Adaptive Control Barrier Functions

Xiao, Wei; Belta, Călin; Cassandras, Christos G.

doi:10.1109/tac.2021.3074895

Cited by 74 publications

(41 citation statements)

References 25 publications

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“…Note that the CLF constraint (13) only works for V (x) with relative degree 1. If the relative degree is larger than 1, we can use input-to-state linearization and state feedback control [26] to reduce the relative degree to one [31].…”

Section: A Trajectory Trackingmentioning

confidence: 99%

“…We achieve this by re-defining the CLF V (x) in (13) 23) is larger than 1, as mentioned in Sec. VI-A, we use input-tostate linearization and state feedback control [26] to reduce the relative degree to one [31]. For example, for the desired speed part in the CLF V (x) ( ( 23) is in linear form from v to u jerk , so we don't need to do linearization), we can find a desired state feedback 2 whose relative degree is just one w.r.t.…”

Section: Case Studymentioning

confidence: 99%

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Rule-based optimal control for autonomous driving

Xiao

Mehdipour²,

Collin³

et al. 2021

Proceedings of the ACM/IEEE 12th International Conference on Cyber-Physical Systems

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Section: A Trajectory Trackingmentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Rule-based optimal control for autonomous driving

Xiao

Mehdipour²,

Collin³

et al. 2021

Proceedings of the ACM/IEEE 12th International Conference on Cyber-Physical Systems

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“…The recently proposed adaptive CBFs (AdaCBFs) (Xiao et al, 2021b) addressed the conservativeness of the HOCBF method by multiplying the class K functions of an HOCBF with some penalty functions. These penalties functions, themselves, are HOCBFs such that they are guaranteed to be non-negative.…”

Section: Related Workmentioning

confidence: 99%

“…This is due to the fact that the main conservativeness of the HOCBF method comes from the class K functions. By multiplying (relaxing) the class K functions with some penalty functions, it has been shown that the satisfaction of the AdaCBF constraint is a necessary and sufficient condition for the satisfaction of the original safety constraint b(x) ≥ 0 (Xiao et al, 2021b). This is conditioned on designing proper auxiliary dynamics for all the penalty functions, based on specific problems.…”

Section: Related Workmentioning

confidence: 99%

“…, m} are the outputs of the previous layer, where R >0 denotes the set of positive scalars. The above formulation is similar to the Adaptive CBF (AdaCBF) (Xiao et al, 2021b), but is trainable, and does not require us to design auxiliary dynamics for p i (an AdaCBF does require), a non-trivial process of the existing AdaCBF method. In order to make sure that the HOCBF method can be solved in a time-discretization way (Ames et al, 2017), we require that each p i is Lipschitz continuous.…”

Section: Barriernetmentioning

confidence: 99%

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BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Xiao¹,

Hasani²,

Li³

et al. 2021

Preprint

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This paper introduces differentiable higher-order control barrier functions (CBF) that are end-toend trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints of a neural controller be adaptable to changing environments. We evaluate them on a series of control problems such as traffic merging and robot navigations in 2D and 3D space, and demonstrate their effectiveness compared to state-of-the-art approaches.

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Safety‐critical control for robotic systems with uncertain model via control barrier function

Zhang

Zhai

Xiong

et al. 2023

Intl J Robust & Nonlinear

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Usually, it is difficult to build accurate dynamic models for real robots, which makes safety-critical control a challenge. In this regard, this article proposes a double-level framework to design safety-critical controller for robotic systems with uncertain dynamics. The high level planner plans a safe trajectory for low level tracker based on the control barrier function (CBF). First, the high level planning is done independently of the dynamic model by quadratic programs subject to CBF constraint. Afterward, a novel method is proposed to learn the uncertainty of drift term and input gain in nonlinear affine-control system by a data-driven Gaussian process (GP) approach, in which the learning result of uncertainty in input gain is associated with CBF. Then, a Gaussian processes-based control barrier function (GP-CBF) is designed to guarantee the tracking safety with a lower bound on the probability for the low level tracker. Finally, the effectiveness of the proposed framework is verified by the numerical simulation of UR3 robot.

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Adaptive Control Barrier Functions

Cited by 74 publications

References 25 publications

Rule-based optimal control for autonomous driving

Rule-based optimal control for autonomous driving

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Safety‐critical control for robotic systems with uncertain model via control barrier function

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