Port-Hamiltonian approach to deployment on a line

In this talk we present a port-Hamiltonian approach to thedeployment on a line of a robotic sensor network (see e.g.[3] for related work). Using the port-Hamiltonian modellingframework has some clear benefits. Including physical interpretationof the model, insight in the system’s energy andstructure, scalability, and use of the Hamiltonian for stabilityanalysis. A concise overview of port-Hamiltonian systemstheory can be found in [2].Deployment on a line fits within the broader context of usingrobotic sensors networks for (autonomous) inspection ofdikes. The aim of the autonomous dike inspection is to makea group (swarm) of robotic sensor move along the surface ofthe dike, while monitoring it with e.g. ground penetrationradars (GPR).The ideas in this talk are inspired by [1], who uses a passivitybased-approach for coordination. It is well known thatthere is a strong link between port-Hamiltonian systems andpassivity, which can be used in the stability analysis of thenetwork.In this talk we’ll look at a network of N robots, which aremodelled as fully actuated point masses. The interactionamong the robots is represented by a graph G. The robotscorrespond to the vertices of the graph. The M edges of thegraph correspond to virtual couplings [4], which are virtualsprings and dampers. The dynamics of the interconnectedsystem [4] are given byq˙vc = −BT ∂H∂ pp˙ = B∂H∂qvc −Dr +BDvcBT∂H∂ p,(1)where qvc, p, B, H, Dr, and Dvc denote respectively therelative distances, momenta, incidence matrix of graphG, Hamiltonian, robots dissipation matrix, and the virtualdampers dissipation matrix.