Constraint-Driven Coordinated Control of Multi-Robot Systems

Abstract

In this paper we present a reformulation-framed as a constrained optimization problem-of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The constraint-based formulation provides a natural way of enabling long-term robot autonomy applications, where resilience and adaptability to changing environmental conditions are essential. Moreover, under certain assumptions on the cost function, the resulting controller is guaranteed to be decentralized. Furthermore, finite-time convergence can be achieved, while using local information only, and therefore preserving the decentralized nature of the algorithm. The developed control framework has been tested on a team of ground mobile robots implementing long-term environmental monitoring.

Control Barrier Functions: Theory and Applications

“…and enforcing differential constraints affine in the control variable u i , which are analogous to (7), as shown in [54]. Considering the environmental monitoring task, we reformulate the task itself using CBFs which can be then combined with the ones related to survivability introduced above in order to implement persistent environmental monitoring [55]. Consider N robots tasked with monitoring a compact and convex set Ω ⊂ R d .…”

“…As shown in [22], the constraint (24) ensures that the zero superlevel set of the function h t (χ) is asymptotically stable, with the effect of minimizing the coverage cost J defined above [55]. Additionally, safety, specifically intended as collision avoidance, can be guaranteed by ensuring that h s (χ i , χ j ) = p(x i ) − p(x j ) 2 − ∆ 2 ≥ 0 ∀ i, j ∈ {1, .…”

An Optimal Task Allocation Strategy for Heterogeneous Multi-Robot Systems

“…The next section introduces some concepts from non-linear control theory and from our previous work [13] which will be used throughout the paper.…”

“…Section II discusses relevant results from the multi-robot task allocation literature and compares them with the approach we propose in this paper. Then, results from non-linear control theory and our previous work [13] are presented, which will be used throughout the paper. Section III formulates an optimization problem to compose multiple tasks as constraints within a single optimization problem.…”

Passivity-Based Decentralized Control of Multi-Robot Systems With Delays Using Control Barrier Functions

“…Theorem 6 (See [24] and [26]). Given a dynamical system in control affine form (9), where x ∈ R n and u ∈ R m denote the state and the input, respectively, f and g are locally Lipschitz, and a set Ω ⊂ R n defined by a continuously differentiable function h as in (10), any Lipschitz continuous controller u such that (11) holds renders the set Ω forward invariant and asymptotically stable, i. e.,…”