Rigidity in Non-Euclidean Frameworks for Formation Control: The Manhattan Metric

Abstract

This paper considers the formation control problem when the target is a rigid framework with respect to inter-agent l1-distance measurements. We present a rigidity theory for frameworks under the l1 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.