Related papers: An Efficient Semi-Real-Time Algorithm for Path Pla…
We consider the optimal control of solutions of first order Hamilton-Jacobi equations, where the Hamiltonian is convex with linear growth. This models the problem of steering the propagation of a front by constructing an obstacle. We prove…
We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic,…
Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential…
Recently, anchor-based trajectory prediction methods have shown promising performance, which directly selects a final set of anchors as future intents in the spatio-temporal coupled space. However, such methods typically neglect a deeper…
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, instead of focusing on the value…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning…
We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and…
This paper focuses on spatial time-optimal motion planning, a generalization of the exact time-optimal path following problem that allows the system to plan within a predefined space. In contrast to state-of-the-art methods, we drop the…
We investigate feedback control for infinite horizon optimal control problems for partial differential equations. The method is based on the coupling between Hamilton-Jacobi-Bellman (HJB) equations and model reduction techniques. It is…
This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately,…
This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid…
In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is…
We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…