Related papers: Collisionless Multi-Agent Path Planning in the Ham…
This paper addresses the motion planning problem for a team of aerial agents under high level goals. We propose a hybrid control strategy that guarantees the accomplishment of each agent's local goal specification, which is given as a…
In this paper, we propose a novel optimization-based trajectory planner that utilizes spherical harmonics to estimate the collision-free solution space around an agent. The space is estimated using a constrained over-determined…
This paper studies optimal consensus tracking problem of heterogeneous linear multi-agent systems. By introducing tracking error dynamics, the optimal tracking problem is reformulated as finding a Nash-equilibrium solution of a multi-player…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…
Planning collision-free paths for multi-robot systems (MRS) is a challenging problem because of the safety and efficiency constraints required for real-world solutions. Even though coupled path planning approaches provide optimal…
In this article we propose a distributed collision avoidance scheme for multi-agent unmanned aerial vehicles(UAVs) based on nonlinear model predictive control (NMPC),where other agents in the system are considered as dynamic obstacles with…
In this paper a deep reinforcement based multi-agent path planning approach is introduced. The experiments are realized in a simulation environment and in this environment different multi-agent path planning problems are produced. The…
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 objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal…
In this paper we treat optimal trajectory planning for an autonomous vehicle (AV) operating in dense traffic, where vehicles closely interact with each other. To tackle this problem, we present a novel framework that couples trajectory…
CASL-HJX is a computational framework designed for solving deterministic and stochastic Hamilton-Jacobi equations in two spatial dimensions. It provides a flexible and efficient approach to modeling front propagation problems, optimal…
We propose a novel numerical method for high dimensional Hamilton--Jacobi--Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework…
Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these…
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…
Efficient, collision-free motion planning is essential for automating large-scale manipulators like timber cranes. They come with unique challenges such as hydraulic actuation constraints and passive joints-factors that are seldom addressed…
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a…
The fundamental goal assignment problem for a multi-robot application aims to assign a unique goal to each robot while ensuring collision-free paths, minimizing the total movement cost. A plausible algorithmic solution to this NP-hard…
This paper addresses the design of an optimization-based cooperative path-following control law for multiple robotic vehicles that optimally balances the transient trade-off between coordination and path-following errors. To this end, we…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. In previous works (Akian, Fodjo, 2016 and…