3,699 research outputs found
Safe & robust reachability analysis of hybrid systems
Hybrid systems—more precisely, their mathematical models—can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability—namely, the reflexive and transitive closure of a transition relation—can be unsafe, i.e., it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states.
Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust w.r.t. small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation
Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems
Robust motion planning entails computing a global motion plan that is safe
under all possible uncertainty realizations, be it in the system dynamics, the
robot's initial position, or with respect to external disturbances. Current
approaches for robust motion planning either lack theoretical guarantees, or
make restrictive assumptions on the system dynamics and uncertainty
distributions. In this paper, we address these limitations by proposing the
robust rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates
forward reachability analysis directly into sampling-based control trajectory
synthesis. We prove that Robust-RRT is probabilistically complete (PC) for
nonlinear Lipschitz continuous dynamical systems with bounded uncertainty. In
other words, Robust-RRT eventually finds a robust motion plan that is feasible
under all possible uncertainty realizations assuming such a plan exists. Our
analysis applies even to unstable systems that admit only short-horizon
feasible plans; this is because we explicitly consider the time evolution of
reachable sets along control trajectories. Thanks to the explicit consideration
of time dependency in our analysis, PC applies to unstabilizable systems. To
the best of our knowledge, this is the most general PC proof for robust
sampling-based motion planning, in terms of the types of uncertainties and
dynamical systems it can handle. Considering that an exact computation of
reachable sets can be computationally expensive for some dynamical systems, we
incorporate sampling-based reachability analysis into Robust-RRT and
demonstrate our robust planner on nonlinear, underactuated, and hybrid systems.Comment: 16 pages of main text + 5 pages of appendix, 5 figures, submitted to
the 2022 International Symposium on Robotics Researc
Safe Neighborhood Computation for Hybrid System Verification
For the design and implementation of engineering systems, performing
model-based analysis can disclose potential safety issues at an early stage.
The analysis of hybrid system models is in general difficult due to the
intrinsic complexity of hybrid dynamics. In this paper, a simulation-based
approach to formal verification of hybrid systems is presented.Comment: In Proceedings HAS 2014, arXiv:1501.0540
Approximated Symbolic Computations over Hybrid Automata
Hybrid automata are a natural framework for modeling and analyzing systems
which exhibit a mixed discrete continuous behaviour. However, the standard
operational semantics defined over such models implicitly assume perfect
knowledge of the real systems and infinite precision measurements. Such
assumptions are not only unrealistic, but often lead to the construction of
misleading models. For these reasons we believe that it is necessary to
introduce more flexible semantics able to manage with noise, partial
information, and finite precision instruments. In particular, in this paper we
integrate in a single framework based on approximated semantics different over
and under-approximation techniques for hybrid automata. Our framework allows to
both compare, mix, and generalize such techniques obtaining different
approximated reachability algorithms.Comment: In Proceedings HAS 2013, arXiv:1308.490
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