We propose a passivity-preserving energy-tank-based framework for the analysis and control design of multi-mode multidimensional switched systems. We present a new design of hybrid energy tank that is modeled as an impulsive switched system and that allows to account for the sudden (and possibly non-passive) jumps in energy of the system due to the change of dimension of the state at the switching instants. Under this framework we establish passivity of the plant-plus-tank system via an energy-based condition for the switching signal. To demonstrate the utility of our framework we apply the methodology to a case-study of growing importance and interest of its own: open multi-robot systems with arbitrary addition and removal of agents in an autonomous energy-aware and passive way.