Triangularly Angle Rigid Formations with Vertex-Dependent Measurement Noise

Measurement noise is inevitable in practical sensor networks and control systems. Due to the introduction of randomness, the problem of multiagent angle rigid formation control with measurement noise becomes more challenging than that without noise. Different from existing works that simply assume the measurement process to be unbiased and white, the measurement noise discussed in this paper has a time-varying expectation, and its values at different time instants are mutually correlated, i.e., the measurement noise is stochastically biased and colored. Since such noise’s expectation and other statistical properties are unknown and cannot be measured beforehand, a distributed estimator of the noise’s expectation is first designed by using only noisy interagent relative position measurements. Through the formulation of a noisy angle-induced linear constraint and the definition of a weighted matrix for the measurement noise, the proposed expectation estimator is embedded into an angle rigid formation controller. Furthermore, with considering the temporal correlation of the measurement noise, the statistical stability of the closed-loop formation dynamics is proven. The corresponding bounds of the estimation and formation errors are also derived in mean and mean-squared senses. Finally, simulation examples are provided to validate the effectiveness of the proposed distributed expectation estimator and formation controller.