Related papers: Reduction of Necessary Conditions for the Variatio…
We consider left-invariant optimal control problems on connected Lie groups such that generic stabilizer of the coadjoint action is connected and has dimension not more than 1. We introduce a construction for symmetries of the exponential…
Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and…
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces \cite{arXiv:1912.04234} by including the agents' body size. The influence of the body size on…
Some model reduction techniques for multiple time-scale dynamical systems make use of the identification of low dimensional slow invariant attracting manifolds (SIAM) in order to reduce the dimensionality of the phase space by restriction…
In this paper, we present an innovative risk-bounded motion planning methodology for stochastic multi-agent systems. For this methodology, the disturbance, noise, and model uncertainty are considered; and a velocity obstacle method is…
Motion planning in environments with multiple agents is critical to many important autonomous applications such as autonomous vehicles and assistive robots. This paper considers the problem of motion planning, where the controlled agent…
Velocity Obstacles (VO) methods form a paradigm for collision avoidance strategies among moving obstacles and agents. While VO methods perform well in simple multi-agent environments, they don't guarantee safety and can show overly…
This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…
Cooperatively planning for multiple agents has been proposed as a promising method for strategic and motion planning for automated vehicles. By taking into account the intent of every agent, the ego agent can incorporate future interactions…
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…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We study the equilibrium problem on general Riemannian manifolds. The results on existence of solutions and on the convex structure of the solution set are established. Our approach consists in relating the equilibrium problem to a suitable…
In multi-agent navigation, agents need to move towards their goal locations while avoiding collisions with other agents and static obstacles, often without communication with each other. Existing methods compute motions that are optimal…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
This research focuses on trajectory planning problems for autonomous vehicles utilizing numerical optimal control techniques. The study reformulates the constrained optimization problem into a nonlinear programming problem, incorporating…
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…
The minimum constraint removal problem seeks to find the minimum number of constraints, i.e., obstacles, that need to be removed to connect a start to a goal location with a collision-free path. This problem is NP-hard and has been studied…
This paper presents a collision avoidance method for elliptical agents traveling in a two-dimensional space. We first formulate a separation condition for two elliptical agents utilizing a signed distance from a supporting line of an agent…
This paper presents a distributed adaptive control strategy for multi-agent systems with heterogeneous dynamics and collision avoidance. We propose an adaptive control strategy designed to ensure leader-following formation consensus while…