Reduction and control of nonlinear symmetric distributed robotic systems

  • Authors:

  • M. Brett Mcmickell;Bill Goodwine

  • Affiliations:

  • -;-

  • Venue:
  • Reduction and control of nonlinear symmetric distributed robotic systems
  • Year:
  • 2004

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Abstract

This study considers the reduction problem for large-scale distributed control systems. The state-space of these systems is often very large making analysis and synthesis difficult. In particular, this study considers systems containing multiple instances of identical controllers or components where the overall system is invariant with respect to interchanging these identical components. A graph-theoretical framework is considered for modeling these systems that clearly identifies the structure of the system's components. Graph symmetries, which naturally arise in many distributed systems, can be used to formulate a reduced-order model of the system. This study presents two applications of the reduction technique; namely, a reduced-order controllability analysis and a reduced-order motion planning algorithm. The controllability result provides a theorem, which shows that for an equivalence class of symmetric systems, controllability of the entire class of systems can be determined by analyzing the smallest member of the equivalence class. This theorem is demonstrated by determining the controllability of a team of mobile robots and a platoon of underwater vehicles. The result of the reduced-order motion planning study is a piecewise-linear motion planning algorithm for rigid-body formations of large-scale symmetric mobile robotic systems. Motion planning is conducted on a reduced-order system then systematically applied to the larger system. Results from simulation and experimental testing of this algorithm are given and demonstrate its utility. The motion planning algorithm was implemented on groups of small mobile robots called Micabots. Micabots are both inexpensive and flexible making it useful for a wide range of experimental goals. The design of the Micabots including such considerations as cost, size, and functionality, is discussed.