Related papers: Hamilton--Jacobi Reachability for Spacecraft Colli…
This paper develops a hierarchical games-in-games control architecture for hybrid stochastic systems governed by regime-switching jump-diffusions. We model the interplay between continuous state dynamics and discrete mode transitions as a…
The Hamilton-Jacobi formalism for a geodetic brane-like universe described by the Regge-Teitelboim model is developed. We focus on the description of the complete set of Hamiltonians that ensure the integrability of the model in addition to…
This paper presents an autonomous guidance and control strategy for a satellite swarm that enables scalable distributed space structures for innovative science and business opportunities. The averaged $J_2$ orbital parameters that describe…
A Hamilton-Poisson system is an approach for the motion of a spacecraft around an asteroid or for the motion of an underwater vehicle. We construct a coordinate chart on the symplectic leaf which contains a specific generic equilibrium…
The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…
Backward reachable tubes (BRTs), computed via viscous Hamilton-Jacobi (HJ) partial differential equations, provide principled safety certificates for learned controllers and planning algorithms in trustworthy machine learning. However,…
In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and…
The minimal area for surfaces whose border are rectangular and circular loops are calculated using the Hamilton-Jacobi (HJ) equation. This amounts to solve the HJ equation for the value of the minimal area, without calculating the shape of…
Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two…
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models…
Many robotic systems must follow planned paths yet pause safely and resume when people or objects intervene. We present an output-space method for systems whose tracked output can be feedback-linearized to a double integrator (e.g.,…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
We study the planar problem of two satellites attracted by a center of force. Assuming that the center of mass of the two-satellite system is on a circular orbit around the center of force and using Levi-Civita regularization we prove the…
Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road -- a key challenge in doing so is…
This paper investigates the application of reachability analysis to the re-entry problem faced by vehicles entering Earth's atmosphere. The study delves into the time evolution of reachable sets for the system, particularly when subject to…
Classically, the optimal control problem in the presence of an adversary is formulated as a two-player zero-sum differential game or an $H_\infty$ control problem. The solution to these problems can be obtained by solving the…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
In this paper, we first give the regular point reduction and the two types of Hamilton-Jacobi equation for a regular controlled Hamiltonian (RCH) system with symmetry and momentum map on the generalization of a semidirect product Lie group.…
As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as…
Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in…