String Instability in Classes of Linear Time Invariant Formation Control With Limited Communication Range

• Published in: IEEE transactions on automatic control Vol. 55; no. 7; pp. 1519 - 1530
• Main Authors: Middleton, Richard H, Braslavsky, Julio H
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Arrays; Bullwhip effect; Communication system control; Computer science; control theory; systems; Control systems; Control theory. Systems; Distributed control; distributed systems; Exact sciences and technology; formation control; Frequency response; Ground, air and sea transportation, marine construction; Instability; Invariants; Lower bounds; Mobile robots; performance limitations; Policies; Remotely operated vehicles; Road transportation and traffic; Robotics; Stability; string stability; Strings; Sufficient conditions; Transfer functions; Vehicle dynamics; Vehicles; Lower bound; Data transmission; Bullwhip effect; string stability; Spacing; Distributed system; formation control; Linear time invariant system; distributed systems; Frequency response; Causality; Transfer function; Automatic driving; Formation; performance limitations
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2042318

This paper gives sufficient conditions for string instability in an array of linear time-invariant autonomous vehicles with communication constraints. The vehicles are controlled autonomously and are subject to a rigid or semi-rigid formation policy. The individual controllers are assumed to have a limited range of forward and backward communication with other vehicles. Sufficient conditions are given that imply a lower bound on the peak of the frequency response magnitude of the transfer function mapping a disturbance to the leading vehicle to a vehicle in the chain. This lower bound quantifies the effect of spacing separation policy, intervehicle communication policy, and vehicle settling response performance. These results extend earlier works to give a unified treatment of heterogeneous, non-nearest neighbor communication and semi-rigid one-dimensional formation control.