Distributed weighted centroid formation tracking of multi-agent systems without velocity measurement

This paper introduces a novel fixed-time sliding mode-based control strategy for weighted centroid formation tracking of multiple Euler-Lagrange systems without velocity measurements. As the absence of global position information, we propose a fixed-time weighted centroid estimator, leveraging relative measurements and limited information exchange among agents. Additionally, a fixed-time velocity observer based on homogeneity theory is developed to accurately estimate the velocity of each agent, particularly in scenarios where direct velocity information is unavailable. By integrating the centroid estimator and velocity observer, a state-dependent sliding mode function is formulated, leading to a fixed-time centroid tracking controller. This controller ensures not only the formation’s movement in a predefined shape but also rapid tracking of the weighted centroid along any continuous reference trajectory. Numerical simulations validate the effectiveness of the proposed approach.