Control Barrier Functions: Theory and Applications

Ames, Aaron D.; Coogan, Samuel; Egerstedt, Magnus; Notomista, Gennaro; Sreenath, Koushil; Tabuada, Paulo

doi:10.23919/ecc.2019.8796030

Cited by 1,118 publications

(899 citation statements)

References 54 publications

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“…Much like a physical barrier prevents physical objects from entering restricted regions, barrier functions (BFs) were first implemented in the optimization literature to prevent solutions being returned from undesirable regions [12], [13], [14]. Ames et al extended the notion of BFs to control barrier functions (CBFs) by adding safety constraints to optimization-based control methods [15].…”

Section: B Control Barrier Functionsmentioning

confidence: 99%

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Haptic Teleoperation of UAVs Through Control Barrier Functions

Zhang

Yang

Khurshid

2020

IEEE Trans. Haptics

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This paper presents a novel approach to haptic teleoperation. Specifically, we use control barrier functions (CBFs) to generate force feedback to help human operators safely fly quadrotor UAVs. CBFs take a control signal as input and output a control signal that is as close as possible to the initial control signal, while also meeting specified safety constraints. In the proposed method, we generate haptic force feedback based on the difference between a command issued by the human operator and the safe command returned by a CBF. In this way, if the user issues an unsafe control command, the haptic feedback will help guide the user towards the safe input command that is closest to their current command. We conducted a within-subject user study, in which 12 participants flew a simulated UAV in a virtual hallway environment. Participants completed the task with our proposed CBFbased haptic feedback, no haptic feedback, and haptic feedback generated via parametric risk fields, which is a state-of-the-art method described in the literature. The results of this study show that CBF-based haptic feedback can improve a human operator's ability to safely fly a UAV and reduce the operator's perceived workload, without sacrificing task efficiency.

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Section: B Control Barrier Functionsmentioning

confidence: 99%

“…In this section we provide a brief introduction to CBFs, and refer the reader to [14], [15], [20], [21] for complete details. CBFs can be applied to continuous time affine control systems of the form:…”

Section: A Control Barrier Function Implementationmentioning

confidence: 99%

Haptic Teleoperation of UAVs Through Control Barrier Functions

Zhang

Yang

Khurshid

2020

IEEE Trans. Haptics

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“…Time-varying CBFs were used to accomplish tasks specified in signal temporal logic in [30]. A survey of the use of CBFs to design safety-critical controllers is presented in [5]. The use of barrier certificates or CBFs in these works were all for continuous time dynamical systems and did not consider the effect of the actions of an adversarial player.…”

Section: Related Workmentioning

confidence: 99%

“…This will allow for determining bounds on the probability of satisfaction of the LTL formula without discretizing the state space. In contrast, if the underlying state space is continuous, computing the satisfaction probability and the corresponding agent policy using dynamic programming will necessitate a discretization of the state space in order to approximate the integral in Equation (5).…”

Section: Computing An S-cbcmentioning

confidence: 99%

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Ramasubramanian

Niu

Clark

et al. 2019

Lecture Notes in Computer Science

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This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in sa f e − LTL F , a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discretetime dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a sa f e − LTL F formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.

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“…The study also hypothesized that a fixed trajectory training strategy would drive the spinal circuitry toward a state of learned helplessness. These "assist-as-needed" algorithms, which have also been explored in other publications [13]- [15], utilize velocity field control to provide gentle guidance at a The algorithm presented in this paper proposes a complementary approach that leverages tools from controlled set invariance [16], [17] -in particular, control barrier functions [18], [19] -to enable assist-as-needed strategies while guaranteeing coherence of the walking pattern. The method allows users to control their own motions when they are performing well (i.e.…”

mentioning

confidence: 99%

Towards Variable Assistance for Lower Body Exoskeletons

Gurriet

Tucker

Duburcq³

et al. 2020

IEEE Robot. Autom. Lett.

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This paper presents and experimentally demonstrates a novel framework for variable assistance on lower body exoskeletons, based upon safety-critical control methods. Existing work has shown that providing some freedom of movement around a nominal gait, instead of rigidly following it, accelerates the spinal learning process of people with a walking impediment when using a lower body exoskeleton. With this as motivation, we present a method to accurately control how much a subject is allowed to deviate from a given gait while ensuring robustness to patient perturbation. This method leverages control barrier functions to force certain joints to remain inside predefined trajectory tubes in a minimally invasive way. The effectiveness of the method is demonstrated experimentally with able-bodied subjects and the Atalante lower body exoskeleton.

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Control Barrier Functions: Theory and Applications

Cited by 1,118 publications

References 54 publications

Haptic Teleoperation of UAVs Through Control Barrier Functions

Haptic Teleoperation of UAVs Through Control Barrier Functions

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Towards Variable Assistance for Lower Body Exoskeletons

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