Double-integrator Dynamics Research Articles

Consensus algorithms for double-integrator dynamics with different velocity and actuator saturation constraints

This paper considers consensus strategy design for double-integrator multi-agent systems with matched disturbances under a directed graph. Specifically, we consider the case where both the control inputs and velocities of the agents are subject to different and asymmetric constraints. A novel distributed algorithm exploiting saturation functions is proposed to achieve asymptotic consensus without violating the predefined velocity and actuator saturation constraints. Subsequently, we extend the obtained results to event-triggered communication, where agent position broadcasting occurs only when specific triggering conditions are met. We rigorously prove that there exists a positive minimum inter-event time to rule out Zeno behavior. Finally, the simulation results confirm the theoretical findings and illustrate the achievable performance.

Decentralized, norm-free, and adaptive event-triggered distributed control of nonholonomic mobile robots

The overarching contribution of this paper is a novel event-triggered distributed control architecture for multiagent systems that are composed of a team of nonholonomic mobile robots. Specifically, the robot dynamics are first feedback linearised to equivalently represent each robot with double integrator dynamics and the event-triggering law is then presented. This law is characterised by being decentralised (depending only on own signals of a robot), norm-free (independent of distances for reducing robot-to-robot data transmissions), and adaptive (estimating signals without using global information). Moreover, its system-theo- retical analysis is provided, which holds for both the sampled data exchange method and the solution-predictor curve-based data exchange method. In contrast to the well-studied sampled data exchange, the solution-predictor curve method further reduces robot-to-robot data transmissions by making each agent to store a generic form of this curve and exchange its parameters when an event occurs for approximating the solution trajectory of each robot. Finally, an illustrative numerical example is included to demonstrate the overall architecture.

A Novel Distributed Adaptive Controller for Multi-Agent Systems with Double-Integrator Dynamics: A Hedging-Based Approach

In this paper, we focus on designing a model reference adaptive control-based distributed control law to drive a set of agents with double-integrator dynamics in a leader–follower fashion in the presence of system anomalies such as agent-based uncertainties, unknown control effectiveness, and actuator dynamics. In particular, we introduce a novel hedging-based reference model with second-order dynamics to allow an adaptation in the presence of actuator dynamics. We show the stability of the overall closed-loop multi-agent system by utilizing the Lyapunov Stability Theory, where we analyze the stability condition by using the Linear Matrix Inequalities method to show the boundedness of the reference model and actuator states. Finally, we illustrate the efficacy of the proposed distributed adaptive controller on an undirected and connected line graph in five cases.

Consensus-Based Merging and Spacing Method for Aircraft Self-Separation at Intersections

Within the context of delegating separation related tasks from an air traffic controller to the flight deck, this paper analyzes the merging and spacing problem for autonomous aircraft operations at busy airway intersections. A consensus-based control protocol is developed to achieve an ordered and safe traffic flow at a given intersection waypoint. Two primary implementation steps are covered in the protocol. In the first step, consensus on the target merging flow is achieved, where the merging stream is modeled as a straight line with the minimum total converging distance. In the second step, multiple aircraft with double-integrator dynamics and time-varying communication topologies are guided to merge into the target flow while maintaining appropriate interaircraft spacing. A state control law is designed, and the Lyapunov analysis method is leveraged to derive sufficient conditions on the communication topology and the control parameter for merging agents to reach consensus in finite time. Performance of the proposed method is evaluated through experimental simulations under different hypothetical scenarios in the two-dimensional plane.

Prescribed Time Fault-Tolerant Affine Formation Control for Multi-Agent Systems with Double-Integrator Dynamics

There is an increasing interest in the affine formation control of multi-agent systems, because it can change the centroid, orientation and scale of the formation by controlling only a few leaders. In this paper, the fault-tolerant affine formation control problem is addressed for double-integrator multi-agent systems with partial loss of efficiency and bias faults. Firstly, in order to track the leaders with dynamically changing accelerations, an acceleration observer with prescribed time convergence is proposed, which can estimate the ideal acceleration for each follower. Then, based on the acceleration observer, a fault-tolerant control algorithm is given. A new Lyapunov function candidate is constructed, based on which a sufficient condition to achieve the control objective is derived. Theoretical analysis shows that the formation tracking error can converge to zero within a prescribed time, and remain in a small neighborhood of zero after that time. Finally, numerical simulations are given to show the effectiveness of the proposed algorithm and compare it with existing results.

Trochoidal patterns generation using generalized consensus strategy for double-integrator dynamic agents

This article studies a distributed consensus law to achieve a coordinated trochoidal formation among a team of mobile agents. The mobile agents are modeled as double integrators. We generalize an existing consensus algorithm for double-integrator dynamics (1) to achieve trochoidal patterns under a general network topology and (2) to extend the pattern formation in a 3-D plane. Since the trochoidal patterns are 2-D curves, the proposed control law allows us to specify the 2-D plane in the 3-D space on which the patterns will be formed. We modify the standard consensus protocol and manipulate the gains to create trochoidal motion through local information exchange by appropriately placing the eigenvalues of the system. Trochoids have been used in multifaceted robotic applications such as area coverage, hurricane sampling, and orbit designs for satellites, apart from their aesthetic appeal. Computer simulations and multi-robot experiments are presented to validate the theoretical findings.

Coverage Control for Mobile Sensor Networks With Double-Integrator Dynamics and Unknown Disturbances

Coverage Control for Mobile Sensor Networks With Double-Integrator Dynamics and Unknown Disturbances

Spherical formation control of mobile target by multi-agent systems with collision avoidance: A limit-cycle-based design approach

This paper focuses on the control of spherical formation for multi-agent systems with double-integrator dynamics in three-dimensional space. To achieve the desired formation pattern on a spherical surface, N agents must be distributed evenly around a target. Based on the information gathered about the target and its immediate neighbors, all agents can either remain stationary or rotate around the target at the same velocity on a spherical surface while the target moves in three-dimensional space. A decoupled control method with limit cycle oscillator characteristics is explored to achieve the desired formation geometric pattern. Accordingly, three subproblems are proposed to achieve the spherical formation more effectively. The first subproblem, target-spherical-surface, requires the agents to converge on a specified spherical surface with the target as its center. The second subproblem, target-circling, requires the agents to follow three prescribed orthometric circular orbits on the spherical surface to avoid collisions while moving. The final subproblem is distributed-adjustment, which involves agents to maintaining a prescribed angular distance from their immediate neighbors while remaining relatively stationary or rotating around the target. By addressing the first two sub-problems simultaneously, the agents can be guided to the desired position. The properties of the limit-cycle-based spherical formation controller are analyzed theoretically, and its effectiveness is demonstrated through numerical simulations.

Robust Consensus-based Formation Control of a Group of UAV

Consensus-based formation control (CFC) is one of the most phenomenal formation control methods designed to achieve consensus between any vehicles that using and sharing their position and/or linear velocity with each other in a swarm mission. In this paper, a robust CFC (R-CFC) has been designed and proposed to realize pre-defined formation shapes with a team of unmanned aerial vehicles (UAVs). First, the double integrator dynamics of an UAV is presented. Second, the graph theory is explained briefly to understand any adjacency between UAVs. Then, the proposed R-CFC algorithm has been derived and the stability analysis has been proven via algebraic Riccati stability theory based on Lyapunov stability theorem. After that, the effectiveness of the proposed controller has been tested in real time outdoor tests. The experimental results show that the UAVs have been able to create the desired formation shapes and are less affected by external disturbances such as wind thanks to the proposed control algorithm.

Limbic System-Inspired Performance-Guaranteed Control for Nonlinear Multi-Agent Systems With Uncertainties.

We introduce a performance-guaranteed limbic system-inspired control (LISIC) strategy for nonlinear multi-agent systems (MASs) with uncertain high-order dynamics and external perturbations, where each agent in the MAS incorporates a LISIC structure to support the consensus controller. This novel approach, which we call double integrator LISIC (DILISIC), is designed to imitate double integrator dynamics after closing the agent-specific control loop, allowing the control designer to apply consensus techniques specifically formulated for double integrator agents. The objective of each DILISIC structure is then to identify and compensate model differences between the theoretical assumptions considered when tuning the consensus protocol and the actual conditions encountered in the real-time system to be controlled. A Lyapunov analysis is provided to demonstrate the stability of the closed-loop MAS enhanced with the DILISIC. Additionally, the stabilization of a complex system via DILISIC is addressed in a synthetic scenario: the consensus control of a team of flexible single-link arms. The dynamics of these agents are of fourth order, contain uncertainties, and are subject to external perturbations. The numerical results validate the applicability of the proposed method.

Multirobot Transport of Deformable Objects With Collision Avoidance

In the problem of autonomous transport of deformable objects, we propose a multirobot approach for steering a large object to a target configuration (object dimensions, orientation, and position). Firstly, we present a deformation model based on the evolution over time of the dimensions and rotation of the object's bounding box (BB). We consider the object is grasped by a set of mobile robots with double-integrator dynamics. Then, we propose a set of nominal controllers that allows reaching a desired configuration of the BB that models the deformable object. In order to prevent collisions of the object with static or dynamic obstacles, we formulate a control barrier function (CBF) that exploits our deformation model. Finally, we integrate the nominal controllers and the CBF into a quadratic-programming controller, which includes overstretching avoidance and velocity constraints. We report simulation results to show the performance of this approach in different test scenarios.

Formation and Flocking Control Algorithms for Robot Networks with Double Integrator Dynamics and Time-Varying Formations.

In this work, we study the problem of designing control laws that achieve time-varying formation and flocking behaviors in robot networks where each agent or robot presents double integrator dynamics. To design the control laws, we adopt a hierarchical control approach. First, we introduce a virtual velocity, which is used as a virtual control input for the position subsystem (outer loop). The objective of the virtual velocity is to achieve collective behaviors. Then, we design a velocity tracking control law for the velocity subsystem (inner loop). An advantage of the proposed approach is that the robots do not require the velocity of their neighbors. Additionally, we address the case in which the second state of the system is not available for feedback. We include a set of simulation results to show the performance of the proposed control laws.

Robust Cooperative Control of UAV Swarms for Dual-Camp Divergent Tracking of a Heterogeneous Target

Agents are used to exhibit swarm intelligence in the sense of convergence, while divergence is equivalently common in nature and useful in complex applications for multi-UAV systems. This paper proposes a robust target-tracking control algorithm, where UAV swarms are partitioned by a signed graph to perform opposite movements along or against the trajectory of the target. Uncertainties take place in both the fractional-order model of the target and the double-integrator dynamics of the UAVs. To tackle the challenge induced by the bipartite behavior and unknown components in the multi-UAV systems, the article comes up with a backstepping cascade controller and a new method for uncertainty estimation-compensation via a combined approach based on a neural network (NN) and an Uncertainty and Disturbance Estimator (UDE). Steered by the controller, UAVs in a structurally balanced network will display symmetry of their paths, pursuing or away from the target with respect to the origin. Theoretical derivation and numerical simulations have evidenced that the tracking errors converge to zero. Compared with the traditional NN method to solve such problems, this method is proposed for the first time, which can effectively improve the precision of cooperative target tracking and reduce the chattering phenomena of the controller.

Stochastic convergence problems on switching networks: An event-triggered method

The paper investigates stochastic convergence problems of multi-agent systems with double-integrator dynamics. Based on the consideration of external interference and dynamic topology, a robust controller is proposed to avoid continuous communication between agents via time-dependent event-triggered protocol. The advantage of time-dependent event-triggered protocol is that its effectiveness does not decrease with the increase of the number of agents. Then, in the framework of fixed topology and Markov switching topologies, the convergence conditions are obtained respectively. In addition, singular triggering and Zeno phenomena are excluded. Finally, the effectiveness of the proposed theory is verified by numerical simulations.

Consensus of double integrator multiagent systems under nonuniform sampling and changing topology

<abstract><p>This article considers a consensus problem of multiagent systems with double integrator dynamics under nonuniform sampling. In the considered problem, the maximum sampling time can be selected arbitrarily. Moreover, the communication graph can change to any possible topology as long as its associated graph Laplacian has eigenvalues in an arbitrarily selected region. Existence of a controller that ensures consensus in this setting is shown when the changing topology graphs are undirected and have a spanning tree. Also, explicit bounds for controller parameters are given. A sufficient condition is given to solve the consensus problem based on making the closed loop system matrix a contraction using a particular coordinate system for general linear dynamics. It is shown that the given condition immediately generalizes to changing topology in the case of undirected topology graphs. This condition is applied to double integrator dynamics to obtain explicit bounds on the controller.</p></abstract>

Connectivity Preservation for Flocking Control of Multi-Agent Systems under Deception Attacks on Velocity⋆

This paper studies the multi-task problem of connectivity preservation and flocking control for multi-agent systems with double-integrator dynamics under deception attacks on velocity. All agents are assumed to be able to measure the relative position of their neighbors and communicate their own velocity with the neighbors. First, a connectivity controller is designed to preserve the local connectivity of the communication graph under deception attacks. Then, a sufficient condition is proposed such that we can design an asymptotically flocking controller for the multi-agent system. Finally, several discussions on the combination of connectivity and flocking tasks to a connectivity-preserving flocking multi-task problem are proposed. Simulation results are provided to support the theoretical analysis.

Double-integrator consensus for a switching network without dwell time.

Due to a failure of communication, the connections among multi-agent system may switch extremely frequently. This paper focuses on the consensus of a multi-agent system with double-integrator dynamics in a generalized uniformly jointly connected switching network environment without dwell time. We prove that the distributed controller is robust against unreliable communication. The stability of the closed-loop system is proved by a virtual output technique and the generalized Krasovskii-LaSalle theorem. To validate the effectiveness of the proposed controller, a simulation example including a uniformly jointly connected network with dwell time and generalized uniformly jointly connected network without dwell time is presented.

Nonlinear Distributed Model Predictive Flocking with Obstacle Avoidance

In this paper, we present a framework for nonlinear distributed model predictive flocking with obstacle avoidance, the pursuit of group objectives, and input constraints. While most existing predictive flocking frameworks are only applicable to agents with double-integrator dynamics, we propose a general framework for nonlinear agents that furthermore allows for the independent tuning of cohesive and repulsive inter-agent forces. To reduce the computational complexity, the resulting nonlinear program is solved as a sequential quadratic program with a limited number of iterations. The performance of the proposed algorithms is demonstrated in simulation and compared to a non-predictive flocking algorithm.

Finite-Time Cooperative Control for Bearing-Defined Leader-Following Formation of Multiple Double-Integrators.

In this article, the finite-time cooperative control problem for leader-following bearing-defined formation tracking of multiagent systems with double-integrator dynamics is investigated. Different from the existing works on finite-time containment control, our objective is to make followers track leaders' trajectories and form a shape-preserving formation rather than a convex hull. The target formation is defined by both leaders' motions and bearing constraints among neighboring agents, which enables the formation not only to form and preserve a geometric pattern but also to have the ability to achieve both translational and scaling formation maneuver. To satisfy the bearing constraints, a matrix-weighted estimator/controller is developed. The finite-time stabilization of the target formation is achieved, though the matrix-weighted design makes the stability analysis complicated. Finally, an illustrative example is presented to demonstrate the effectiveness.

Stabilizing and Maneuvering Angle Rigid Multiagent Formations With Double-Integrator Agent Dynamics

This article studies 2-D formation stabilization and maneuvering of mobile agents governed by double-integrator dynamics. The desired formation is described by a set of triple-agent interior angles. A carefully chosen such set of angle constraints guarantees that the desired formation is angle rigid. To achieve the desired angle rigid formation, a stabilization control law is proposed using only local velocity and direction measurements. We show that the closed-loop dynamics of the formation, when each agent is modeled by a double-integrator, are closely related to the corresponding one in single-integrator agent dynamics. Sufficient conditions are constructed to guarantee the closed-loop stability for identical and distinct velocity damping gains, respectively. To guide an angle rigid formation to move with the desired translational velocity, orientation, and scale, formation maneuvering laws are then proposed. Simulation examples are also provided to validate the results.