A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems

Abstract

The proven efficacy of learning-based control schemes strongly motivates their application to robotic systems operating in the physical world. However, guaranteeing correct operation during the learning process is currently an unresolved issue, which is of vital importance in safety-critical systems. We propose a general safety framework based on Hamilton-Jacobi reachability methods that can work in conjunction with an arbitrary learning algorithm. The method exploits approximate knowledge of the system dynamics to guarantee constraint satisfaction while minimally interfering with the learning process. We further introduce a Bayesian mechanism that refines the safety analysis as the system acquires new evidence, reducing initial conservativeness when appropriate while strengthening guarantees through real-time validation. The result is a least-restrictive, safety-preserving control law that intervenes only when (a) the computed safety guarantees require it, or (b) confidence in the computed guarantees decays in light of new observations. We prove theoretical safety guarantees combining probabilistic and worst-case analysis and demonstrate the proposed framework experimentally on a quadrotor vehicle. Even though safety analysis is based on a simple point-mass model, the quadrotor successfully arrives at a suitable controller by policygradient reinforcement learning without ever crashing, and safely retracts away from a strong external disturbance introduced during flight.

An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments

“…In our experiment, the vehicle needs to navigate through an unknown cluttered indoor environment to reach its goal (shown in Figure 1). For the BRS computation, we use the dynamics model in (13). We pre-map the environment using an open-source Simultaneous Localization and Mapping (SLAM) algorithm and the onboard stereo camera.…”

“…Even though stability is often desirable, it is insufficient to guarantee collision avoidance. In contrast, our formulation uses a stronger definition of safety, and is more in line with [15], [13], which characterize safety using reachable sets.…”

“…Apply the least restrictive control u(t) given by (10) 11 for every T seconds do 12 Obtain the current map M t of the environment using (11) 13 Warm-start the BRS computation using V last , M, and (12) 14 Obtain the new safe region, W t , by solving HJI-VI with the warm-started value function…”

Linear Model Predictive Safety Certification for Learning-Based Control

“…Closely related to the approach proposed in this paper, the concept of a safety framework for learning-based control emerged from robust reachability analysis, robust invariance, as well as classical Lyapunov-based methods [30], [11], [31], [32]. The concept consists of a safe set in the state space and a safety controller as originally proposed in [33] for the case of perfectly known system dynamics in the context of safety barrier functions.…”

“…Note that the model error between (11) and (13) is unbounded by definition, if we consider an unbounded domain as required by (3)…”