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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). A dynamical system is defined to be safe if a subset of its states remains within the prescribed set, also called the safe set. CBFs achieve safety by designing a candidate function a priori. However, designing such a function can be challenging. Consider designing a CBF in a disaster recovery scenario where safe and navigable regions need to be determined. The decision boundary for safety here is unknown and cannot be designed a priori. Moreover, CBFs employ a parametric design approach and cannot handle arbitrary changes to the safe set in practice. In our approach, we work with safety samples 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 such as analytical tractability and robust uncertainty estimation. This allows realizing the posterior with high safety guarantees while also computing associated partial derivatives analytically for safe control. Moreover, Gaussian CBFs can change the safe set arbitrarily based on sampled data, thus allowing non-convex safe sets. We validated experimentally on a quadrotor by demonstrating safe control for 1) arbitrary safe sets, 2) collision avoidance with online safe set synthesis, 3) and juxtaposed Gaussian CBFs with CBFs in the presence of noisy states. The experiment video link is: https://youtu.be/HX6uokvCiGk.
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Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach
Control barrier functions are mathematical constructs used to guarantee safety for robotic systems. When integrated as constraints in a quadratic programming optimization problem, instantaneous control synthesis with real-time performance demands can be achieved for robotics applications. Prevailing use has assumed full knowledge of the safety barrier functions, however there are cases where the safe regions must be estimated online from sensor measurements. In these cases, the corresponding barrier function must be synthesized online. This paper describes a learning framework for estimating control barrier functions from sensor data. Doing so affords system operation in unknown state space regions without compromising safety. Here, a support vector machine classifier provides the barrier function specification as determined by sets of safe and unsafe states obtained from sensor measurements. Theoretical safety guarantees are provided. Experimental ROS-based simulation results for an omnidirectional robot equipped with LiDAR demonstrate safe operation.
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- Award ID(s):
- 1849333
- PAR ID:
- 10318590
- Date Published:
- Journal Name:
- International Conference on Intelligent Robots and Systems
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Conference Paper:
- https://doi.org/10.1109/IROS45743.2020.9341190
