Velocity-free containment control with binary relative measurements only

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This paper introduces a containment control law for a multi-agent system (MAS) of double integrator agents using only relative position information. Unlike existing methods, this approach eliminates the need for velocity or exact position measurements as feedback, reducing communication and sensor requirements. Using the non-smooth Lyapunov analysis, we prove the convergence of the proposed control law under any detailed-balanced network with any positive gains. Moreover, the controller inherently guarantees bounded control effort and finite-time or fixed-time convergence without needing any additional update law. Finally, the numerical simulations demonstrate the effectiveness of the proposed method.