Journal ArticleDOI
Hamilton–Jacobi Formulation for Reach–Avoid Differential Games
Kostas Margellos,John Lygeros +1 more
TLDR
The main advantage of the approach proposed is that it can be applied to a general class of target-hitting continuous dynamic games with nonlinear dynamics, and has very good properties in terms of its numerical solution, since the value function and the Hamiltonian of the system are both continuous.Abstract:
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics, and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems in hybrid systems. Earlier approaches to reach-avoid computations are either restricted to linear systems, or face numerical difficulties due to possible discontinuities in the Hamiltonian of the optimal control problem. The main advantage of the approach proposed in this paper is that it can be applied to a general class of target-hitting continuous dynamic games with nonlinear dynamics, and has very good properties in terms of its numerical solution, since the value function and the Hamiltonian of the system are both continuous. The performance of the proposed method is demonstrated by applying it to a case study, which involves the target-hitting problem of an underactuated underwater vehicle in the presence of obstacles.read more
Citations
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Journal ArticleDOI
Convex Computation of the Region of Attraction of Polynomial Control Systems
Didier Henrion,Milan Korda +1 more
TL;DR: The ROA can be computed by solving a convex linear programming (LP) problem over the space of measures and this problem can be solved approximately via a classical converging hierarchy of convex finite-dimensional linear matrix inequalities (LMIs).
Journal ArticleDOI
Optimization-Based Collision Avoidance
TL;DR: A novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable constraints using strong duality of convex optimization on a controlled object whose goal is to avoid obstacles while moving in an $n$ -dimensional space is presented.
Journal ArticleDOI
Convex computation of the maximum controlled invariant set for polynomial control systems
TL;DR: This work describes a hierarchy of finite-dimensional linear matrix inequality (LMI) relaxations whose optimal values converge to the volume of the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems.
Journal ArticleDOI
A Noncooperative Game Approach to Autonomous Racing
Alexander Liniger,John Lygeros +1 more
TL;DR: In this article, the authors consider autonomous racing of two cars and present an approach to formulate racing decisions as a noncooperative nonzero-sum game, where the players aim to fulfill static track constraints as well as avoid collision with each other.
Journal ArticleDOI
On infusing reachability-based safety assurance within planning frameworks for human–robot vehicle interactions:
Karen Leung,Edward Schmerling,Mengxuan Zhang,Mo Chen,John Talbot,J. Christian Gerdes,Marco Pavone +6 more
TL;DR: A minimally interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled counterpart while respecting static obstacles such as a road boundary wall is introduced.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
Book
Level set methods and fast marching methods : evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
TL;DR: In this paper, the Hamilton-Jacobi equations and associated theory are used to formulate the interface propagation problem and then algorithms for the initial and boundary value formulations are proposed for semi-conductor manufacturing.
Journal ArticleDOI
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games
TL;DR: An algorithm for computing the set of reachable states of a continuous dynamic game based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation.