Periodic coordinated rotating motion control of second-Order multi-Agent systems under directed interaction topologies

This paper investigates the problem of periodic motion control of second-order multi-agent systems in three dimensions under directed interaction topologies. Distributed algorithms for periodic rotating motion around a static and moving target were proposed by exploring the introduction of Cartestian coordinate coupling for each agent. In case of a static target, we show that when the nonsymmetric Laplacian matrix has certain properties, the damping gain is above a certain bound, and the Euler angle is equal to a critical value, all the agents will eventually rotate around the target periodically. In case of a moving target, the composite motion behaviours with translation and rotation will emerge, when this moving target's information can only be available to one or one subset of these agents and all agents have only local interactions. Tools like matrix theory, linear system theory and other mathematical skills were used for convergence analysis. Simulation results were provided to illustrate the effectiveness of the theoretical results.     

Toward Optimal Rendezvous of Multiple Underwater Gliders: 3D Path Planning with Combined Sawtooth and Spiral Motion

In this paper, a path planning system is proposed for optimal rendezvous of multiple underwater gliders in three-dimensional (3D) space. Inspired by the Dubins Paths consisting of straight lines and circular arcs, this paper presents the first attempt to extend the 3D Dubins curve to accommodate the characteristic glider motions include upwards and downwards straight glides in a sawtooth pattern and gliding in a vertical spiral. This modified 3D Dubins scheme is combined with genetic algorithm (GA), together with a rendezvous position selection scheme to find rendezvous trajectories for multiple gliders with minimal energy consumption over all participating vehicles. The properties and capabilities of the proposed path planning methodology are illustrated for several rendezvous mission scenarios. First, a simple application was performed for a single glider to rendezvous with a fix dock. Simulation results show the proposed planner is able to obtain more optimized trajectories when compared with the typical Dubins trajectory with nominal velocity. Additional representative simulations were run to analyse the performance of this path planner for multiple gliders rendezvous. The results demonstrate that the proposed path planner identifies the optimal rendezvous location and generates the corresponding rendezvous trajectories for multiple gliders that ensures they reach their destination with optimized energy consumption.     

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. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus of switched multi-agent systems under quantised measurements

This paper deals with the quantised consensus problem for switched multi-agent system which is composed of continuous-time and discrete-time subsystems. We adopt the distributed consensus protocols based on the quantised relative state measurements of agents. By using the properties of Laplacian matrix, it is shown that the switched multi-agent system can reach consensus exponentially with logarithmic quantiser under arbitrary switching. It is also proved that the distance between the states of any pair of neighbouring agents just converges to a bounded set when uniform quantisers are utilised. Simulation examples are presented to illustrate the effectiveness of the theoretical results.     

椭圆参考轨道指定区域最优交会研究

研究了椭圆参考轨道指定区域最优交会问题。为了实现在指定区域完成最优交会,采用以参考轨道真近点角为自变量的线性化时变Tschauner-Hempel交会动力学模型,按照设定的真近点角交会域和最优二次性能指标设计最优交会控制,加权矩阵随真近点角变化。为方便指定区域最优控制问题求解,采用区段混合能法递推求解时变黎卡提矩阵微分方程和状态轨线。对远距、近距异面交会和共面交会三种情况设定不同的交会域进行了仿真研究,结果表明方法能保证在设定的真近点角域内完成交会,交会控制能耗小,精度高。     

Performance improvement of the PD-based bilateral teleoperators with time delay by introducing relative D-control

In a force-reflecting bilateral teleoperator with a time delay, teleoperator stability is a serious problem. We have studied a bilateral teleoperator system with a time delay. We obtained stable conditions using proportional derivative-based (PD-based) control law. In this paper, PD-based control law is further studied. First, we study a PD control law with relative damping gain and its stabilizing effect that previously has not been studied quantitatively. A stable condition is derived with this PD-based controller with relative damping gain. Next, teleoperator performance by the PD control law with relative damping is evaluated and compared to PD control laws with only grounded damping using transparency analysis with a hybrid matrix. We showed that, the performance of the PD-based controller can be improved by introducing relative damping gain into the controller. As a controller design example, numerical simulations and 1-DOF experiments were conducted. Finally, peg-in-hole experiments and performance evaluations in realistic multi-DOF environments were conducted to demonstrate performance improvements by introducing the relative damping. A controller design that guarantees both stability and performance was achieved by iterating stable gain setting and performance evaluation.     

多航天器相对轨道与姿态耦合分布式自适应协同控制

基于一致性理论,在有向通讯拓扑结构下对多航天器系统相对轨道及姿态的耦合协同控制问题进行了研究.本文考虑近地航天器相对轨道的非线性方程以及用罗德里格参数描述的航天器姿态运动方程,建立了考虑控制输入耦合的六自由度航天器运动模型.在仅有部分跟随航天器可获取参考状态(记为领航航天器)的情形下,针对航天器存在未建模动态以及外部环境干扰等问题,提出了一种基于切比雪夫神经网络(Chebyshev neural networks,CNN)的自适应增益控制律,使得各跟随航天器在轨道交会的同时姿态保持一致.因为每个航天器上的控制算法仅依赖其自身及相邻航天器的信息,因此控制算法是分布式的.同时考虑到航天器之间的相对速度及相对角速度难以测量,提出了无需相对速度及角速度信息的分布式自适应协同控制律使得各航天器保持一定的队形且具有期望的相对指向.最后对6颗航天器的编队飞行进行了仿真分析,仿真结果表明本文设计的分布式自适应协同控制律是有效可行的.     

Stabilization of collective motion on a sphere

We provide a Lyapunov-based design of decentralized control laws that stabilize relative equilibria in a model of self-propelled particles that travel on the surface of a sphere. Such control laws have applications in planetary-scale mobile sensing networks in air, sea, and space. Relative equilibria of the closed-loop model include formations in which all of the particles travel around a common circular trajectory. Particle interaction can be time-invariant or time-varying and directed or undirected. The algorithm for time-invariant and undirected particle interaction uses a gradient-like control induced from the associated Laplacian matrix. The algorithm for time-varying and directed interaction replaces average quantities in the control law with dynamic consensus variables. An augmented Laplacian algorithm is also proposed to stabilize symmetric circular formations.     

Tethered space orientation via adaptive sliding mode

Here, we study the problem of a rotating tethered satellite system (TSS) orientation. The rotation TSS is used for propellantless delivery of the payload from low earth orbits to geostationary orbits or other transfer orbits. Driving the angular positions to correct desired orientation in rendezvous and tossing moments, in fact, is important operation in many real sceneries. We suggest the mathematical model describing the dynamics of TSS and catch mechanism/payload rendezvous with external disturbance terms. Here is shown that using sliding mode control (SMC), we are able to control successfully the position of TSS. The conventional and adaptive versions of SMC are considered. We show that SMC with the gain matrix adaptation based on the equivalent control method can significantly reduce the undesirable chattering effect provoking possible damages of TSS. Copyright © 2015 John Wiley & Sons, Ltd.     

Distributed adaptive consensus for linear multi-agent systems with quantised information

This paper considers the distributed adaptive consensus problem for linear multi-agent systems with quantised relative information. By using a lemma in algebraic graph theory and introducing a projection operator in adaptive law, a novel distributed adaptive state feedback controller is designed with quantised relative state information. It is shown that the practical consensus for multi-agent systems with a uniform quantiser is achieved via the Lyapunov theory and the non-smooth analysis. In contrast with the existing quantised controllers, which rely on the minimum nonzero eigenvalue of the Laplacian matrix, the developed controller is only dependent on the number of nodes. Furthermore, a dynamic output feedback controller based on quantised relative output information is proposed. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.     

No-beacon collective circular motion of jointly connected multi-agents

In this paper, a decentralized control algorithm is proposed for a group of nonholonomic vehicles to form a class of collective circular motion behavior. Without the guidance of a global beacon, the desired collective behavior occurs provided that the multi-agent system is jointly connected. Moreover, a repulsion mechanism is considered to improve the distribution evenness of the agents’ circular motion phases and hence to avoid collision. The effectiveness of the approach is verified through both theoretical analysis and numerical simulation. Moreover, some interesting variations of the circular motion model are investigated to enrich the collective behaviors.     

Robust global stabilization of spacecraft rendezvous system via gain scheduling

The problem of robust global stabilization of a spacecraft circular orbit rendezvous system with input saturation and inputadditive uncertainties is studied in this paper. The relative models with saturation nonlinearity are established based on Clohessey-Wiltshire equation. Considering the advantages of the recently developed parametric Lyapunov equation-based low gain feedback design method and an existing high gain scheduling technique, a new robust gain scheduling controller is proposed to solve the robust global stabilization problem. To apply the proposed gain scheduling approaches, only a scalar nonlinear equation is required to be solved. Different from the controller design, simulations have been carried out directly on the nonlinear model of the spacecraft rendezvous operation instead of a linearized one. The effectiveness of the proposed approach is shown.     

Optimization of formation for multi-agent systems based on LQR

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.     

空间机器人捕获运动目标的协调规划与控制方法

针对目标以任意轨迹运动且其轨迹可能与``有保证工作空间'不相交的问题, 提出了空间机器人捕获运动目标的协调规划与控制方法. 首先, 根据手眼视觉测量数据, 预测目标的运动路径, 由此确定空间机器人对目标的最优交会姿态及最佳捕获臂型; 其次, 规划基座姿态及机械臂关节角的轨迹; 最后, 采用协调控制的方法, 实现空间机器人系统对运动目标的最优捕获(以最优交会姿态及最佳捕获臂型对目标进行捕获). 仿真结果表明了该方法的有效性.     

Model predictive control system design and implementation for spacecraft rendezvous

This paper presents the design and implementation of a model predictive control (MPC) system to guide and control a chasing spacecraft during rendezvous with a passive target spacecraft in an elliptical or circular orbit, from the point of target detection all the way to capture. To achieve an efficient system design, the rendezvous manoeuvre has been partitioned into three main phases based on the range of operation, plus a collision-avoidance manoeuvre to be used in event of a fault. Each has its own associated MPC controller. Linear time-varying models are used to enable trajectory predictions in elliptical orbits, whilst a variable prediction horizon is used to achieve finite-time completion of manoeuvres, and a 1-norm cost on velocity change minimises propellant consumption. Constraints are imposed to ensure that trajectories do not collide with the target. A key feature of the design is the implementation of non-convex constraints as switched convex constraints, enabling the use of convex linear and quadratic programming. The system is implemented using commercial-off-the-shelf tools with deployment using automatic code generation in mind, and validated by closed-loop simulation. A significant reduction in total propellant consumption in comparison with a baseline benchmark solution is observed.     

二阶多智能体系统的线性广义一致性

首次针对二阶多智能体系统提出广义一致性的概念;然后探讨有向网络拓扑结构下的二阶多智能体系统的线性广义一致性问题.通过设计有效的控制协议,使用代数图论和稳定性理论,推导获得二阶的多智能体系统以及带有通信延迟的二阶系统实现线性广义一致性的充分且必要条件.结果表明,在有向网络中,耦合增益参数和拉普拉斯矩阵的特征值对达到广义一致起着关键作用;最后,数值仿真验证了结果的正确性.     

Convergence analysis using the edge Laplacian: Robust consensus of nonlinear multi‐agent systems via ISS method

This study develops an original and innovative matrix representation with respect to the information flow for networked multi‐agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic properties. Benefit from this novel graph‐theoretic tool, we can build a bridge between the consensus problem and the edge agreement problem, we also show that the edge Laplacian sheds a new light on solving the leaderless consensus problem. Based on the edge agreement framework, the technical challenges caused by unknown but bounded disturbances and inherently nonlinear dynamics can be well handled. In particular, we design an integrated procedure for a new robust consensus protocol that is based on a blend of algebraic graph theory and the newly developed cyclic‐small‐gain theorem. Besides, to highlight the intricate relationship between the original graph and cyclic‐small‐gain theorem, the concept of edge‐interconnection graph is introduced for the first time. Finally, simulation results are provided to verify the theoretical analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Regional consensus of linear differential inclusions subject to input saturation

In this article, we consider regional consensus problem for a group of identical linear systems represented by a linear differential inclusion over an undirected communication topology. Each vertex system of the linear differential inclusion is represented by a general linear system subject to input saturation, and hence only regional consensus can be achieved. For given saturated distributed linear control protocols, we establish a set of conditions under which these control protocols achieve regional consensus and a level set of a Laplacian quadratic function can be used as an estimate of the domain of consensus. These conditions are given in the form of matrix inequalities and involve the properties of the communication topology. Based on these matrix inequalities, we formulate a linear matrix inequalities based optimization problem for obtaining as large an estimate of the domain of consensus as possible. By viewing the gain matrix in the consensus algorithms as an additional variable, this optimization problem can be adapted for the design of the consensus protocols. Simulation results illustrate the effectiveness of our proposed approach.     

The deformed consensus protocol

This paper studies a generalization of the standard continuous-time consensus protocol, obtained by replacing the Laplacian matrix of the communication graph with the so-called deformed Laplacian  . The deformed Laplacian is a second-degree matrix polynomial in the real variable s$s$ which reduces to the standard Laplacian for s$s$ equal to unity. The stability properties of the ensuing deformed consensus protocol   are studied in terms of parameter s$s$ for some special families of undirected and directed graphs, and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems. Examples and simulation results are provided to illustrate our theoretical findings.