Generalized controllers for rigid formation stabilization with application to event-based controller design

This paper discusses generalized controllers for rigid formation shape stabilization. We provide unified analysis to show convergence using different controllers reported in the literature, and further prove an exponential stability of the formation system when using the general form of shape controllers. We also show that different agents can use different controllers for controlling different distances to achieve a desired rigid formation, which enables the implementation of heterogeneous agents in practice for formation shape control. We further propose an event-triggered rigid formation control scheme based on the generalized controllers. The triggering condition, event function and convergence analysis are discusse

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

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

Certifying non-existence of undesired locally stable equilibria in formation shape control problems

A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a large and growing literature has recently emerged on distance-based formation shape control, global stability properties remain a significant open problem. Even in four-agent formations, the basic question of whether or not there can exist locally stable incorrect equilibrium shapes remains open. This paper shows how this question can be answered for any size formation in principle using semidefinite programming techniques for semialgebraic problems, involving solutions sets of polynomial equations, inequations, and inequalities.Comment: 6 pages; to appear in the 2013 IEEE Multiconference on Systems and Contro

Exponential stability for formation control systems with generalized controllers: A unified approach

This paper discusses generalized controllers for distance-based rigid formation shape stabilization and aims to provide a unified approach for the convergence analysis. We consider two types of formation control systems according to different characterizations of target formations: minimally rigid target formation and non-minimally rigid target formation. For the former case, we firstly prove the local exponential stability for rigid formation systems when using a general form of shape controllers with certain properties. From this viewpoint, different formation controllers proposed in previous literature can be included in a unified framework. We then extend the result to the case that the target formation is non-minimally rigid, and show that exponential stability of the formation system is still guaranteed with generalized controllers

Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements

In this paper, we discuss quantization effects in rigid formation control systems when target formations are described by inter-agent distances. Because of practical sensing and measurement constraints, we consider in this paper distance measurements in their quantized forms. We show that under gradient-based formation control, in the case of uniform quantization, the distance errors converge locally to a bounded set whose size depends on the quantization error, while in the case of logarithmic quantization, all distance errors converge locally to zero. A special quantizer involving the signum function is then considered with which all agents can only measure coarse distances in terms of binary information. In this case, the formation converges locally to a target formation within a finite time. Lastly, we discuss the effect of asymmetric uniform quantization on rigid formation control.Comment: 29 pages, International Journal of Robust and Nonlinear Control 201