacecraft in the Medium Earth Orbit as a reference orbit with an altitude of 20 × 10 3 km.…”

“…Regarding the trajectory-tracking problem, the notion of contractive pH systems is used in Yaghmaei and Yazdanpanah (2017) to develop a tracking version of IDA-PBC, named timed IDA-PBC (tIDA-PBC). Recently, in Javanmardi et al (2020), this method has been used to address the spacecraft formation flying (SFF) problem. This paper proposes a distributed nonlinear control scheme that ensures tracking of the reference trajectories while maintaining the desired formation geometry for a class of large-scale networks of mechanical systems.…”

“…We stress that compared with the centralized controller reported in Javanmardi et al (2020), this work proposes a distributed controller suitable for solving the SFF problem. Moreover, in contrast to Valk and Keviczky (2018), Tsolakis and Keviczky (2021), where only stabilization is investigated, this paper addresses the trajectory-tracking problem while assessing the performance of the large-scale networked system.…”

Passive robust control for uncertain Hamiltonian systems by using operator theory

“…The Hamiltonian system has a prominent symmetrical form, and the Hamiltonian function itself is an energy function, with the most obvious regularity of motion; meanwhile, compared with Newton System and Lagrange System, the Hamiltonian system are most applied into the real applications [1,2], that is, all conserved real physical processes can be expressed in the Hamiltonian form, whether classical [3,4], quantum [5,6] or relativistic, whether the number of degrees of freedom is finite [7] or infinite [8,9], as is well known that the Hamiltonian function is one form of energy function; meanwhile, another method-passivity-based control method is also based on the change of the energy and by redistributing the energy to achieve a satisfactory control performance. The passivity-based control method (PBC) proposed in refs.…”

“…Therefore, the contributions of this paper are summarised: (1) The design scheme combining the operator-based robust right coprime factorisation (RCF) and the PBC is extended into the design and control for the Hamiltonian system which is more popular in the modelling of the physical dynamics. (2) The general robust controller is designed which extends the application of the existing results, by which the asymptotic tracking performance can be improved while the robustness is maintained. (3)By introducing the adjustment variable, a general form of the storage function is constructed to ensure that the passivity of the uncertain non-linear feedback system to overcome the disadvantage of two different storage function.…”