Minh Hoang Trinh

The Fermat-Weber location problem in single integrator dynamics using only local bearing angles

This paper proposes a modified gradient control law to solve the Fermat-Weber location problem. The control law may guide an autonomous agent to the point that minimizes the weighted sum distance with regard to some stationary beacons using only bearing measurements. Based on previous results from Fermat-Weber location problem and Lyapunov stability theory, we prove that the agent will globally asymptotically reach the destination only using local bearing measurements. We also consider a scenario when the beacons are not stationary. Simulation results are provided to verify the mathematical analysis.

Comments on Global stabilization of rigid formations in the plane [Automatica 49 (2013) 14361441]

This paper shows that the modified gradient control law proposed in Tian and Wang (2013) does not globally stabilize rigid formation shapes. Also, further analysis on the control law and a numerical example showing that the control law cannot drive the agents out from a stable incorrect equilibrium of the corresponding gradient control system are provided.

Distance-based control of K4 formation with almost global convergence

In this paper, we propose a distance-based formation control strategy that can enable four mobile agents, which are modelled by a group of single-integrators, to achieve the desired formation shape specified by using six consistent inter-agent distances in a 2-dimensional space. The control law is closely related to a gradient-based control law formed from a potential function reflecting the error between the actual inter-agent distances and the desired inter-agent distances. There are already control strategies achieving the same objective in a distance-based control manner in the literature, but the results do not yet include a global as opposed to local stability analysis. We propose a control strategy modified from the existing gradient-based control law so that we can achieve almost global convergence to the desired formation shape, and the control law uses known properties for an associated formation shape control problem involving a four-agent tetrahedron formation in 3-dimensional space. Simulation results verifying our analysis are also presented.

Control of a mobile agent using only bearing measurements in triangular region

We introduce a new control strategy to navigate in the plane for an autonomous agent (mobile robot, unmanned vehicle, etc). The strategy uses only bearing measurements from the three noncolinear stationary beacons. Under some assumptions, this strategy is proved to drive the agent to all desired positions inside the triangle region formed by the beacons. An application and simulation results are also given.

Matrix-weighted consensus and its applications

Abstract This paper proposes the matrix-weighted consensus algorithm, which is a generalization of the consensus algorithm. Given a networked dynamical system where the interconnections between agents are weighted by nonnegative definite matrices, it is shown that consensus and clustering phenomena naturally exist. We examine algebraic and algebraic graph conditions for achieving a consensus.

Distance-based directed formation control in three-dimensional space

This paper concentrates on the distance-based formation control problem in three-dimensional space. The objective is to achieve and maintain the formation of overall group of a multi-agent system, whose interaction graph is acyclic minimally persistent. The gradient-based control law derived from a class of potential functions is considered to address this problem. The trajectories of agents converge to a set of equilibria under the proposed control law. Every desired equilibrium, where all inter-agent distance constraints are satisfied, is locally exponentially stable and the undesired equilibrium set is repulsive.

Further analysis on graph rigidity

This paper presents novel results on the symmetric rigidity matrix. Based on these results, new concepts in rigidity theory are proposed, including the worst-case, and imbalance rigidity indices of planar frameworks. These new indices are scale free and could be useful in rigid network synthesis problems.