Hamilton-Jacobi reachability: A brief overview and recent advances
Somil Bansal,Mo Chen,Sylvia L. Herbert,Claire J. Tomlin +3 more
- 01 Dec 2017
- pp 2242-2253
571
TL;DR: In this paper, the authors present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets.
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Abstract: Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights.
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Citations
Reachability of Chen-Fliess series: A Gradient Descent Approach
27 Sep 2022
TL;DR: In this paper , a gradient descent algorithm based on the Chen-Fliess formalism is proposed for computing output reachable sets, which requires extending the notion of Gâteaux derivatives to this domain together with conditions for its existence.
Efficient Computation of Inner Approximations of Reachable Sets for a Verified Motion Planning Concept
Christopher Bohn,Joel Riegert,Florian Siebenrock,Manuel Schwartz,Sören Hohmann +4 more
TL;DR: This paper presents a novel method for computing convex inner approximations of reachable sets for non-linear input-affine systems, integrated into a motion planning concept for mobile robots, ensuring planned motions can be reached by an accurate model.
Computing Robust Forward Invariant Sets of Multidimensional Non-linear Systems Via Geometric Deformation of Polytopes
Taha Ameen,Shayok Mukhopadhyay,Nasser Qaddoumi +2 more
Abstract: This article develops an algorithm to compute the sequences of polytopic robust forward invariant sets (RFIS) that vary in size for a nonlinear dynamical system. This is done through a novel approach that geometrically deforms a polytope into an invariant set using a sequence of homeomorphisms, based on an invariance condition that only needs to be satisfied at a finite set of test points. A fast computational test is also developed to check if a given polytopic set is an RFIS. Our approach is applicable to arbitrary Lipschitz continuous nonlinear systems in the presence of bounded additive disturbances, and its versatility is presented through simulation results on a variety of nonlinear dynamical systems in two and three dimensions.
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Sever Topan,Karen Leung,Yuxiao Chen,Pritish Tupekar,Edward Schmerling,Jonas Nilsson,Michael Cox,Marco Pavone +7 more
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Conservative and Adaptive Penalty for Model-Based Safe Reinforcement Learning
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