Real-time controllers must satisfy strict safety
requirements. Recently, Control Barrier Functions (CBFs) have
been proposed that guarantee safety by ensuring that a suitablydefined
barrier function remains bounded for all time. The
CBF method, however, has only been developed for deterministic
systems and systems with worst-case disturbances and
uncertainties. In this paper, we develop a CBF framework for
safety of stochastic systems. We consider complete information
systems, in which the controller has access to the exact system
state, as well as incomplete information systems where the
state must be reconstructed from noisy measurements. In the
complete information case, we formulate a notion of barrier
functions that leads to sufficient conditions for safety with
probability 1. In the incomplete information case, we formulate
barrier functions that take an estimate from an extended
Kalman filter as input, and derive bounds on the probability
of safety as a function of the asymptotic error in the filter. We
show that, in both cases, the sufficient conditions for safety can
be mapped to linear constraints on the control input at each
time, enabling the development of tractable optimization-based
controllers that guarantee safety, performance, and stability.
Our approach is evaluated via simulation study on an adaptive
cruise control case study.
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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
- NSF-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
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IROS45743.2020.9341190
