Safety Uncertainty in Control Barrier Functions using Gaussian Processes

Khan, Mouhyemen; Ibuki, Tatsuya; Chatterjee, Abhijit

doi:10.1109/icra48506.2021.9561504

Cited by 9 publications

(15 citation statements)

References 20 publications

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Section: A Gaussian Control Barrier Functionmentioning

confidence: 99%

“…By using the GP prior, we fully specify the candidate safety function unlike our previous work in [24]. Only the GP posterior variance was used in [24] to handle safety uncertainty for a given deterministic CBF. Note that this is a far more flexible realization since the data is used for informing both the safety belief and associated uncertainty.…”

Section: A Gaussian Control Barrier Functionmentioning

confidence: 99%

“…where the desired yaw is assumed to be zero and small angle approximations are made to invert the dynamics in (24) for simplicity [36], [37]. Next, we discuss the safety rectification of u to compute u rect using the Gaussian CBF.…”

Section: B Setpoint Generation For Quadrotormentioning

confidence: 99%

“…Moreover, we differ from [23] in modeling the safety function with GPs rather than the underlying dynamical system, and are not limited to any one type of kernel parameterization. In our previous work [24], safety uncertainty was introduced in CBFs by augmenting the GP posterior variance to an existing CBF using data. We experimentally validated augmentation of safety uncertainty to a given CBF in hardware.…”

Section: Introductionmentioning

confidence: 99%

“…However, it required a parametric CBF as the underlying safety function. Moreover, the safe set expansion in [24] was limited only to convex safe sets. Here, we consider a fully nonparametric formulation for synthesizing the safety function without requiring any parametric CBF candidate function.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety

Khan¹,

Ibuki²,

Chatterjee³

2022

Preprint

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Inspired by the success of control barrier functions (CBFs) in addressing safety, and the rise of data-driven techniques for modeling functions, we propose a non-parametric approach for online synthesis of CBFs using Gaussian Processes (GPs). Mathematical constructs such as CBFs have achieved safety by designing a candidate function a priori. However, designing such a candidate function can be challenging. A practical example of such a setting would be to design a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety in such an example is unknown and cannot be designed a priori. In our approach, we work with safety samples or observations to construct the CBF online by assuming a flexible GP prior on these samples, and term our formulation as a Gaussian CBF. GPs have favorable properties, in addition to being non-parametric, such as analytical tractability and robust uncertainty estimation. This allows realizing the posterior components with high safety guarantees by incorporating variance estimation, while also computing associated partial derivatives in closed-form to achieve safe control. Moreover, the synthesized safety function from our approach allows changing the corresponding safe set arbitrarily based on the data, thus allowing non-convex safe sets. We validate our approach experimentally on a quadrotor by demonstrating safe control for fixed but arbitrary safe sets and collision avoidance where the safe set is constructed online. Finally, we juxtapose Gaussian CBFs with regular CBFs in the presence of noisy states to highlight its flexibility and robustness to noise. The experiment video can be seen at: https://youtu.be/HX6uokvCiGk.

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Section: A Gaussian Control Barrier Functionmentioning

confidence: 99%

Section: A Gaussian Control Barrier Functionmentioning

confidence: 99%