Formation shape and orientation control using projected collinear tensegrity structures

  • Authors:

  • Darren Pais;Ming Cao;Naomi Ehrich Leonard

  • Affiliations:

  • Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ;Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, The Netherlands;Mechanical and Aerospace Engineering Department, Princeton University, Princeton, NJ

  • Venue:
  • ACC'09 Proceedings of the 2009 conference on American Control Conference
  • Year:
  • 2009

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Abstract

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 interagent 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.