Related papers: Variational collision avoidance problems on Rieman…

Autonomous vehicles are suited for continuous area patrolling problems. Finding an optimal patrolling strategy can be challenging due to unknown environmental factors, such as wind or landscape; or autonomous vehicles' constraints, such as…

Collision avoidance requires tradeoffs in planning time horizons. Depending on the planner, safety cannot always be guaranteed in uncertain environments given map updates. To mitigate situations where the planner leads the vehicle into a…

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…

Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…

We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

This article proposes a modular optimal control framework for local three-dimensional ellipsoidal obstacle avoidance, exemplarily applied to model predictive path-following control. Static as well as moving obstacles are considered. Central…

This paper addresses the problem of decentralized abstractions for multiple mobile manipulators with 2nd order dynamics. In particular, we propose decentralized controllers for the navigation of each agent among predefined regions of…

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

Navigating through intersections is one of the main challenging tasks for an autonomous vehicle. However, for the majority of intersections regulated by traffic lights, the problem could be solved by a simple rule-based method in which the…

A central aspect of robotic motion planning is collision avoidance, where a multitude of different approaches are currently in use. Optimization-based motion planning is one method, that often heavily relies on distance computations between…

Coordinating multiple autonomous agents to reach a target region while avoiding collisions and maintaining communication connectivity is a core problem in multi-agent systems. In practice, agents have a limited communication range. Thus,…

The collision of a fixed point with a switching manifold (or border) in a piecewise-smooth map can create many different types of invariant sets. This paper explores two techniques that, combined, establish a chaotic attractor is created in…

We derive a continuum model for incompatible elasticity as a variational limit of a family of discrete nearest-neighbor elastic models. The discrete models are based on discretizations of a smooth Riemannian manifold $(M,\mathfrak{g})$,…

We focus on decentralized navigation among multiple non-communicating rational agents at \emph{uncontrolled} intersections, i.e., street intersections without traffic signs or signals. Avoiding collisions in such domains relies on the…

In this paper, we present a novel method for using Riemannian Motion Policies on volumetric maps, shown in the example of obstacle avoidance for Micro Aerial Vehicles (MAVs). While sampling or optimization-based planners are widely used for…

An impulsive feedback-adaptive control is developed in order to drive trajectories of a dynamical system towards an invariant manifold with fixed and spaced impulsive controls. The approach requires the explicit knowledge of the set of…

With the rapid development of autonomous driving, the attention of academia has increasingly focused on the development of anti-collision systems in emergency scenarios, which have a crucial impact on driving safety. While numerous…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

By an undirected rigid formation of mobile autonomous agents is meant a formation based on graph rigidity in which each pair of "neighboring" agents is responsible for maintaining a prescribed target distance between them. In a recent paper…