Related papers: Computation of avoidance regions for driver assist…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
Obstacle avoidance is central to safe navigation, especially for robots with arbitrary and nonconvex geometries operating in cluttered environments. Existing Control Barrier Function (CBF) approaches often rely on analytic clearance…
We present a new approach for modeling avoidance constraints in 2D environments, in which waypoints are assigned to obstacle-free polyhedral regions. Constraints of this form are often formulated as mixed-integer programming (MIP) problems…
We consider nonconvex obstacle avoidance where a robot described by nonlinear dynamics and a nonconvex shape has to avoid nonconvex obstacles. Obstacle avoidance is a fundamental problem in robotics and well studied in control. However,…
This article examines a symbolic numerical approach to optimize a vehicle's track for autonomous driving and collision avoidance. The new approach uses the classical cost function definition incorporating the essential aspects of the…
This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…
Safe trajectory planning for high-performance automated vehicles in an environment with both static and moving obstacles is a challenging problem. Part of the challenge is developing a formulation that can be solved in real-time while…
Real-world autonomous systems often employ probabilistic predictive models of human behavior during planning to reason about their future motion. Since accurately modeling human behavior a priori is challenging, such models are often…
We prove optimal regularity for the double obstacle problem when obstacles are given by solutions to Hamilton-Jacobi equations that are not $C^2$. When the Hamilton-Jacobi equation is not $C^2$ then the standard Bernstein technique fails…
This paper presents a method for local motion planning in unstructured environments with static and moving obstacles, such as humans. Given a reference path and speed, our optimization-based receding-horizon approach computes a local…
Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
This paper investigates a Hamilton-Jacobi (HJ) analysis to solve finite-horizon optimal control problems for high-dimensional systems. Although grid-based methods, such as the level-set method [1], numerically solve a general class of HJ…
Understanding collision avoidance behavior is of key importance in traffic safety research and for designing and evaluating advanced driver assistance systems and autonomous vehicles. While existing experimental work has primarily focused…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…