Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators

This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies. The dual quaternion algebra is used to model the agents' poses and also in the distributed control laws, making the proposed technique easily applicable to time-varying formation control of general robotic systems. The proposed pose consensus protocol has guaranteed convergence when the interaction among the agents is represented by directed graphs with directed spanning trees, which is a more general result when compared to the literature on formation control. In order to illustrate the proposed pose consensus protocol and its extension to the problem of formation control, we present a numerical simulation with a large number of free-flying agents and also an application of cooperative manipulation by using real mobile manipulators

Properties of interconnected negative imaginary systems and extension to formation‐containment control of networked multi‐UAV systems with experimental validation results

This paper extends the properties of a positive feedback interconnection of two negative imaginary (NI) systems to multi-agent NI systems and proposes a new formation-containment control methodology relying on the characteristic loci technique. Inspired by recent applications of NI and passivity-based control techniques in the multi-agent systems (MAS) domain, a new formation-tracking and containment control scheme is developed for a class of networked multi-UAV systems. The proposed scheme offers a two-stage and two-loop control configuration where the inner loop uses a cascaded PID controller to ensure stable hovering of the UAVs, and the outer loop deploys a distributed “mixed” SNI and strictly passive controller to achieve the formation-containment objectives. This scheme works with a dynamic output feedback control strategy; hence, it offers advantages when the full-state measurement is not possible. In contrast to the well-known Lyapunov theory-based cooperative control schemes, the present one exploits the characteristic loci technique to prove the formation-tracking and containment phenomena theoretically. The paper also provides experimental validation results on a fleet of Crazyflie 2.1 nano quadcopters.<br/

Robust Formation Control for Networked Robotic Systems Using Negative Imaginary Dynamics

This paper proposes a consensus-based formation tracking scheme for multi-robot systems utilizing the Negative Imaginary (NI) theory. The proposed scheme applies to a class of networked robotic systems that can be modelled as a group of single integrator agents with stable uncertainties connected via an undirected graph. NI/SNI property of networked agents facilitates the design of a distributed Strictly Negative Imaginary (SNI) controller to achieve the desired formation tracking. A new theoretical proof of asymptotic convergence of the formation tracking trajectories is derived based on the integral controllability of a networked SNI systems. The proposed scheme is an alternative to the conventional Lyapunov-based formation tracking schemes. It offers robustness to NI/SNI-type model uncertainties and fault-tolerance to a sudden loss of robots due to hardware/communication fault. The feasibility and usefulness of the proposed formation tracking scheme were validated by lab-based real-time hardware experiments involving miniature mobile robots

Scale-free Linear Observer-based Protocol Design for Global Regulated State Synchronization of Homogeneous Multi-agent Systems with Non-introspective Agents Subject to Input Saturation

This paper studies global regulated state synchronization of homogeneous networks of non-introspective agents in presence of input saturation. We identify three classes of agent models which are neutrally stable, double-integrator, and mixed of double-integrator, single-integrator and neutrally stable dynamics. A \textit{scale-free linear observer-based} protocol design methodology is developed based on localized information exchange among neighbors where the reference trajectory is given by a so-called exosystem which is assumed to be globally reachable. Our protocols do not need any knowledge about the communication network topology and the spectrum of associated Laplacian matrix. Moreover, the proposed protocol is scalable and is designed based on only knowledge of agent models and achieves synchronization for any communication graph with arbitrary number of agents.Comment: arXiv admin note: text overlap with arXiv:2004.09498, arXiv:1908.06535, arXiv:2001.02117, arXiv:2002.0657

Synchronization of Diverse Agents via Phase Analysis

In this paper, the synchronization of heterogeneous agents interacting over a dynamical network is studied. The edge dynamics can model the inter-agent communications which are often heterogeneous by nature. They can also model the controllers of the agents which may be different for each agent or uniform for all the agents. Novel synchronization conditions are obtained for both cases from a phase perspective by exploiting a recently developed small phase theorem. The conditions scale well with the network and reveal the trade-off between the phases of node dynamics and edge dynamics. We also study the synchronizability problem which aims to characterize the allowable diversity of the agents for which controllers can be designed so as to achieve synchronization. The allowable diversity is captured in terms of phase conditions engaging the residue matrices of the agents at their persistent modes. Controller design algorithms are provided for the cases of agent-dependent and uniform controllers, respectively