Rigid formation control of double-integrator systems

In this paper, we study rigid formation control systems modelled by double integrators. Two kinds of double-integrator formation systems are considered, namely formation stabilisation systems and flocking control systems. Novel observations on the measurement requirement, the null space and eigenvalues of the system Jacobian matrix will be provided, which reveal important properties of system dynamics and the associated convergence results.We also establish some new links between single-integrator formation systems and double-integrator formation systems via a parameterised Hamiltonian system, which, in addition, provide novel stability criteria for different equilibria in double-integrator formation systems by using available results in single-integrator formation systems.This work is supported by NICTA, which is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program. It is also partially supported by National Natural Science Foundation of China [grant number 61501282]. B. D. O. Anderson was supported by the ARC [grant number DP130103610]. H.-S. Ahn is supported by the National Research Foundation of Korea [grant number NRF- 2013R1A2A2A01067449]. Z. Sun is supported by the Prime Minister’s Australia Asia Incoming Endeavour Postgraduate Award from Australian Government

Robustness issues in double-integrator undirected rigid formation systems

In this paper we consider rigid formation control systems modelled by double integrators (including formation stabilization systems and flocking control systems), with a focus on their robustness property in the presence of distance mismatch. By introducing additional state variables we show the augmented double-integrator distance error system is self-contained, and we prove the exponential stability of the distance error systems via linearization analysis. As a consequence of the exponential stability, the distance error still converges in the presence of small and constant distance mismatches, while additional motions of the resulted formation will occur. We further analyze the rigid motions induced by constant mismatches for both double-integrator formation stabilisation systems and flocking control systems.This work was supported by the Australian Research Council (ARC) under grant DP130103610 and DP160104500. Z. Sun was supported by the Australian Prime Minister's Endeavour Postgraduate Award from Australian Government. The work of S. Mou was supported by funding from Northrop Grumman Corporation

Graph rigidity-based formation control of planar multi-agent systems

A multi-agent system is a network of interacting agents that collectively perform a complex task. This dissertation is concerned with the decentralized formation control of multi-agent systems moving in the plane. The formation problem is defined as designing control inputs for the agents so that they form and maintain a pre-defined, planar geometric shape. The focus is on three related problems with increasing level of complexity: formation acquisition, formation maneuvering, and target interception. Three different dynamic models, also with increasing level of complexity, are considered for the motion of the agents: the single-integrator model, the double-integrator model, and the full mechanical dynamic model. Rigid graph theory and Lyapunov theory are the primary tools utilized in this work for solving the aforementioned formation problems for the three models. The backstepping control technique also plays a key role in the cases of the double-integrator and full dynamic models. Starting with the single-integrator model, a basic formation acquisition controller is proposed that is only a function of the relative position of agents in an infinitesimally and minimally rigid graph. A Lyapunov analysis shows that the origin of the inter-agent distance error system is exponentially stable. It is then shown how an extra term can be added to the controller to enable formation maneuvering or target interception. The three controllers for the single-integrator model are used as a stepping stone and extended to the double-integrator model with the aid of backstepping. Finally, an actuator-level, formation acquisition control law is developed for multiple robotic vehicles that accounts for the vehicle dynamics. Specifically, a class of underactuated vehicles modeled by Euler-Lagrange-like equations is considered. The backstepping technique is again employed while exploiting the structural properties of the system dynamics. Computer simulations are provided throughout the dissertation to show the proposed control laws in action

Bearing-based formation control with second-order agent dynamics

We consider the distributed formation control problem for a network of agents using visual measurements. We propose solutions that are based on bearing (and optionally distance) measurements, and agents with double integrator dynamics. We assume that a subset of the agents can track, in addition to their neighbors, a set of static features in the environment. These features are not considered to be part of the formation, but they are used to asymptotically control the velocity of the agents. We analyze the convergence properties of the proposed protocols analytically and through simulations.Published versionSupporting documentatio

Taming mismatches in inter-agent distances for the formation-motion control of second-order agents

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.Comment: 14 pages, conditionally accepted in Automatic Control, IEEE Transactions o

Position and Orientation Based Formation Control of Multiple Rigid Bodies with Collision Avoidance and Connectivity Maintenance

This paper addresses the problem of position- and orientation-based formation control of a class of second-order nonlinear multi-agent systems in a $3$D workspace with obstacles. More specifically, we design a decentralized control protocol such that each agent achieves a predefined geometric formation with its initial neighbors, while using local information based on a limited sensing radius. The latter implies that the proposed scheme guarantees that the initially connected agents remain always connected. In addition, by introducing certain distance constraints, we guarantee inter-agent collision avoidance as well as collision avoidance with the obstacles and the boundary of the workspace. The proposed controllers employ a novel class of potential functions and do not require a priori knowledge of the dynamical model, except for gravity-related terms. Finally, simulation results verify the validity of the proposed framework