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This paper proposes a passivity-based port-Hamiltonian (pH) framework formulti-agent displacement-based and rigid formation control and velocitytracking. The control law consists of two parts, where the internal feedback isto track the velocity and the external feedback is to achieve formationstabilization by steering variables of neighboring agents that prescribe thedesired geometric shape. Regarding the external feedback, a general frameworkis proposed for all kinds of formations by means of the advantage that the pHmodel is energy-based and coordinate-free. To solve the issue that theincidence matrix is not of full column rank over cyclic graphs, the matrixproperty is used to prove the convergence to the target sets for thedisplacement-based formation, while for rigid formations, the algebraicconditions of infinitesimal rigidity are investigated to achieve asymptoticlocal stability. Furthermore, the rigid formation with heterogeneousconstraints is further investigated under this framework and the asymptoticlocal stability is proved under a mild assumption. Simulations are performed toillustrate the effectiveness of the framework.

A port-Hamiltonian framework for displacement-based and rigid formation tracking