Decentralized Connectivity Maintenance with Time Delays using Control Barrier Functions

Abstract

Connectivity maintenance is crucial for the real world deployment of multi-robot systems, as it ultimately allows the robots to communicate, coordinate and perform tasks in a collaborative way. A connectivity maintenance controller must keep the multi-robot system connected independently from the system's mission and in the presence of undesired real world effects such as communication delays, model errors, and computational time delays, among others. In this paper we present the implementation, on a real robotic setup, of a connectivity maintenance control strategy based on Control Barrier Functions. During experimentation, we found that the presence of communication delays has a significant impact on the performance of the controlled system, with respect to the ideal case. We propose a heuristic to counteract the effects of communication delays, and we verify its efficacy both in simulation and with physical robot experiments.

Multirobot Adversarial Resilience Using Control Barrier Functions

“…where d i,j = ∥x i − x j ∥ is the Euclidean distance between robot i and robot j, and σ > 0 is a constant to normalize the edge weights. We choose the communication function used in [3,4] because it is continuously differentiable with respect to the distance between robots, decreases with increasing distance, and has positive edge weights a i,j ≥ 0 when d i,j ≤ R.…”

“…In order to employ collision or obstacle avoidance, different CBFs can be used. The CBF used in [4,6] can be used for collision avoidance:…”

“…Unlike previous works that rely on the careful linear combinations of control constraints, our CBF inherits the generality that is typical of CBF-based approaches of simultaneously considering any combination of realistic constraints that can be formulated as an inequality that is controllable by the input. For example, the authors in [4,6] implement collision and obstacle avoidance constraints while the authors in [11] impose constraints such as coverage, energy, and battery charging using CBFs. This is done without the need to tune control weights that trade-off the different constraints, making our controller more practical to implement in realworld settings.…”

Decentralized Risk-Aware Tracking of Multiple Targets

“…To enable multi-robot multi-target tracking in a decentralized framework, it is typically required that the connectivity of the underlying network graph is maintained. To do this, [16] formulates the connected region as a safety set and uses a CBF to render it forward invariant such that the network will always remain connected as long as the robots are initialized properly. For a systematic elaboration of the theory of CBF and its relationship with Lyapunov control, see [17].…”

“…is satisfied, we could render C forward invariant and ensure that if the robots initially start from an arbitrary state inside C, they will always remain within C. Note that 𝐿 𝑓 and 𝐿 𝑔 represent the Lie derivatives of ℎ(•) along the vector fields 𝑓 and 𝑔, respectively. 𝛼(•) is an extended class K function as introduced in [16]. Back to our case, to ensure network connectivity, we define ℎ(•) as:…”