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

Second-Order Consensus of Networked Mechanical Systems With Communication Delays

In this paper, we consider the second-order consensus problem for networked mechanical systems subjected to nonuniform communication delays, and the mechanical systems are assumed to interact on a general directed topology. We propose an adaptive controller plus a distributed velocity observer to realize the objective of second-order consensus. It is shown that both the positions and velocities of the mechanical agents synchronize, and furthermore, the velocities of the mechanical agents converge to the scaled weighted average value of their initial ones. We further demonstrate that the proposed second-order consensus scheme can be used to solve the leader-follower synchronization problem with a constant-velocity leader and under constant communication delays. Simulation results are provided to illustrate the performance of the proposed adaptive controllers.Comment: 16 pages, 5 figures, submitted to IEEE Transactions on Automatic Contro

Distributed Control of Networked Nonlinear Euler-Lagrange Systems

Motivated by recent developments in formation and cooperative control of networked multi-agent systems, the main goal of this thesis is development of efficient synchronization and formation control algorithms for distributed control of networked nonlinear systems whose dynamics can be described by Euler-Lagrange (EL) equations. One of the main challenges in the design of the formation control algorithm is its optimality and robustness to parametric uncertainties, external disturbances and ability to reconfigure in presence of component, actuator, or sensor faults. Furthermore, the controller should be capable of handling switchings in the communication network topology. In this work, nonlinear optimal control techniques are studied for developing distributed controllers for networked EL systems. An individual cost function is introduced to design a controller that relies on only local information exchanges among the agents. In the development of the controller, it is assumed that the communication graph is not fixed (in other words the topology is switching). Additionally, parametric uncertainties and faults in the EL systems are considered and two approaches, namely adaptive and robust techniques are introduced to compensate for the effects of uncertainties and actuator faults. Next, a distributed H_infinity performance measure is considered to develop distributed robust controllers for uncertain networked EL systems. The developed distributed controller is obtained through rigorous analysis and by considering an individual cost function to enhance the robustness of the controllers in presence of parametric uncertainties and external bounded disturbances. Moreover, a rigorous analysis is conducted on the performance of the developed controllers in presence of actuator faults as well as fault diagnostic and identification (FDI) imperfections. Next, synchronization and set-point tracking control of networked EL systems are investigated in presence of three constraints, namely, (i) input saturation constraints, (ii) unavailability of velocity feedback, and (iii) lack of knowledge on the system parameters. It is shown that the developed distributed controllers can accomplish the desired requirements and specification under the above constraints. Finally, a quaternion-based approach is considered for the attitude synchronization and set-point tracking control problem of formation flying spacecraft. Employing the quaternion in the control law design enables handling large rotations in the spacecraft attitude and, therefore, any singularities in the control laws are avoided. Furthermore, using the quaternion also enables one to guarantee boundedness of the control signals both with and without velocity feedback

Task space consensus in networks of heterogeneous and uncertain robotic systems with variable time-delays

This work deals with the leader-follower and the leaderless consensus problems in networks of multiple robot manipulators. The robots are non-identical, kinematically different (heterogeneous), and their physical parameters are uncertain. The main contribution of this work is a novel controller that solves the two consensus problems, in the task space, with the following features: it estimates the kinematic and the dynamic physical parameters; it is robust to interconnecting variable-time delays; it employs the singularity-free unit-quaternions to represent the orientation; and, using energy-like functions, the controller synthesis follows a constructive procedure. Simulations using a network with four heterogeneous manipulators illustrate the performance of the proposed controller.Peer ReviewedPostprint (author's final draft