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In this paper, finite-time attitude consensus control laws for multi-agent rigid body systems are presented using rotation matrices. The control objective is to stabilize the relative configurations in a finite convergence time. First, the control design is done on the kinematic level where the angular velocities are the control signals. Next, the design is conducted on the dynamic level in the framework of the tangent bundle TSO(3) associated with SO(3), where the torques implement the feedback control of relative attitudes and angular velocities. The Lyapunov-based almost global finite-time stability of the consensus subspace is demonstrated for both cases. Finally, numerical simulations are provided to verify the effectiveness of the proposed consensus control algorithms. 

Motivated by real-world applications with intermittent sensor data, an extended Kalman filter is formulated as a hybrid system and constructive conditions on its parameters guaranteeing an asymptotic stability property are provided. The dynamical properties of the estimation error are first characterized infinitesimally so to yield bounds on the rate of convergence and overshoot that depend on the parameters. By recasting the problem as the stabilization of a compact set, robustness properties of the proposed algorithm in the presence of disturbances in the system dynamics as well as measurement noise in the output are established. The proposed strategy is applied to spacecraft relative motion control with position-only measurements. 

We consider the problem of rendezvous, proximity operations, and docking of an autonomous spacecraft. The problem can be conveniently divided into four phases: 1) rendezvous with angles-only measurements; 2) rendezvous with range measurements; 3) docking phase; and 4) docked phase. Due to the different constraints, available measurements, and tasks to perform on each phase, we study this problem using a hybrid systems approach, in which the system has different modes of operation for which a suitable controller is to be designed. Following this approach, we characterize the family of individual controllers and the required properties they should induce to the closed-loop system to solve the problem within each phase of operation. Furthermore, we propose a supervisor that robustly coordinates the individual controllers so as to provide a solution to the problem. Due to the stringent mission requirements, the solution requires hybrid controllers that induce convergence, invariance, or asymptotic stability properties, which can be designed using recent techniques in the literature of hybrid systems. In addition, we outline specific controller designs that appropriately solve the control problems for individual phases and validate them numerically1.