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

Consensus control in robot networks and cooperative teleoperation : an operational space approach

An interesting approach in cooperative control is to design distributed control strategies which use only local information so that a multi-agent system achieves specified behaviors. A basic behavior in cooperative control is the consensus. Given a multi-agent system, like a multiple robot network, it is said that the agents reach a consensus if the state of each agent converges to a common state. Examples of cooperative tasks in which consensus algorithms are employed include formation control, flocking theory, rendezvous problems and synchronization. These cooperative tasks have several possible applications, like: transportation systems (intelligent highways, air-traffic control); military systems (formation flight, surveillance, reconnaissance, cooperative attack and rendezvous) and mobile sensor networks (space-based interferometers, environmental sampling). The solution to the consensus problems involves the design of control algorithms such that the agents can reach an agreement on their states. There are two main problems that are studied in consensus, the leader-follower consensus and the leaderless consensus. In the leader-follower consensus problem, there exists a leader that specifies the state for the whole group while in a leaderless consensus problem, there is not a priori reference state. The main goal of this thesis is the design of operational space controllers that solve the leader-follower and the leaderless consensus problems in networks composed of multiple heterogeneous robots. Furthermore, this document proposes novel operational space control schemes for bilateral teleoperation systems. In both scenarios, different conditions are studied, such as the absence of robot velocity measurements, constant and variable time-delays in the robot's interconnection, and uncertainty in the robot's physical parameters. Most of the previous consensus control algorithms, only work with the position or orientation but not with both. On the contrary, this dissertation deals with the entire pose of the robots that contains both the position and the orientation. Moreover, in order to render a singularity-free description of the orientation, the unit-quaternions are employed. The dissertation provides a rigorous stability analysis of the control algorithms and presents simulations and experiments that validate the effectiveness of the proposed controllers.Un enfoque interesante en el control cooperativo es el diseño de estrategias de control distribuido que requieran sólo información local para que un sistema multi-agente logre comportamientos específicos. Un comportamiento básico del control cooperativo es el consenso. Dado un sistema multi-agente, como una red de múltiples robots, se dice que los agentes llegan a un consenso si el estado de cada agente converge a un estado común. Algunos ejemplos de tareas cooperativas en las que los algoritmos de consenso son utilizados son los siguientes: el control de la formación, flocking, rendezvous y sincronización. Estas tareas cooperativas tienen varias aplicaciones posibles, como: sistemas de transporte (carreteras inteligentes , control de tráfico aéreo); sistemas militares (vuelo en formación, vigilancia, reconocimiento, ataque cooperativo) y redes de sensores móviles (interferómetros en el espacio, el muestreo del ambiente). La solución a los problemas de consenso implica el diseño de algoritmos de control de tal manera que los agentes pueden llegar a un acuerdo sobre sus estados. Hay dos problemas principales que se estudian en el consenso, el consenso líder-seguidor y el consenso sin líder. En el problema de consenso líder-seguidor, existe un líder que especifica el estado de todo el grupo, mientras que en un problema de consenso sin líder, no hay ningún estado de referencia definido a priori. El objetivo principal de esta tesis es el diseño de controladores en el espacio operacional que resuelvan los problemas de consenso líder-seguidor y sin líder en redes compuestas de múltiples robots heterogéneos. Además, este documento propone novedosos esquemas de control en el espacio operacional para sistemas de teleoperación bilateral. En ambos escenarios, se estudian diferentes condiciones, tales como la ausencia de medidas de velocidad de los robots, retardos constantes y variables en la interconexión de los robots y la incertidumbre en los parámetros físicos de los robots. La mayoría de los anteriores algoritmos de control que resuelven el consenso, sólo trabajan con la posición o la orientación, pero no con ambos. Por el contrario, esta tesis doctoral se ocupa de toda la pose de los robots que contiene tanto la posición y la orientación. Por otra parte, a fin de usar una representación de la orientación libre de singularidades, se emplean los cuaterniones unitarios. Esta tesis doctoral proporciona un análisis riguroso de la estabilidad de los algoritmos de control y presenta simulaciones y experimentos que validan la eficacia de los controladores propuesto

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

Adaptive command-filtered finite-time consensus tracking control for single-link flexible-joint robotic multi-agent systems

This article presents a command-filtered finite-time consensus tracking control strategy for the considered single-link flexible-joint robotic multi-agent systems. First, each agent system considered in this article is a nonlinear nonstrict-feedback system with unknown nonlinearities, so the traditional backstepping method cannot be directly applied to the design controller. However, by applying the unique structure of the Gaussian function in radial basis function neural networks, the challenges in controller design caused by the aforementioned nonstrict-feedback system have been overcome. Second, the problem of unknown nonlinearities in the system is solved by the approximation property of radial basis function neural network technology. In addition, the traditional backstepping approach often leads to an “explosion of complexity” resulting from repeated derivation of virtual control signals. Our design addresses this issue by employing command filtering technology, which simplifies the controller design process. Meanwhile, new compensation signals are designed, which successfully eliminate the error influence posed by the filters. It is seen that the control strategy presented in this article can guarantee the tracking errors converge to a small neighborhood of origin in a finite time, and all signals in the closed-loop systems remain bounded. Eventually, the simulation results show the validity of the acquired control scheme

Event-Triggered Consensus and Formation Control in Multi-Agent Coordination

The focus of this thesis is to study distributed event-triggered control for multi-agent systems (MASs) facing constraints in practical applications. We consider several problems in the field, ranging from event-triggered consensus with information quantization, event-triggered edge agreement under synchronized/unsynchronized clocks, event-triggered leader-follower consensus with Euler-Lagrange agent dynamics and cooperative event-triggered rigid formation control. The first topic is named as event-triggered consensus with quantized relative state measurements. In this topic, we develop two event-triggered controllers with quantized relative state measurements to achieve consensus for an undirected network where each agent is modelled by single integrator dynamics. Both uniform and logarithmic quantizers are considered, which, together with two different controllers, yield four cases of study in this topic. The quantized information is used to update the control input as well as to determine the next trigger event. We show that approximate consensus can be achieved by the proposed algorithms and Zeno behaviour can be completely excluded if constant offsets with some computable lower bounds are added to the trigger conditions. The second topic considers event-triggered edge agreement problems. Two cases, namely the synchronized clock case and the unsynchronized clock case, are studied. In the synchronized clock case, all agents are activated simultaneously to measure the relative state information over edge links under a global clock. Edge events are defined and their occurrences trigger the update of control inputs for the two agents sharing the link. We show that average consensus can be achieved with our proposed algorithm. In the unsynchronized clock case, each agent executes control algorithms under its own clock which is not synchronized with other agents' clocks. An edge event only triggers control input update for an individual agent. It is shown that all agents will reach consensus in a totally asynchronous manner. In the third topic, we propose three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work concerning event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics which include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain agent parameters. The last topic discusses cooperative stabilization control of rigid formations via an event-triggered approach. We first design a centralized event-triggered formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the trigger condition, event function and trigger behaviour are discussed in detail, and the exponential convergence of the formation system is guaranteed

Cooperative Control of Nonlinear Multi-Agent Systems

Multi-agent systems have attracted great interest due to their potential applications in a variety of areas. In this dissertation, a nonlinear consensus algorithm is developed for networked Euler-Lagrange multi-agent systems. The proposed consensus algorithm guarantees that all agents can reach a common state in the workspace. Meanwhile, the external disturbances and structural uncertainties are fundamentally considered in the controller design. The robustness of the proposed consensus algorithm is then demonstrated in the stability analysis. Furthermore, experiments are conducted to validate the effectiveness of the proposed consensus algorithm. Next, a distributed leader-follower formation tracking controller is developed for networked nonlinear multi-agent systems. The dynamics of each agent are modeled by Euler-Lagrange equations, and all agents are guaranteed to track a desired time-varying trajectory in the presence of noise. The fault diagnosis strategy of the nonlinear multi-agent system is also investigated with the help of differential geometry tools. The effectiveness of the proposed controller is verified through simulations. To further extend the application area of the multi-agent technique, a distributed robust controller is then developed for networked Lipschitz nonlinear multi-agent systems. With the appearance of system uncertainties and external disturbances, a sampled-data feedback control protocol is carried out through the Lyapunov functional approach. The effectiveness of the proposed controller is verified by numerical simulations. Other than the robustness and sampled-data information exchange, this dissertation is also concerned with the event-triggered consensus problem for the Lipschitz nonlinear multi-agent systems. Furthermore, the sufficient condition for the stochastic stabilization of the networked control system is proposed based on the Lyapunov functional method. Finally, simulation is conducted to demonstrate the effectiveness of the proposed control algorithm. In this dissertation, the cooperative control of networked Euler-Lagrange systems and networked Lipschitz systems is investigated essentially with the assistance of nonlinear control theory and diverse controller design techniques. The main objective of this work is to propose realizable control algorithms for nonlinear multi-agent systems

OPTIMAL LEADER-FOLLOWER FORMATION CONTROL USING DYNAMIC GAMES

Formation control is one of the salient features of multi-agent robotics. The main goal of this field is to develop distributed control methods for interconnected multi-robot systems so that robots will move with respect to each other in order to keep a formation throughout their joint mission. Numerous advantages and vast engineering applications have drawn a great deal of attention to the research in this field. Dynamic game theory is a powerful method to study dynamic interactions among intelligent, rational, and self-interested agents. Differential game is among the most important sub-classes of dynamic games, because many important problems in engineering can be modeled as differential games. The underlying goal of this research is to develop a reliable formation control algorithm for multi-robot systems based on differential games. The main idea is to benefit from powerful machinery provided by dynamic games, and design an improved formation control scheme with careful attention to practical control design requirements, namely state feedback, and computation costs associated to implementation. In this work, results from algebraic graph theory is used to develop a quasi-static optimal control for heterogeneous leader{follower formation problem. The simulations are provided to study capabilities as well as limitations associated to this approach. Based on the obtained results, a finite horizon open-loop Nash differential game is developed as adaptation of differential games methodology to formation control problems in multi-robot systems. The practical control design requirements dictate state-feedback; therefore, proposed controller is complimented by adding receding horizon approach to its algorithm. It leads to a closed loop state-feedback formation control. The simulation results are presented to show the effectiveness of proposed control scheme

Decentralized receding horizon control of cooperative vehicles with communication delays

This thesis investigates the decentralized receding horizon control (DRHC) for a network of cooperative vehicles where each vehicle in the group plans its future trajectory over a finite prediction horizon time. The vehicles exchange their predicted paths with the neighbouring vehicles through a communication channel in order to maintain the cooperation objectives. In this framework, more frequent communication provides improved performance and stability properties. The main focus of this thesis is on situations where large inter-vehicle communication delays are present. Such large delays may occur due to fault conditions with the communication devices or limited communication bandwidth. Large communication delays can potentially lead to poor performance, unsafe behaviour and even instability for the existing DRHC methods. The main objective of this thesis is to develop new DRHC methods that provide improved performance and stability properties in the presence of large communication delays. Fault conditions are defined and diagnosis algorithms are developed for situations with large communication delays. A fault tolerant DRHC architecture is then proposed which is capable of effectively using the delayed information. The main idea with the proposed approach is to estimate the path of the neighbouring faulty vehicles, when they are unavailable due to large delays, by adding extra decision variables to the cost function. It is demonstrated that this approach can result in significant improvements in performance and stability. Furthermore, the concept of the tube DRHC is proposed to provide the safety of the fleet against collisions during faulty conditions. In this approach, a tube shaped trajectory is assumed in the region around the delayed trajectory of the faulty vehicle instead of a line shaped trajectory. The neighbouring vehicles calculate the tube and are not allowed to enter that region. Feasibility, stability, and performance of the proposed fault tolerant DRHC are also investigated. Finally, a bandwidth allocation algorithm is proposed in order to optimize the communication periods so that the overall teaming performance is optimized. Together, these results form a new and effective framework for decentralized receding horizon control with communication faults and large communication delays