High-Order Control Barrier Functions

Xiao, Wei; Belta, Călin

doi:10.1109/tac.2021.3105491

Cited by 74 publications

(51 citation statements)

References 26 publications

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“…The training data is obtained by solving the CBF controller introduced in (Xiao and Belta, 2021), and we generate 100 trajectories of different destinations as the training data set. We compare the FC model, the deep foward-backward model (referred as DFB) (Pereira et al, 2020) that is equivalent to take the CBF-based QP as a safety filter, and our proposed Bar-rierNet.…”

Section: Results and Dicussionmentioning

confidence: 99%

“…The training data is obtained by solving the CBF controller introduced in (Xiao and Belta, 2021). We compare the FC model with our proposed BarrierNet.…”

Section: Results and Dicussionmentioning

confidence: 99%

“…The inter-sampling effect is considered in (Yang et al, 2019;Xiao et al, 2021a). Replacing CBFs by HOCBFs allows us to handle constraints with arbitrary relative degree (Xiao and Belta, 2021). The common observation is that as the uncertainty of models increases, CBFs make the system's behavior excessively conservative (Csomay-Shanklin et al, 2021).…”

Section: Related Workmentioning

confidence: 99%

“…In the present study, we address this over-conservativeness of CBFs by replacing the set of hard constraints in high order CBFs (HOCBFs) (Xiao and Belta, 2021) for arbitrary-relative-degree systems, with a set of differentiable soft constraints without loss of safety guarantees. This way, we obtain a versatile safety guaranteed barrier layer, termed a BarrierNet, that can be combined with x is the vehicle state, and z is the observation variable.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: Results and Dicussionmentioning

confidence: 99%

“…The training data is obtained by solving the CBF controller introduced in (Xiao and Belta, 2021). We compare the FC model with our proposed BarrierNet.…”

Section: Results and Dicussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Xiao¹,

Hasani²,

Li³

et al. 2021

Preprint

Self Cite

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show abstract

“…The CBF-based method has been used for obstacle avoidance, bipedal walking and robotic grasping [12]- [14]. The improved CBFs for uncertain disturbances and systems with high degree of freedom have been studied in [15]- [17]. An ongoing difficult part is to design a good CBF to reduce the conservativeness of decision space and ensure control set invariance, referred to [18], [19].…”

mentioning

confidence: 99%

Suboptimal Safety-Critical Control for Continuous Systems Using Prediction-Correction Online Optimization

Wang¹,

wen²,

Shi³

et al. 2022

Preprint

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This paper investigates the control barrier function (CBF) based safety-critical control for continuous nonlinear control affine systems using more efficient online algorithms by the time-varying optimization method. The idea of the algorithms is that when quadratic programming (QP) or other convex optimization algorithms needed in the CBF-based method is not computation affordable, the alternative suboptimal feasible solutions can be obtained more economically. By using the barrier-based interior point method, the constrained CBF-QP problems are transformed into unconstrained ones with suboptimal solutions tracked by two continuous descent-based algorithms. Considering the lag effect of tracking and exploiting the system information, the prediction method is added to the algorithms, which achieves exponential convergence to the time-varying suboptimal solutions. The convergence and robustness of the designed methods as well as the safety criteria of the algorithms are studied theoretically. The effectiveness is illustrated by simulations on the antiswing and obstacle avoidance tasks.

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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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High-Order Control Barrier Functions

Cited by 74 publications

References 26 publications

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Suboptimal Safety-Critical Control for Continuous Systems Using Prediction-Correction Online Optimization

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

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