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We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…
This paper addresses the problem of navigation control of a general class of uncertain nonlinear multi-agent systems in a bounded workspace of $\mathbb{R}^n$ with static obstacles. In particular, we propose a decentralized control protocol…
This text presents the proofs of the technical facts underlying theoretical justification of the convergence and performance of the novel algorithm for reactive navigation of differential drive wheeled robots in dynamic uncertain…
Solving multiagent problems can be an uphill task due to uncertainty in the environment, partial observability, and scalability of the problem at hand. Especially in an urban setting, there are more challenges since we also need to maintain…
In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently…
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 investigates the collision-free control problem for multi-agent systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or…
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…
This paper presents an algorithm for the synchronization of blind agents (agents are unable to observe other agents, i.e. no communication) evolving on a connected Lie group $G$. We employ the method of extremum seeking control for…
In this paper, we consider the coordination control of a group of autonomous mobile agents with multiple leaders. Different interconnection topologies are investigated. At first, a necessary and sufficient condition is proved in the case of…
It has long been a prominent challenge in multi-agent systems to achieve distributed coverage of non-convex annulus environments while ensuring workload equalization among agents. To address this challenge, a distributed circumferential…
This paper addresses the problem of navigation control of a general class of 2nd order uncertain nonlinear multi-agent systems in a bounded workspace, which is a subset of $R^3$ , with static obstacles. In particular, we propose a…
Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized…
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution…
We prove an equivariant implicit function theorem for variational problems that are invariant under a varying symmetry group (corresponding to a bundle of Lie groups). Motivated by applications to families of geometric variational problems…
We are concerned with the relaxation and existence theories of a general class of geometrical minimisation problems, with action integrals defined via differential forms over fibre bundles. We find natural algebraic and analytic conditions…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
This article explores minimum of an extremal in the variational problem with delay under the degeneracy of the Weierstrass condition. Here for study the minimality of extremal, variations of the Weierstrass type are used in two forms: in…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…
This paper presents an approach to exploring a multi-objective reinforcement learning problem with Model-Agnostic Meta-Learning. The environment we used consists of a 2D vehicle equipped with a LIDAR sensor. The goal of the environment is…