Energy-independent translocation involves passive diffusion or facilitated diffusion, where molecules move down their concentration gradients. On the other hand, energy-dependent transport involves active transport, which requires energy to move molecules against their concentration gradients or for processes like receptor-mediated endocytosis that involve cellular machinery and energy.
The assay which you may be interested would be to treat cells with metabolic inhibitors (such as sodium azide) that block cellular energy production, or you could lower the temperature of the cell culture. If the molecule's translocation is significantly reduced or stopped under these conditions, it suggests an energy-dependent mechanism. If uptake continues despite energy deprivation, the process is likely to be energy-independent. Try this out.