Control Barrier Functions for Multi-Agent Systems Under Conflicting Local Signal Temporal Logic Tasks

Lindemann, Lars; Dimarogonas, Dimos V.

doi:10.1109/lcsys.2019.2917975

Cited by 82 publications

(52 citation statements)

References 19 publications

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“…We show in Section IV that C i ⊂ D i+1 (guaranteed by bound on the rate change of the reference trajectory z(t) in (11c)) along with D i ⊂ X and C i ⊂ X T (guaranteed by (11e)) guarantees that closed-loop trajectories meet the objectives in (3). Under these considerations, the low-level control objective for t ∈ T i = [(i − 1)T, iT ) is to design the policy π l such that the set D i is FxT-DoA for the set C i .…”

Section: B Low-level Control Synthesismentioning

confidence: 99%

“…Most popular approaches on the control synthesis under such specifications include quadratic programming techniques, where the safety requirements are encoded via control barrier functions (CBFs) and convergence requirements via control Lyapunov functions (CLFs), see e.g. [1], [2], or via one function that encodes both the safety and convergence requirements [3], [4].…”

Section: Introductionmentioning

confidence: 99%

“…Quadratic program (QP)-based approaches have gained popularity for control synthesis [1], [2], [4], [5] in real-time, since QPs can be solved efficiently. Most of the prior work, except [3], [4], deals with asymptotic or exponential convergence of the system trajectories to the desired goal set. Fixed-time stability (FxTS) [6] is a stronger notion of stability, where the time of convergence does not depend on the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions

Garg

Cosner

Rosolia

et al. 2022

IEEE Control Syst. Lett.

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In this paper, we introduce the notion of periodic safety, which requires that the system trajectories periodically visit a subset of a forward-invariant safe set, and utilize it in a multi-rate framework where a high-level planner generates a reference trajectory that is tracked by a low-level controller under input constraints. We introduce the notion of fixed-time barrier functions which is leveraged by the proposed low-level controller in a quadratic programming framework. Then, we design a model predictive control policy for high-level planning with a bound on the rate of change for the reference trajectory to guarantee that periodic safety is achieved. We demonstrate the effectiveness of the proposed strategy on a simulation example, where the proposed fixed-time stabilizing low-level controller shows successful satisfaction of control objectives, whereas an exponentially stabilizing low-level controller fails.

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Section: B Low-level Control Synthesismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions

Garg

Cosner

Rosolia

et al. 2022

IEEE Control Syst. Lett.

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“…Barrier functions are analogues to Lyapunov functions are have been usually used to guarantee safety in dynamical systems [103,104]. They have been also used for networked systems in [105][106][107][108][109]. Recently, in [110], barrier functions are used to show safety for hybrid systems in the form of H. However, to the best of our knowledge, establishing distributed safety criteria for hybrid networks has not been done yet.…”

Section: Safety Specifications In Hybrid Networkmentioning

confidence: 99%

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

Maghenem

Lorı́a

Panteley

2020

Annual Reviews in Control

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Synchronization pertains to the property of interconnected systems according to which their dynamic behavior is coordinated in an appropriate sense. That is to say, some of their state variables, or functions of the latter for that matter, converge to each other. Synchronization may occur naturally or may be induced, controlled, and it may be present between two systems or among a large number. In the latter case, it is convenient to speak of a network of interconnected systems. Understanding synchronization, and how to control it, is an important paradigm as it is present in a variety of scenarios. These involve, e.g., networks of technological systems (robots and vehicles of different kinds), social networks (by which people exchange opinions and agree, or not), networks of biological systems (uni or pluricellular), etc. Owing to the context, the mathematical models to describe such networks and to define synchronization formally, varies dramatically. Ordinary continuous-time or discrete-time models for which modern control theory and Lyapunov stability theory are tailored result inappropriate to incorporate hybrid phenomena that intervene in the network. These may stem from sudden topology changes, the use of digital or intermittent control strategies, the presence of impacts in the intrinsic dynamics of the nodes, etc. In this invited paper, we give an overview of synchronization control problems, mostly of cooperative control of networks of autonomous vehicles (based on continuous-time models). For that matter, the first part of the paper focuses on the main contributions of [1]. Then, we give further perspectives on what we consider significant open problems on synchronization of hybrid systems and hybrid networks.

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“…CBFs provide a framework for formally incorporating general safety constraints into quadratic programs. This was first applied to adaptive cruise control, and has since been utilized in a variety of application domains: automotive safety [9], robotics [10], [11] and multi-agent systems [12], [13]. See [14] for a recent survey.…”

Section: Introductionmentioning

confidence: 99%

Safety-Critical Kinematic Control of Robotic Systems

Singletary

Kolathaya

Ames

2021

2021 American Control Conference (ACC)

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Over the decades, kinematic controllers have proven to be practically useful for applications like set-point and trajectory tracking in robotic systems. To this end, we formulate a novel safety-critical paradigm by extending the methodology of control barrier functions (CBFs) to kinematic equations governing robotic systems. We demonstrate a purely kinematic implementation of a velocity-based CBF, and subsequently introduce a formulation that guarantees safety at the level of dynamics. This is achieved through a new form of CBFs that incorporate kinetic energy with the classical forms, thereby minimizing model dependence and conservativeness. The approach is then extended to underactuated systems. This method and the purely kinematic implementation are demonstrated in simulation on two robotic platforms: a 6-DOF robotic manipulator, and a cart-pole system.

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Control Barrier Functions for Multi-Agent Systems Under Conflicting Local Signal Temporal Logic Tasks

Cited by 82 publications

References 19 publications

Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions

Multi-Rate Control Design Under Input Constraints via Fixed-Time Barrier Functions

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

Safety-Critical Kinematic Control of Robotic Systems

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