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Connected Autonomous Vehicles will make autonomous intersection management a reality replacing traditional traffic signal control. Autonomous intersection management requires time and speed adjustment of vehicles arriving at an intersection…
Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…
Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this…
Robotic motion optimization often focuses on task-specific solutions, overlooking fundamental motion principles. Building on Riemannian geometry and the calculus of variations (often appearing as indirect methods of optimal control), we…
We consider minimizing a nonconvex, smooth function $f$ on a Riemannian manifold $\mathcal{M}$. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to…
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical…
Multi-agent pathfinding (MAPF) is concerned with planning collision-free paths for a team of agents from their start to goal locations in an environment cluttered with obstacles. Typical approaches for MAPF consider the locations of…
We study variational problems for integral invariants, which are defined as integrations of invariant functions of the second fundamental form, of a smooth map between pseudo-Riemannian manifolds. We derive the first variational formulae…
We consider the problem of a quantum particle interacting with $N$ attractive point $\delta$-interactions in two and three dimensional Riemannian manifolds and discuss its some spectral properties. The main aim of this paper is to give a…
A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…
In the real world, unmanned surface vehicles (USV) often need to coordinate with each other to accomplish specific tasks. However, achieving cooperative control in multi-agent systems is challenging due to issues such as non-stationarity…
This article proposes a novel control architecture using a centralized nonlinear model predictive control (CNMPC) scheme for controlling multiple micro aerial vehicles (MAVs). The control architecture uses an augmented state system to…
We focus on navigation among rational, non-communicating agents at unsignalized street intersections. Following collision-free motion under such settings demands nuanced implicit coordination among agents. Often, the structure of these…
For autonomous agents to successfully operate in real world, the ability to anticipate future motions of surrounding entities in the scene can greatly enhance their safety levels since potentially dangerous situations could be avoided in…
Traditional task assignment approaches for multi-agent motion control do not take the possibility of collisions into account. This can lead to challenging requirements for path planning. We derive an assignment method that not only…
This paper addresses the challenge of navigating unmanned aerial vehicles in contested environments by introducing a cooperative multi-agent framework that increases the likelihood of safe UAV traversal. The approach involves two types of…
This paper presents a novel methodology to enforce motion safety guarantees even in the event of a sudden loss of control capabilities by any agent within a multi-agent system. This passive safety methodology permits the replacement of…