Related papers: A Hamilton-Jacobi Formulation for Time-Optimal Pat…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
In this paper, we consider first order Hamilton-Jacobi (HJ) equations posed on a ``junction'', that is to say the union of a finite number of half-lines with a unique common point. For this continuous HJ problem, we propose a finite…
We present an algorithm for a multi-agent path planning problem with pattern coordination based on dynamic programming and a Hamilton-Jacobi-Bellman equation. This falls broadly into the class of partial differential equation (PDE) based…
To perform autonomous driving maneuvers, such as parallel or perpendicular parking, a vehicle requires continual speed and steering adjustments to follow a generated path. In consequence, the path's quality is a limiting factor of the…
Efficient path planning for autonomous mobile robots is a critical problem across numerous domains, where optimizing both time and energy consumption is paramount. This paper introduces a novel methodology that considers the dynamic…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is…
In this paper, a novel method for path planning of mobile robots is proposed, taking into account the non-holonomic turn radius constraints and finite dimensions of the robot. The approach involves rasterizing the environment to generate a…
In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal…
This paper addresses the problem of finding multiple near-optimal, spatially-dissimilar paths that can be considered as alternatives in the decision making process, for finding optimal corridors in which to construct a new road. We further…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…
This paper presents a method based on linear programming for trajectory planning of automated vehicles, combining obstacle avoidance, time scheduling for the reaching of waypoints and time-optimal traversal of tube-like road segments.…
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…
Numerical methods for the optimal transport problem is an active area of research. Recent work of Kitagawa and Abedin shows that the solution of a time-dependent equation converges exponentially fast as time goes to infinity to the solution…
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…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
Path planning is an essential component of autonomous driving. A global planner is responsible for the high-level planning. It basically performs a shortest-path search on a known map, thereby defining waypoints used to control the local…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…