Leader–Follower Synchronisation for a Class of Underactuated Systems

Abstract

In this work leader-follower synchronization is considered for underactuated followers in an inhomogeneous multi-agent system. The goal is to synchronise the motion of a leader and an underactuated follower. Measurements of the leader's position, velocity, acceleration, and jerk are available, while the dynamics of the leader is unknown. The leader velocities are used as input for a constant bearing guidance algorithm to assure that the follower synchronises its motion to the leader. It is also shown that the proposed leader-follower scheme can be applied to multi-agent systems that are subjected to unknown environmental disturbances. Furthermore, the trajectory of the leader does not need to be known. The closed-loop dynamics are analysed and it is shown that under certain conditions all solutions remain bounded and the synchronisation error kinematics are shown to be integral input-to-state stable with respect to changes in the unactuated sway velocity. For straight-line motions, i.e. where the desired yaw rate and sway velocity go to zero, synchronisation is achieved. Simulation results are presented to validate the proposed control strategy.

Formation Path Following Control of Underactuated USVs -- With Proofs

“…where σ = σ d − σ is the task error, J ∈ R m×4 is the configuration-dependent task Jacobian matrix, (•) † denotes the Moore-Penrose pseudoinverse and Λ ∈ R m×m > 0 is a matrix of proportional gains. Now, let v d,i denote the solution of the i th priority task, given by (11). The velocities of each task are then combined by…”

“…σ ca < σ ca,d . As (15) is scalar, the collision avoidance gain in (11) is reduced to λ ca ∈ R. Moreover, the vessel formation task is defined as…”

“…When considering the control problem for formations of marine vessels, several leader-follower approaches have been proposed where the follower adapts its speed and position relative to the leader to obtain the desired formation, e.g. [8]- [11]. However, leaderfollower methods suffer from the fact that communication is *This work was partly supported by the Research Council of Norway through the Centres of Excellence funding scheme, project No.…”

Lyapunov-based synchronization of networked systems: From continuous-time to hybrid dynamics

“…Such is the case in engineering disciplines where technological solutions involve groups of systems required to cooperate to complete a common task. Some common examples of these are related, but are not limited, to robotic manipulation and the use of autonomous vehicles [5][6][7][8][9], but they are also common in energy networks [10], for instance. Other disciplines include neuroscience, in which networks and sub-networks (clusters) formed due to neuronal population activities and interactions are studied [11], social science, in which a subject of study is that of opinion networks formed due to the interactions among individuals [12], and geography, in which groups of populations that interact when reacting to catastrophes are studied [13].…”

Decentralized synchronization of time-varying oscillators under time-varying bidirectional graphs

“…Decentralized coordination control for networked systems consists in designing a control law for each system in order to achieve a coordinated task or, more concretely, to make certain quantities of interest in each system reach a common value [1]. For instance, it may be required for these systems to reach a certain geometric pattern [2], [3], follow a target or a leader [4], [5], or also describe a common steady-state behavior [6], [7], [8]. When the control law is decentralized, the input of each system is designed using only local information provided by a set of agents called neighbors.…”