Risk-Bounded Control with Kalman Filtering and Stochastic Barrier Functions
This work addresses safety-critical control for autonomous systems like vehicles, but it is incremental as it builds on existing Stochastic Control Barrier Functions by integrating Kalman filtering.
The paper tackles the problem of designing probabilistic safe real-time controllers for systems with uncertainties and noisy measurements, achieving a method that bounds the probability of system failure to a desired value, as demonstrated in a lane-changing simulation with dense traffic.
In this paper, we study Stochastic Control Barrier Functions (SCBFs) to enable the design of probabilistic safe real-time controllers in presence of uncertainties and based on noisy measurements. Our goal is to design controllers that bound the probability of a system failure in finite-time to a given desired value. To that end, we first estimate the system states from the noisy measurements using an Extended Kalman filter, and compute confidence intervals on the filtering errors. Then, we account for filtering errors and derive sufficient conditions on the control input based on the estimated states to bound the probability that the real states of the system enter an unsafe region within a finite time interval. We show that these sufficient conditions are linear constraints on the control input, and, hence, they can be used in tractable optimization problems to achieve safety, in addition to other properties like reachability, and stability. Our approach is evaluated using a simulation of a lane-changing scenario on a highway with dense traffic.