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Almost Global Convergence on (d + 1)-Agent Formations Employing Narrow Weak Rigidity in the d-Dimensional Space

In this paper, we review the concept of the infinitesimal narrow weak rigidity (INWR). Then, we apply the concept to a formation control problem with the gradient flow law to explore almost global convergence on (d + 1)-agent formations in ℝd. We also analyze the stability of incorrect equilibrium points of the control problem. In particular, we show that all of incorrect equilibrium points are unstable. Consequently, we show that a formation with (d + 1) agents in ℝd converges to a desired equilibrium point (desired formation) exponentially fast. Finally, a simulation is presented to validate the result.