Distributed observer‐based coordination for multiple Lagrangian systems using only position measurements

Abstract

This study addresses the distributed coordination problem for multiple Lagrangian systems under a directed graph. Two cases are considered, namely, the distributed tracking control problem with a dynamic leader and the leaderless synchronisation problem. To overcome the difficulty that only positions are measured, a kind of new distributed observer is designed to estimate the velocity for each follower. The velocity observer is updated using only position information from the agent itself and from its neighbours. Based on the outputs of the observer, the distributed control protocols are proposed, respectively, such that the tracking errors locally exponentially converge to zero in the tracking scenario and the agents synchronise in the leaderless synchronisation scenario. Furthermore, the stability of the overall scheme is discussed under the directed interaction graphs that contain a directed spanning tree. Finally, cooperative simulations are provided to show the effectiveness of the proposed observer and control algorithms.

Formation‐containment control of networked collision‐free Lagrangian systems

“…Moreover, compared with existing works concerning a stationary formation configuration, 30,33,34 this control scheme can tackle a time-varying formation case, which is more general and practical. Last but not least, this article deals with systems governed by MELSs with model uncertainties, while most existing approaches consider linear systems, 25,27,28 systems with the known dynamic model, 35 or systems which has the "linearity-in-parameters" property. 36,37 The remainder of this article is organized as follows.…”

Sampled‐data leader‐following consensus of second‐order nonlinear multiagent systems without velocity measurements

“…[25][26][27][28][29][30] In practical engineering systems, it is usually difficult or even impossible to obtain velocity measurements of agents; therefore, it is of great significance to consider the consensus protocol design without velocity measurements. 19,[31][32][33][34][35] In the works of Zhang and Yang 31 and Zhao et al, 32 the finite-time consensus for second-order multiagent systems without velocity measurements was studied. Du et al 19 presented an output feedback control protocol for second-order nonlinear multiagent systems.…”

Distributed formation stabilization for mobile agents using virtual tensegrity structures

“…Even though a wide range of issues have been studied, and hence several theoretical frameworks have been established to design control strategies, see, for example, [4] [5] establishing estimation strategy for Euler-Lagrange systems with partial states available, [6] [7] using matrix theory and graph theory, [8] based on gradient-descent control approach, graph rigidity theory [9][10], networked small-gain theory [11], sample-data for circle formation [12], to name a few, it should be noted that the desired formation shape can only be guaranteed to be locally stable in most of the research. In particular, based on the graph rigidity approach, it is challenging to coordinate a group of mobile robots globally converging to the prescribed formation [13].…”