Abstract
This paper considers the formation control problem when the target is a rigid framework with respect to inter-agent l 1 -distance measurements. We present a rigidity theory for frameworks under the l 1 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.
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