Formation shape and orientation control using projected collinear tensegrity structures

The goal of this work is to stabilize the shape and orientation of formations of N identical and fully actuated agents, each governed by double-integrator dynamics. Using stability and rigidity properties inherent to tensegrity structures, we first design a tensegrity-based, globally exponentially stable control law in one dimension. This stabilizes given inter-agent spacing along the line, thereby enabling shape control of one-dimensional formations. We then couple one-dimensional control laws along independent orthogonal axes to design a distributed control law capable of stabilizing arbitrary shapes and orientations in n dimensions. We also present two methods for formation shape and orientation change, one using smooth parameter variations of the control law, and the other, an n-step collision-free algorithm for shape change between any two formations in n-dimensional space.