7 research outputs found
Parameter-Conditioned Reachable Sets for Updating Safety Assurances Online
Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing
the safety of autonomous systems. However, the provided safety assurances are
often predicated on the assumption that once deployed, the system or its
environment does not evolve. Online, however, an autonomous system might
experience changes in system dynamics, control authority, external
disturbances, and/or the surrounding environment, requiring updated safety
assurances. Rather than restarting the safety analysis from scratch, which can
be time-consuming and often intractable to perform online, we propose to
compute \textit{parameter-conditioned} reachable sets. Assuming expected system
and environment changes can be parameterized, we treat these parameters as
virtual states in the system and leverage recent advances in high-dimensional
reachability analysis to solve the corresponding reachability problem offline.
This results in a family of reachable sets that is parameterized by the
environment and system factors. Online, as these factors change, the system can
simply query the corresponding safety function from this family to ensure
system safety, enabling a real-time update of the safety assurances. Through
various simulation studies, we demonstrate the capability of our approach in
maintaining system safety despite the system and environment evolution
Patching Neural Barrier Functions Using Hamilton-Jacobi Reachability
Learning-based control algorithms have led to major advances in robotics at
the cost of decreased safety guarantees. Recently, neural networks have also
been used to characterize safety through the use of barrier functions for
complex nonlinear systems. Learned barrier functions approximately encode and
enforce a desired safety constraint through a value function, but do not
provide any formal guarantees. In this paper, we propose a local dynamic
programming (DP) based approach to "patch" an almost-safe learned barrier at
potentially unsafe points in the state space. This algorithm, HJ-Patch, obtains
a novel barrier that provides formal safety guarantees, yet retains the global
structure of the learned barrier. Our local DP based reachability algorithm,
HJ-Patch, updates the barrier function "minimally" at points that both (a)
neighbor the barrier safety boundary and (b) do not satisfy the safety
condition. We view this as a key step to bridging the gap between
learning-based barrier functions and Hamilton-Jacobi reachability analysis,
providing a framework for further integration of these approaches. We
demonstrate that for well-trained barriers we reduce the computational load by
2 orders of magnitude with respect to standard DP-based reachability, and
demonstrate scalability to a 6-dimensional system, which is at the limit of
standard DP-based reachability.Comment: 8 pages, submitted to IEEE Conference on Decision and Control (CDC),
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A review of safe online learning for nonlinear control systems
Learning for autonomous dynamic control systems that can adapt to unforeseen environmental changes are of great interest but the realisation of a practical and safe online learning algorithm is incredibly challenging. This paper highlights some of the main approaches for safe online learning of stabilisable nonlinear control systems with a focus on safety certification for stability. We categorise a non-exhaustive list of salient techniques, with a focus on traditional control theory as opposed to reinforcement learning and approximate dynamic programming. This paper also aims to provide a simplified overview of techniques as an introduction to the field. It is the first paper to our knowledge that compares key attributes and advantages of each technique in one paper