Modern nonlinear control theory seeks to develop feedback controllers that endow systems with properties such as safety and stability. The guarantees ensured by these controllers often rely on accurate estimates of the system state for determining control actions. In practice, measurement model uncertainty can lead to error in state estimates that degrades these guarantees. In this paper, we seek to unify techniques from control theory and machine learning to synthesize controllers that achieve safety in the presence of measurement model uncertainty. We define the notion of a Measurement-Robust Control Barrier Function (MR-CBF) as a tool for determining safe control inputs when facing measurement model uncertainty. Furthermore, MR-CBFs are used to inform sampling methodologies for learning-based perception systems and quantify tolerable error in the resulting learned models. We demonstrate the efficacy of MR-CBFs in achieving safety with measurement model uncertainty on a simulated Segway system.
Gaussian Control Barrier Functions: Safe Learning and Control
Safety is a critical component in today's autonomous and robotic systems. Many modern controllers endowed with notions of guaranteed safety properties rely on accurate mathematical models of these nonlinear dynamical systems. However, model uncertainty is always a persistent challenge weakening theoretical guarantees and compromising safety. For safety-critical systems, this is an even bigger challenge. Typically, safety is ensured by constraining the system states within a safe constraint set defined a priori by relying on the model of the system. A popular approach is to use Control Barrier Functions (CBFs) that encode safety using a smooth function. However, CBFs fail in the presence of model uncertainties. Moreover, an inaccurate model can either lead to incorrect notions of safety or worse, incur system critical failures. Addressing these drawbacks, we present a novel safety formulation that leverages properties of CBFs and positive definite kernels to design Gaussian CBFs. The underlying kernels are updated online by learning the unmodeled dynamics using Gaussian Processes (GPs). While CBFs guarantee forward invariance, the hyperparameters estimated using GPs update the kernel online and thereby adjust the relative notion of safety. We demonstrate our proposed technique on a safety-critical quadrotor on SO(3) in the presence of model uncertainty in more »
- Award ID(s):
- 1723997
- Publication Date:
- NSF-PAR ID:
- 10274777
- Journal Name:
- IEEE Conference on Decision and Control
- Page Range or eLocation-ID:
- 3316 to 3322
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Publisher's Version of Record
- https://doi.org/10.1109/CDC42340.2020.9303753
