How do you ensure safety when the robot behavior is only known with uncertainty? We propose Probabilistic Safety Constraints for High Relative Degree System Dynamics. We show how to learn a system with a Bayesian Learning method that keeps track of uncertainty while ensuring safety upto an acceptable risk factor, for example, 99.999%. We use the framework of Control Barrier Functions and extend it to higher-order relative degree systems while propagating uncertainty in model dynamics to the safety constraints.
This paper focuses on learning a model of system dynamics online while satisfying safety constraints. Our motivation is to avoid offline system identification or hand-specified dynamics models and allow a system to safely and autonomously estimate and adapt its own model during online operation. Given streaming observations of the system state, we use Bayesian learning to obtain a distribution over the system dynamics. In turn, the distribution is used to optimize the system behavior and ensure safety with high probability, by specifying a chance constraint over a control barrier function.