Formation shape and orientation control using projected collinear tensegrity structures

Darren Pais, Ming Cao and Naomi Ehrich Leonard

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.