An orthogonal basis approach to formation shape control

In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled variables that form an orthogonal space and uniquely characterize a tetrahedron formation in 3D. This orthogonal space incorporates constraints on the inter-agent distances and the signed volume of tetrahedron substructures. The formation is modeled using a directed graph with a leader-follower type configuration and single-integrator dynamics. We show that the proposed decentralized formation controller ensures the \textit{global} asymptotic stability and the local exponential stability of the desired formation for an \textit{n}-agent system with no ambiguities. Unlike previous work, this result is achieved without conditions on the tetrahedrons that form the desired formation or on the control gains.

An Orthogonal Basis Approach to Formation Shape Control (Extended Version).

This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in the agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, various simulation studies clarify and verify the proposed approach.

2-D Directed Formation Control Based on Bipolar Coordinates

This work proposes a novel 2-D formation control scheme for acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) based on bipolar coordinates with (almost) global convergence to the desired shape. Prescribed performance control is employed to devise a decentralized control law that avoids singularities and introduces robustness against external disturbances while ensuring predefined transient and steady-state performance for the closed-loop system. Furthermore, it is shown that the proposed formation control scheme can handle formation maneuvering, scaling, and orientation specifications simultaneously. Additionally, the proposed control law is implementable in agents' arbitrarily oriented local coordinate frames using only low-cost onboard vision sensors, which are favorable for practical applications. Finally, a formation maneuvering simulation study verifies the proposed approach. 

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In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary feedback variable for the purpose of preventing formation ambiguities. We introduce two variables that form an orthogonal space and uniquely characterize a triangular formation in two dimensions. We show that the resulting controller ensures the almost-global asymptotic stability of the desired formation for an $n$ -agent system without conditions on the triangulations of the desired formation or control gains.

Distance-Based Planar Formation Control using Orthogonal Variables

We introduce here a distance-based formation ma-neuvering control scheme for a group of nonholonomic mobile robots operating in 2D environments with unknown static obstacles. We merge the distance-based formation controller with the Vector Field Histogram method such that the robots temporarily separate into subsets of the full formation for obstacle avoidance purposes, thus facilitating the subsequent reassembly. The overall control system is decentralized since it only requires onboard sensors for inter-robot relative positioning and obstacle detection. We illustrate the proposed control via simulations for two typical obstacle avoidance scenarios.

Farid Sahebsara

Papers

Distance-Based Planar Formation Control using Orthogonal Variables

Distance-Based Formation Maneuvering of Mobile Robots with Static Obstacles