Finite-Time Attitude Synchronization With Distributed Discontinuous Protocols

Abstract

The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.

Optimal attitude consensus for multi rigid bodies network considered on the lie group SO(3) with connectivity preserving property

“…Besides, the local and global convergence strategy represented in ref. [9] is based on a restrictive assumption on the initial rotations in SO(3), while in our strategy, the only initial connected condition is enough for reaching synchronisation and this condition is also relaxed with the optimal control problem. Finally, ref.…”

“…The problem in ref. [9] is formulated on SO(3); however, under the represented control, the states of the system leave the manifold. Since the SO(3) manifold is a lie group, it benefits from the advantages of Lie groups.…”

“…While by the presented method in ref. [9], the topology is not conserved and the metric is distorted; in our method, the topology of the SO(3) is always conserved that results in a fast and more accurate consensus especially for the systems with high number of agents. Using Rimannian metric for calculating the rotational distances between agents, and implementing the exponential map yields the new rotation matrix in each iteration of solving the dynamic of system remains on the manifold.…”

“…In this paper, like ref. [9], attitude synchronisation of rigid bodies on SO (3) is considered in kinematic level where the rotational motions of bodies are expressed with the axis-angle representation. The problem in ref.…”

Consensus with Preserved Privacy against Neighbor Collusion

“…This means that, within finite time, one agent's key updated by the algorithm can only approach, but not equal, the keys of the others. To reach an exact synchronization for the key sequence, finite-time consensus algorithms are needed, such as, e.g., [37][38][39][40]. These finite-time consensus algorithms, however, often depend on particular communication graphs [41], or require first computing a matrix factorization [37] or minimal polynomial [38] of the weight matrix.…”