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

Abstract

This paper addresses formation control of reduced attitudes in which a continuous control protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.

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].…”

Consensus with Preserved Privacy against Neighbor Collusion

“…The formal study of the consensus problem was first introduced by Degroot [1] in the 1970s, which sparked many further extensions and developments (see, e.g., [2][3][4] and the references therein). The methods and results, that were conceived in the study of the consensus problem, were later adapted to network coordination problems in control theory, such as formation control [5][6][7][8][9], distributed optimization [10][11][12][13], and also network games [14,15]. In the control setting, the situation is further complicated, as the the agents are governed by nonlinear dynamics [16,17].…”

Consensus with preserved privacy against neighbor collusion

“…The formal study of the consensus problem was first introduced by Degroot [1] in the 1970s, which sparked many further extensions and developments (see, e.g., [2,3,4] and the references therein). The methods and results, that were conceived in the study of the consensus problem, were later adapted to network coordination problems in control theory, such as formation control [5,6,7,8,9], distributed optimization [10,11,12,13], and also network games [14,15]. In the control setting, the situation is further complicated, as the the agents are governed by nonlinear dynamics [16,17].…”