Related papers: Reduction of Necessary Conditions for the Variatio…
Finding feasible and collision-free paths for multiple nonlinear agents is challenging in the decentralized scenarios due to limited available information of other agents and complex dynamics constraints. In this paper, we propose a fast…
This work presents a distributed MPC-based approach to solving the problem of multi-agent point-to-point transition with optimization-based collision avoidance. The problem is formulated, motivated by the work on collision avoidance for…
This paper presents a three dimensional collision avoidance approach for aerial vehicles inspired by coordinated behaviors in biological groups. The proposed strategy aims to enable a group of vehicles to converge to a common destination…
We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We present a novel algorithm for reciprocal collision avoidance between heterogeneous agents of different shapes and sizes. We present a novel CTMAT representation based on medial axis transform to compute a tight fitting bounding shape for…
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the…
In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale…
Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank…
This paper introduces an approach to address the target enclosing problem using non-holonomic multiagent systems, where agents self-organize on the enclosing shape around a fixed target. In our approach, agents independently move toward the…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
Recent work on the multi-agent pathfinding problem (MAPF) has begun to study agents with motion that is more complex, for example, with non-unit action durations and kinematic constraints. An important aspect of MAPF is collision detection.…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
In this article we propose a distributed collision avoidance scheme for multi-agent unmanned aerial vehicles(UAVs) based on nonlinear model predictive control (NMPC),where other agents in the system are considered as dynamic obstacles with…
We present a scalable and effective multi-agent safe motion planner that enables a group of agents to move to their desired locations while avoiding collisions with obstacles and other agents, with the presence of rich obstacles,…
This work investigates model order reduction for time-dependent parametrized variational inequalities, with a focus on discrete contact problems. As a prototypical example, we consider an agent-based crowd model [Maury et al., 2011] in…
Research on crowd simulation has important and wide range of applications. The main difficulty is how to lead all particles with a same and simple rule, especially when particles are numerous. In this paper, we firstly propose a two…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…
The cooperation of connected and automated vehicles (CAVs) has shown great potential in improving traffic efficiency during intersection management. Existing research mainly focuses on intersections where lane changing is prohibited, which…
Next generation Unmanned Aerial Vehicles (UAVs) must reliably avoid moving obstacles. Existing dynamic collision avoidance methods are effective where obstacle trajectories are linear or known, but such restrictions are not accurate to many…