Intrinsic reduced attitude formation with ring inter-agent graph

Abstract

This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states.

An intrinsic approach to formation control of regular polyhedra for reduced attitudes

“…In our previous work [29], an intrinsic control law only containing the relative attitude { Γ i Γ j : j ∈ N i } is proposed to reach antipodal and cyclic formations under the ring-graph topology. Here, a similar but slightly modified control is employed for Platonic solid formations as…”

“…[19] and [21] propose a leader-follower formation control scheme based on the parametrizations of unit-quaternions and modi-fied Rodrigues parameters respectively, but the relative errors between leaders and followers are identified by the difference of their parametrization variables, and the control implementation also needs the absolute attitude information. To overcome the drawback caused by parametrizations, [29] provides a reduced-attitude formation control scheme directly in S 2 space. Moreover, such control protocol is in a so-called intrinsic manner which does not require any formation errors in control law and the desired formation patterns are constructed totally based on the geometric properties of the configuration space and the designed connection topology.…”

Flocking formation and stabilizer of boosted cooperative control on a sphere

“…The spherical surface has a nonzero curvature rather than a flat space, which yields mathematical challenges. The control system using cooperative manipulation on various manifolds is considered in many studies, such as on a sphere [15,24,32], Stiefel manifold [19], and directed topology [30,37]. In particular, the controllers or algorithms for the uniform deployment of homoclinic agents are investigated using single-integrator model [14,25] or double-integrator model [16].…”

Network Consensus with Privacy: A Secret Sharing Method

“…While consensus problems have a long history, dating back to at least the 1960's and 1970's (see, e.g., [24]), they have perhaps never been as relevant as they are today. The basic problemnamely, to device a method that allows a group of individuals or agents to reach agreement about some parameters through a decentralized communication protocol -naturally appears broadly in numerous IoT contexts, such as sensor fusion [25], [26], [27], [28], load balancing [29], [30], clock synchronization [31], [32], peak power load shedding [33] and resource management [34] in smart grids, distributed optimization [35], [36], swarm coordination [37], [38], [39], [40], distributed and federated learning [41], and large scale peer-to-peer networks [42], [43].…”