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

Abstract

In this paper, we present a solution to the problem of coordinating multiple robots across a communication channel that experiences delays. The proposed approach leverages control barrier functions in order to ensure that the multi-robot system remains dissipative. This is achieved by encoding the dissipativity-preserving condition as a set invariance constraint. This constraint is then included in an optimization problem, whose objective is that of modifying, in a minimally invasive fashion, the nominal input to the robots. The formulated optimization problem is decentralized in the sense that, in order to be solved, it does not require the individual robots to have access to global information. Moreover, owing to its convexity, each robot can solve it using fast and efficient algorithms. The effectiveness of the proposed control framework is demonstrated through the implementation of a formation control algorithm in presence of delays on a team of mobile robots.

A Safety and Passivity Filter for Robot Teleoperation Systems

“…The expression of h u in ( 14) represents the power dissipated by the system. In [20] and [15], methods to ensure the passivity of a system in terms of energy are proposed. While those approaches are more flexible, insofar as they enforce conditions similar to h u (x, u) ≥ 0 in (14), they are also more sensitive to parameter tuning (see, for instance, discussions on T max in [7]).…”

“…Passivity-based approaches, as well as other energy-based methods, for the control of robotic systems are considered in [4,12,26,28,15]. In [6], the authors introduce the concept of energy tanks, which is then extended in [20,21,19,7].…”

An Optimization Approach for a Robust and Flexible Control in Collaborative Applications

“…The velocity controlled robot is wrapped by the modulated tank that is exploited for ensuring the passivity of the controlled system. The CBF-based optimizer receives as an input the desired admittance velocity ẋa and, by solving (23) determines the best value ẋopt for passively implementing the desired admittance behavior and all the tasks that are encoded by the CBFs. The matrix A(t) is modulated by setting γ = ẋopt .…”

“…Passivity can be encoded using Control Barrier Functions [23] but no interaction controllers are available yet.…”

Reinforcement Learning based Distributed Control of Dissipative Networked Systems

“…The following result, given for completeness for a discrete time setting such as ours, shows that the set C defined in ( 23) is forward invariant for every u t ∈ B(t, s t ). Although dissipativity is a property defined by the input, and the output, we can utilize control barrier functions to characterize the set of controllers that ensures dissipativity in the closed loop of the subsystems, which in turn guarantee the stability of the overall networked system [40] . Following Proposition 1, we define a control barrier function for each subsystem i as follows.…”