Rigid members (trusses, beams, whatever) is probably possible. You might need to disconnect them when the weather gets rough though. Or you´ll need to make them somewhat springy or shock absorbent. Depending on the distance they might get very large and heavy as well.
Rods are compression elements, they don’t do tension very well, or at all. By arranging tension elements (cables) and compression elements you can get very robust structures in which all compression stresses end up distributed across the rods, all tension stresses go to the cables, and the shear and bending stresses are avoided entirely, either through conversion into compression/tension or by internal degrees of freedom. That makes tensegrity structures very schock-absorbant and sometimes a little springy, while being extremely lightweight.