Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

I. Introduction

Safety is crucial to many physical control dynamical systems, such as autonomous vehicles, industrial robots, chemical reactors, and air-traffic control systems [2], [4]. The existence of model inaccuracies and unknown disturbances poses a great challenge to the design of safe controllers for these systems.