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This paper provides a solution to the problem of safe region formation control with reference velocity tracking for a second-order multi-agent system without velocity measurements. Safe region formation control is a control problem where the agents are expected to attain the desired formation while reaching the target region and simultaneously ensuring collision and obstacle avoidance. To tackle this control problem, we break it down into two distinct objectives: safety and region formation control, to provide a completely distributed algorithm. Region formation control is modeled as a high-level abstract objective, whereas safety and actuator saturation are modeled as a low-level objective designed independently, without any knowledge of the former, and being minimally invasive. Our approach incorporates connectivity preservation, actuator saturation, safety considerations, and absence of velocity measurement from other agents with second-order system dynamics which are important constraints in practical applications. Both internal safety for collision avoidance among agents and external safety for avoiding unsafe regions are ensured using exponential control barrier functions. We provide theoretical results for asymptotic convergence and numerical simulation to show the approach's effectiveness. [ABSTRACT FROM AUTHOR]

Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge agreements are defined locally to allow more flexibility than a global consensus. This work formulates a multi-agent optimization problem under edge agreements and proposes a continuous-time distributed algorithm to solve it. Both analytical proof and numerical examples are provided to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

For a wide range of control engineering applications, the problem of solving a system of linear equations is often encountered and has been well studied. Traditionally, this problem has been mainly solved in a centralized manner. However, for applications related to large-scale complex networked systems, centralized algorithms are often subjected to some practical issues due to limited computational power and communication bandwidth. As a promising and viable alternative, distributed algorithms can effectively address the issues associated with centralized algorithms by solving the problem efficiently in a multi-agent setting that accords with the distributed nature of networked systems. Distributed algorithms decompose the entire problem into many sub-problems that are solved by individual agents in a cooperative manner. In this survey paper, we provide a detailed overview of the state of the art relevant to distributed algorithms for solving a system of linear equations. We will first review basic distributed algorithms including both discrete-time and continuous-time algorithms. Then we will discuss the extended algorithms to achieve communication efficiency. Furthermore, we will also introduce distributed algorithms to obtain the minimum-norm solution for a system of linear equations with multiple solutions, as well as the least-squares solution when there is no solution. Finally, the relationship of distributed algorithms for solving a system of linear equations to the existing distributed optimization algorithms is discussed. [ABSTRACT FROM AUTHOR]

By the distributed averaging problem is meant the problem of computing the average value of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known approach to the problem which seeks to iteratively arrive at a solution by allowing each agent to interchange information with at most one neighbor at each iterative step. Crafting a gossiping protocol which accomplishes this is challenging because gossiping is an inherently collaborative process which can lead to deadlocks unless careful precautions are taken to ensure that it does not. Many gossiping protocols are request-based which means simply that a gossip between two agents will occur whenever one of the two agents accepts a request to gossip placed by the other. In this paper, we present three deterministic request-based protocols. We show by example that the first can deadlock. The second is guaranteed to avoid deadlocks by exploiting the idea of local ordering together with the notion of an agent’s neighbor queue; the protocol requires the simplest queue updates, which provides an in-depth understanding of how local ordering and queue updates avoid deadlocks. It is shown that a third protocol which uses a slightly more complicated queue update rule can lead to significantly faster convergence; a worst case bound on convergence rate is provided. [ABSTRACT FROM AUTHOR]

In this paper we discuss and discover several conservation and associated decay laws in distributed coordination control systems, in particular in formation shape control systems. Specifically, we reveal conservations of linear momentum and angular momentum for gradient-based multi-agent formation systems modelled by single integrators, and show several corresponding conservation/decay laws for double-integrator formation stabilization systems and double-integrator flocking systems, respectively. By exploiting translation and rotation symmetry properties and insights from Noether’s theorem, we further establish a multi-agent version of the relation between symmetry and conservation laws for gradient-based coordination systems derived from general potential functions, from which we generalize the conservation/decay laws to more general networked coordination control systems. The results hold in ambient spaces of any dimensions, and we focus on the 2-D and 3-D cases due to their natural interpretation as positions of agents. [ABSTRACT FROM AUTHOR]

Most of the existing results on distributed distance-constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non-collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper a new distributed feedback strategy is proposed for controlling a rigid, acyclic formation of kinematic point-modeled mobile autonomous agents in the plane. The strategy makes use of a new concept called a “target point” and is applicable to any two-dimensional, acyclic formation whose underlying directed graph can be generated by a sequence of Henneberg vertex additions. It is shown that the method can cause a group of agents starting in any given initial positions in the plane to move into a prescribed formation exponentially fast provided the formation’s designated leader and first follower start in different positions. [ABSTRACT FROM AUTHOR]

This paper develops a distributed approach for inverse optimal control (IOC) in multi-agent systems. Here each agent can only communicate with certain nearby neighbors and only accesses segments of system's trajectory, which is not sufficient for the agent to solve the IOC problem alone. By introducing the concept of the data effectiveness and bridging the connection between each segment and its contribution to solving IOC, we formulate the IOC problem as a problem of achieving least-square solutions via a distributed algorithm. Simulations are provided to validate the proposed distributed IOC approach. [ABSTRACT FROM AUTHOR]

This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) with unknown weights, and the observed data is a segment of a trajectory of system states and inputs. The proposed technique introduces the concept of the recovery matrix to establish the relationship between any available segment of the trajectory and the weights of given candidate features. The rank of the recovery matrix indicates whether a subset of relevant features can be found among the candidate features and the corresponding weights can be learned from the segment data. The recovery matrix can be obtained iteratively and its rank non-decreasing property shows that additional observations may contribute to the objective learning. Based on the recovery matrix, a method for using incomplete trajectory observations to learn the weights of selected features is established, and an incremental inverse optimal control algorithm is developed by automatically finding the minimal required observation. The effectiveness of the proposed method is demonstrated on a linear quadratic regulator system and a simulated robot manipulator. [ABSTRACT FROM AUTHOR]

Applications of sensor networks usually require events at all nodes to be synchronized. To meet such requirement, this work proposes two multi-timer model based event synchronization schemes which are fully distributed. The proposed model consists of multiple timers with each timer characterizing a sensor node whose events are triggered by timer interrupts. Each timer updates its preset values by only using values from its nearby neighbors. Event synchronization is achieved when all timers reach their preset values simultaneously. One key feature of this work is by unifying the time synchronization part and the embedded system part of the sensor networks to reach the strict event synchronization. The effectiveness of the proposed schemes is demonstrated by simulation examples and a case study in a microgrid. [ABSTRACT FROM AUTHOR]

We consider a scenario where mobile agents are required to collect measurements from a geographically dispersed set of sensors and return them to a base. An agent faces a risk of destruction while traversing the environment to reach the sensors, and gets a reward for gathering a sensor measurement only if it successfully returns to base. We first consider the single agent scenario and characterize several properties of the optimal policy for the agent based on a quantity that we term the "reward-to-risk" ratio of the tasks. We provide the optimal policy when the risk of destruction is sufficiently high, and then extend our analysis to multiple (heterogeneous) agents, with potentially different costs and survival probabilities. In particular, when the risk of destruction is sufficiently high, we show that the multi-agent task allocation problem has a submodular structure, and accordingly provide a greedy algorithm that is guaranteed to return an allocation that is within a 1 2 factor of optimal. [ABSTRACT FROM AUTHOR]

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which results from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider a dynamical system whose trajectory is a result of minimizing a multiphase cost function. The multiphase cost function is assumed to be a weighted sum of specified features (or basis functions) with phase-dependent weights that switch at some unknown phase transition points. A new inverse optimal control approach for recovering the cost weights of each phase and estimating the phase transition points is proposed. The key idea is to use a length-adapted window moving along the observed trajectory, where the window length is determined by finding the minimal observation length that suffices for a successful cost weight recovery. The effectiveness of the proposed method is first evaluated on a simulated robot arm, and then, demonstrated on a dataset of human participants performing a series of squatting tasks. The results demonstrate that the proposed method reliably retrieves the cost function of each phase and segments each phase of motion from the trajectory with a segmentation accuracy above 90%. [ABSTRACT FROM AUTHOR]