Achieving consensus amongst self-propelling agents by enforcing sliding modes

Abstract

An algorithm, based on sliding mode control and graph algebraic theories, for the provision of consensus to a swarm of self-propelling agents is presented. Swarms, comprised of agents with first-order dynamics, that can be described by fully-connected and connected graphs with time-invariant topologies are considered. For consensus, the agents' inputs are designed to enforce sliding mode on surfaces that depend on the graph Laplacian matrix. The property of sliding mode occurring within a finite time interval, which can be varied, is lent to the swarm and it is this facet that distinguishes the proposed algorithm. As will be shown, applying this algorithm results the swarm achieving a constant consensus value equal to the average of the largest and smallest initial states of the agents. Owing to this result, by introducing a virtual agent with a precalculated initial condition, the algorithm allows for the tuning of the consensus value.

Recent advances in sliding-mode based consensus strategies

“…Remark 3: It is worth to remark that protocol (23) can be extended to the task of "distributed leader-tracking" [18] for multi-robot networks (20). Indeed, let agent i = 1 be a autonomous leader with bounded acceleration i.e.…”

“…Consider the network on the left-side of Figure 7, consisting of 10 perturbed agents as in (20). Disturbances ϑ i (t), according to Assumption 2, are selected as harmonic signals with randomly coefficients such that |ϑ i (t)| ≤ Π = 2.…”

“…SMC-based algorithms are well known to improve performance against unmodeled uncertainties and disturbances, useful in distributed multi-robot applications, see for instance the work in [18] and references therein. Conventional SMC solutions for achieving finitetime agreement among first-order single integrators have been discussed for distributed averaging problems in [19] while network synchronization with directed communication has been investigated in [20]. In [21] the consensus problem is studied in the case of quantized information exchange between agents, which is a particular kind of discontinuous feedback where quantization errors can be modeled as an unknown but bounded disturbance.…”

Distributed tracking for mechanical systems using second-order sliding-modes

“…Its main properties such as insensitivity to matched disturbances and finite time convergence have been used to solve the consensus tracking problem. In [7], the consensus amongst first order dynamics is obtained by means of first order sliding mode controllers. The conventional sliding modes are applied in [8] to ensure the finite time consensus for formation, swarm and pursuing.…”

“…Let compute the time derivative of (8) along the trajectories of the system (6), (7). This derivative can be written as:…”