Event-Triggered Algorithms for Leader-Follower Consensus of Networked Euler-Lagrange Agents

This paper proposes 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. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. 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 which requires more information about the agent dynamics but can estimate uncertain agent parameters. For each algorithm, a trigger function is proposed to govern the event update times. At each event, the controller is updated, which ensures that the control input is piecewise constant and saves energy resources. We analyse each controllers and trigger function and exclude Zeno behaviour. Extensive simulations show 1) the advantages of our proposed trigger function as compared to those in existing literature, and 2) the effectiveness of our proposed controllers.Comment: Extended manuscript of journal submission, containing omitted proofs and simulation

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

Synchronization of multiple rigid body systems: a survey

The multi-agent system has been a hot topic in the past few decades owing to its lower cost, higher robustness, and higher flexibility. As a particular multi-agent system, the multiple rigid body system received a growing interest since its wide applications in transportation, aerospace, and ocean exploration. Due to the non-Euclidean configuration space of attitudes and the inherent nonlinearity of the dynamics of rigid body systems, synchronization of multiple rigid body systems is quite challenging. This paper aims to present an overview of the recent progress in synchronization of multiple rigid body systems from the view of two fundamental problems. The first problem focuses on attitude synchronization, while the second one focuses on cooperative motion control in that rotation and translation dynamics are coupled. Finally, a summary and future directions are given in the conclusion

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

Distributed model-independent consensus of Euler-Lagrange agents on directed networks

This paper proposes a distributed model-independent algorithm to achieve leaderless consensus on a directed network where each fully-actuated agent has self-dynamics described by Euler–Lagrange equations of motion. Specifically, we aim to achieve consensus of the generalised coordinates with zero generalised velocity. We show that on a strongly connected graph, a model-independent algorithm can achieve the consensus objective at an exponential rate if an upper bound on the initial conditions is known a priori. By model-independent, we mean that each agent can execute the algorithm with no knowledge of the equations describing the self-dynamics of any agent. For design of the control laws which achieve consensus, a control gain scalar and a control gain matrix are required to satisfy several inequalities involving bounds on the matrices of the agent dynamic model, bounds on the Laplacian matrix describing the network topology and the set of initial conditions; design of the algorithm therefore requires some knowledge on the bounds of the agent dynamical parameters. Because only bounds are required, the proposed algorithm offers robustness to uncertainty in the parameters of the multiagent system. We systematically show that additional relative velocity information improves the performance of the controller. Numerical simulations are provided to show the effectiveness of the algorithm.This work was supported by the National Natural Science Foundation of China (grant 61375072), and by Data61-CSIRO (formerly NICTA)

Containment Control of Multi-Agent Systems with Dynamic Leaders Based on a PInPI^n-Type Approach

This paper studies the containment control problem of multi-agent systems with multiple dynamic leaders in both the discrete-time domain and the continuous-time domain. The leaders' motions are described by $(n-1)$-order polynomial trajectories. This setting makes practical sense because given some critical points, the leaders' trajectories are usually planned by the polynomial interpolations. In order to drive all followers into the convex hull spanned by the leaders, a $PI^n$-type ($P$ and $I$ are short for {\it Proportion} and {\it Integration}, respectively; $I^n$ implies that the algorithm includes high-order integral terms) containment algorithm is proposed. It is theoretically proved that the $PI^n$-type containment algorithm is able to solve the containment problem of multi-agent systems where the followers are described by any order integral dynamics. Compared with the previous results on the multi-agent systems with dynamic leaders, the distinguished features of this paper are that: (1) the containment problem is studied not only in the continuous-time domain but also in the discrete-time domain while most existing results only work in the continuous-time domain; (2) to deal with the leaders with the $(n-1)$-order polynomial trajectories, existing results require the follower's dynamics to be $n$-order integral while the followers considered in this paper can be described by any-order integral; and (3) the "sign" function is not employed in the proposed algorithm, which avoids the chattering phenomenon. Furthermore, in order to illustrate the practical value of the proposed approach, an application, the containment control of multiple mobile robots is studied. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed algorithm