Fixed-Time Rigidity-Based 3-D Formation Maneuvering Control With Distributed Finite-time Velocity Estimators

In this paper, a fixed-time rigidity-based formation maneuvering control system with distributed finite-time velocity estimator is studied. The controller of the system is realized by using the local coordinate frames of the agents without the global coordinate information. We design a distributed finite-time velocity estimator, in which the desired velocity vector is considered to be available to part with agents directly, and it can be estimated at finite-time for each agent. The target formation graph is assumed to be minimally and infinitesimally rigid. A distance-based formation maneuvering controller has been presented, which proves that in 3-D space, the agents could escape from collinear environment. Meanwhile, the formation can achieve the desired shape and track the velocity trajectory in fixed-time after the estimator estimates the velocity in finite-time. The stability and convergence of the formation maneuvering system is proved by Lyapunov and input-to-state stability theory. Finally, simulations are provided to validate the performance and effectiveness of the proposed schemes.