Rigidity in Non-Euclidean Frameworks for Formation Control: The Manhattan Metric
D Burke, A Chapman, E Schoof
Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC) | IEEE | Published : 2020
This paper considers the formation control problem when the target is a rigid framework with respect to inter-agent -distance measurements. We present a rigidity theory for frameworks under the norm and show that, under this type of rigidity, infinitesimally rigid frameworks are uniquely determined up to a translation. Based on the characterizations of the theory, we propose a distributed control law and prove local exponential stability to the target formation. We also present results on the non-target equilibriums and convergence speed of the control law, supporting these claims with illustrative examples.
The research of the authors was supported by the LOral-UNESCO Australia For Women in Science Fellowship and the University of Melbourne Summer Research Internship Program. The first and second authors are with the Department of Mechanical Engineering and third with the Department of Electrical and Electronic Engineering, The University of Melbourne, VIC, 3010 Australia. Emails: f declanb@student.,airlie.chapman@,firstname.lastname@example.org.