Related papers: Variational collision avoidance problems on Rieman…

This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly…

Aircraft collision avoidance systems is critical to modern aviation. These systems are designed to predict potential collisions between aircraft and recommend appropriate avoidance actions. Creating effective collision avoidance systems…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

Safety is the primary concern when it comes to air traffic. In-flight safety between Unmanned Aircraft Vehicles (UAVs) is ensured through pairwise separation minima, utilizing conflict detection and resolution methods. Existing methods…

This paper presents the use of robust model predictive control for the design of an intent-aware collision avoidance system for multi-agent aircraft engaged in horizontal maneuvering scenarios. We assume that information from other agents…

Autonomous agents such as self-driving cars or parcel robots need to recognize and avoid possible collisions with obstacles in order to move successfully in their environment. Humans, however, have learned to predict movements intuitively…

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…

Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and…

We study a graph pathfinding problem Distance-$r$ Independent Unlabeled Multi-Agent Pathfinding, finding a set of collision-free paths between two sets where agents must stay at pairwise distance at least $r+1$ at all times. This additional…

We address the problem of planning collision-free paths for multiple agents using optimization methods known as proximal algorithms. Recently this approach was explored in Bento et al. 2013, which demonstrated its ease of parallelization…

The environment plays a critical role in multi-agent navigation by imposing spatial constraints, rules, and limitations that agents must navigate around. Traditional approaches treat the environment as fixed, without exploring its impact on…

In this paper, variational techniques are used to analyze the dynamics of nonholonomic mechanical systems with impacts. Implicit nonholonomic smooth Lagrangian and Hamiltonian systems are extended to a nonsmooth context appropriate for…

We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…

Navigation and guidance of autonomous vehicles is a fundamental problem in robotics, which has attracted intensive research in recent decades. This report is mainly concerned with provable collision avoidance of multiple autonomous vehicles…

In this article, we explore the feasibility of applying proximal policy optimization, a state-of-the-art deep reinforcement learning algorithm for continuous control tasks, on the dual-objective problem of controlling an underactuated…

This work in progress considers reachability-based safety analysis in the domain of autonomous driving in multi-agent systems. We formulate the safety problem for a car following scenario as a differential game and study how different…

We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models self-collective behaviour with intrinsic interactions that…