Double-integrator Dynamics Research Articles

Robust output tracking for heterogeneous double-integrator dynamics with external disturbance

ABSTRACTThis paper studies the robust output tracking for heterogeneous double-integrator dynamics with external disturbance. It is assumed that there exist interactions among agents and their neighbours. All the agents have non-identical dynamics with others, and all the system matrices are unknown. A state feedback control protocol with only neighbours information is proposed based on a distributed compensator for non-identical dynamics and an internal-model compensator for the unknown parts. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that all the outputs of the agents converge to the reference output as time tends to infinity. Finally, two numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Error-transformation-based consensus algorithms of multi-agent systems: connectivity-preserving approach

ABSTRACTThis paper investigates distributed connectivity-preserving consensus problems of networked multi-agent systems with limited communication ranges. Compared with existing literature, a main contribution of this paper is to present a new nonlinear transformation approach of consensus errors for preserving the initial interaction patterns of multi-agent systems. Both the consensus and the connectivity preservation can be achieved by using one transformed error function. Based on the proposed nonlinear error transformation, we derive distributed connectivity-preserving consensus algorithms for single-integrator dynamics, double-integrator dynamics and second-order nonlinear systems. The asymptotic stability of consensus errors and the connectivity preservation among agents are established through Lyapunov stability analysis.

Appointed-time consensus: Accurate and practical designs

This paper investigates the appointed-time consensus problem under directed and periodical switching topologies. Here, the appointed finite time means that the consensus arriving time can be off-line pre-assigned according to task requirements without conservative estimation and is independent of the initial conditions of agents’ states. From a motion-planning perspective, a novel distributed appointed-time algorithm is developed for a multi-agent system with double-integrator dynamics. Under the assumption that the union of the directed periodical switching topologies contains a directed spanning tree, the proposed distributed algorithms can guarantee the multi-agent system to achieve consensus at an appointed time. Furthermore, the robustness and the practicability of the proposed algorithms are extended. It is the first time here to solve the finite- and appointed-time consensus problem for double-integrator systems under directed switching topologies.

Geometric Pattern Formation with Coordinated Double-Integrator Agents

Abstract This paper deals with the problem of geometric pattern formation by a group of mobile autonomous agents. The patterns are formed by the trajectories of the agents modeled with double integrator dynamics. The patterns can either be closed or can cover the entire space. We build upon an existing consensus law, by introducing self position feedback and study the collective motion of a team of agents. The patterns are not only aesthetically appealing but can also be used in civilian applications like search, exploration and surveillance. There is no restriction on the underlying graph topology. The control law manipulates the location of the eigenvalues of the overall system to achieve the pattern. We present simulation results to validate the developed theory.

Fully distributed consensus in Multi Agent Systems in the presence of disturbances

Consensus analysis in Multi Agent Systems (MAS) has been a topic of utmost interest among researchers due to its applications in diverse fields such as rescue and surveillance, mobile sensor networks and co-operative control of unmanned aerial vehicles. Consensus in MAS with a fixed directed network topology and consisting of agents with double integrator dynamics using static state feedback control, when the agents are subjected to external disturbances, is investigated in this paper. The two scenarios considered includes semi distributed leaderless consensus using the knowledge of information about the entire network topology and fully distributed adaptive consensus where the agents follows a leader, when global information is not available. The proposed Linear Matrix Inequality (LMI) based protocols simulated using MATLAB in MAS with double integrator agents are found to be effective in driving the agents towards consensus with a guaranteed H∞ disturbance rejection performance.

Single-Delay Proportional-Retarded (PR) Protocols for Fast Consensus in a Multi-Agent System

This paper investigates a derivative-free control scheme called the single-delay Proportional-Retarded (PR) protocol to achieve fast consensus in a multi-agent system (MAS) with double-integrator agent dynamics. The PR protocol intentionally introduces a delay in the feedback loop to create a derivative-like mechanism that relies only on position measurements, thus providing high reactivity on the system while mitigating undesirable noise effects. The main result shows how the PR parameters must be tuned, subject to the MAS topology, to effectively place the spectral abscissa of the collective dynamics at a desired locus with the purpose of achieving fast consensus.

Specified-time coordination control algorithms of multiple harmonic oscillators over directed graphs

This paper investigates distributed specified-time coordination consensus and containment control problems for multiple harmonic oscillators over directed graphs. First, by using Pontryagin’s maximum principle, a class of specified-time control algorithms are designed for multiple harmonic oscillators, which solve the consensus problems within a specified settling time if the directed graph of the communication topology has a directed spanning tree. Furthermore, by considering the case with multiple leaders in systems, a specified-time containment control algorithm is then developed for the followers in networks such that their positions and velocities can converge to the convex hulls formed by those of the leaders in a specified settling time over directed graphs. Compared with the existing algorithms, one of main contributions of this paper is that by using the proposed specified-time control algorithms, the consensus and containment control problems are solved over directed graphs and the settling time can be off-line pre-specified according to task requirements. Further, when the frequency of the oscillators is zero, the proposed specified-time control algorithms can also solve the coordination consensus and containment control problems for multiple double-integrator dynamics over directed graphs. Finally, some numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.

Trajectory Tracking Control with Heterogeneous Input Delay in Multi-Agent System

In this paper we present a protocol to track a general trajectory for a multi-agent system in the presence of heterogeneous constant finite input delays. We consider two different multi-agent cases: agents with single-integrator and double-integrator dynamics. For the single-integrator case, we assume that the velocity along the desired trajectory is known to all agents for all time. Similar assumption is made only for the acceleration along the desired trajectory for the double-integrator case. It is assumed that at least one agent has the complete information about the desired trajectory for all time. The tracking strategy comprises of a consensus-based estimator and a simple independent tracking controller for each agent in the system. Only the state estimates are exchanged among the agents. The communication graph for the multi-agent system along with the desired trajectory has a rooted directed spanning tree with the desired trajectory being the root. The proposed tracking strategy ensures asymptotic convergence of the multi-agent system. The controller and estimator gains do not depend on the edge weights of the graph. The chosen controller gains of individual agent are bounded by their respective input delays. We present a particular form of control gains in order to achieve a desired possible exponential convergence rate and maximize the upper bound of the convergence rate for these selective gains. Finally, we present simulation results to substantiate the effectiveness of the proposed methodology. Comparison of the proposed strategy with the existing work in the literature show a better performance.

Optimal convergence speed of consensus under constrained damping for multi-agent systems with discrete-time double-integrator dynamics

This paper considers the optimization of the convergence speed of consensus under given damping constraints for multi-agent systems with discrete-time double-integrator dynamics with fixed interconnection topology. This work summarizes and details existing results in the case of undirected topologies and extends them to directed ones. The interconnection topology is assumed to be connected or to contain a rooted-out branching, respectively. Depending on the minimum required damping, for undirected interconnection topologies in most cases analytic solutions are provided. The structure of these solutions is independent of the size of the network and only depends on the largest and second smallest eigenvalue of the corresponding Laplacian. For the remaining cases without analytic solutions provided, a combined bisection grid search is presented that solves the constrained optimization problem efficiently. This algorithm can also be applied to directed interconnection topologies and, as for the undirected case, converges to the single optimum. Simulation results are provided that demonstrate the effectiveness of the proposed approach.

Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach

This paper studies distributed maneuver control of multi-agent formations in arbitrary dimensions. The objective is to control the translation and scale of the formation while maintaining the desired formation pattern. Unlike conventional approaches where the target formation is defined by relative positions or distances, we propose a novel bearing-based approach where the target formation is defined by inter-neighbor bearings. Since the bearings are invariant to the translation and scale of the formation, the bearing-based approach provides a simple solution to the problem of translational and scaling formation maneuver control. Linear formation control laws for double-integrator dynamics are proposed and the global formation stability is analyzed. This paper also studies bearing-based formation control in the presence of practical problems including input disturbances, acceleration saturation, and collision avoidance. The theoretical results are illustrated with numerical simulations.

A simple structure robust attitude synchronization with input saturation

The attitude synchronization problem of multiple spacecraft is investigated in this paper. A simple cooperative control law, which can render spacecraft formation synchronized to a time-varying reference trajectory globally in the presence of model uncertainties, external disturbances and input saturation, is proposed. The globally asymptotic stability of the controller in the presence of model uncertainties and external disturbances is proven rigorously through a three-step proof technique. The controller can be used in orbit without modification due to its low computational complexity. Then, the proposed controller is extended to solve the consensus problem for multiple inertial agents with double-integrator dynamics. Finally, Numerical simulations are included to demonstrate the effectiveness of the developed controller.

Cooperative Collision Avoidance and Formation Control for Objects with Heterogeneous Shapes

This paper addresses the problem of formation control with collision avoidance, in scenarios comprising robots of heterogeneous shapes and with double integrator dynamics, moving on a plane. The exact shapes of the robots are taken into account in developing two cooperative collision avoidance strategies, and these are based on the collision cone approach. The two collision avoidance strategies treat the acceleration magnitude and direction, respectively, as inputs to facilitate cooperative collision avoidance. Analytical expressions for these cooperative collision avoidance laws are presented. These are then integrated with formation control laws, and simulations demonstrate the satisfactory performance of the overall system.

Finite-Time Consensus Analysis under Directed Communication Topologies for Multi-Agent Systems

This paper is concerned with the problem of finite-time consensus under directed communication topologies for multi-agent systems with double-integrator dynamics. First, a relationship between the weights of in-edges and the ones of out-edges for each agent is established and is used in finite-time consensus analysis. Second, based on our previously proposed finite-time consensus controller, the consensus conditions in the framework of directed topologies are derived. Finally, the effectiveness of the finite-time consensus conditions is illustrated by numerical examples.

String Stability towards Leader thanks to Asymmetric Bidirectional Controller

This paper deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g. acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle is coupled solely to its immediate predecessor and to its immediate follower with different gains in these two directions. We show that in this setting, unlike with unidirectional or symmetric bidirectional controllers, string stability can be recovered when disturbances act only on a small (TV-independent) set of leading vehicles. This improves existing results from the literature with this assumption. We also indicate that string stability with respect to arbitrarily distributed disturbances cannot be achieved with this controller.

Emulating Scaled Clohessy–Wiltshire Dynamics on an Air-Bearing Spacecraft Simulation Testbed

This work addresses the problem of experimentally reproducing the orbital relative motion on a planar floating spacecraft simulator testbed. Floating spacecraft simulators are characterized by double-integrator dynamics on their three degrees of freedom. In this paper, the Clohessy–Wiltshire planar dynamics is scaled down, and it is emulated using an autonomous floating vehicle actuated using compressed-air thrusters. The dynamics scaling criteria are determined through the use of the Pi theorem; subsequently, the problem of accurate actuation of the equivalent transport acceleration and Coriolis acceleration is solved. Three different thrust modulation strategies (namely, pulse-width modulation, delta sigma modulation, and hybrid pulse-width delta sigma modulation) have been used to achieve an accurate conversion of the requested continuous-thrust time histories into sequences of actuated fixed-thrust pulses. The performances of the resulting system are evaluated through a set of simulations by comparing the nominal spacecraft trajectories with the correspondent equivalent floating simulator trajectories. Finally, a set of experimental results is presented.

Structural controllability of multi-agent systems with absolute protocol under fixed and switching topologies

The paper investigates the structural controllability of leader-follower multi-agent systems underfixed and switching topologies. Three models of agents: double-integrator, high-orderintegrator and general-linear dynamics are analyzed. Necessary and sufficient graphical conditionsare provided for structural controllability based on communication topology of thesystem. In particular, a linear neighbor-based control protocol is designed for generic linearagents under which structural controllability is proved to be uniquely determined bycommunication topology structure. The role that leaders play in the structural controllabilityof multi-agent system is characterized, and a method is developed to realize structural controllabilityunder single leader. The results clearly indicate the role of leaders and theeffect of communication topology on structural controllability.

Distributed Position-Based Consensus of Second-Order Multiagent Systems With Continuous/Intermittent Communication.

This paper considers the position-based consensus in a network of agents with double-integrator dynamics and directed topology. Two types of distributed observer algorithms are proposed to solve the consensus problem by utilizing continuous and intermittent position measurements, respectively, where each observer does not interact with any other observers. For the case of continuous communication between network agents, some convergence conditions are derived for reaching consensus in the network with a single constant delay or multiple time-varying delays on the basis of the eigenvalue analysis and the descriptor method. When the network agents can only obtain intermittent position data from local neighbors at discrete time instants, the consensus in the network without time delay or with nonuniform delays is investigated by using the Wirtinger's inequality and the delayed-input approach. Numerical examples are given to illustrate the theoretical analysis.

Resilient consensus of second-order agent networks: Asynchronous update rules with delays

We study the problem of resilient consensus of sampled-data multi-agent networks with double-integrator dynamics. The term resilient points to algorithms considering the presence of attacks by faulty/malicious agents in the network. Each normal agent updates its state based on a predetermined control law using its neighbors’ information which may be delayed while misbehaving agents make updates arbitrarily and might threaten the consensus within the network. Assuming that the maximum number of malicious agents in the system is known, we focus on algorithms where each normal agent ignores large and small state values among its neighbors to avoid being influenced by malicious agents. The malicious agents are assumed to be omniscient in that they know the updating times and delays and can collude with each other. We deal with both synchronous and partially asynchronous cases with delayed information and derive topological conditions in terms of graph robustness.

Effects of Preview on Human Control Behavior in Tracking Tasks With Various Controlled Elements.

This paper investigates how humans use a previewed target trajectory for control in tracking tasks with various controlled element dynamics. The human's hypothesized "near" and "far" control mechanisms are first analyzed offline in simulations with a quasi-linear model. Second, human control behavior is quantified by fitting the same model to measurements from a human-in-the-loop experiment, where subjects tracked identical target trajectories with a pursuit and a preview display, each with gain, single-, and double-integrator controlled element dynamics. Results show that target-tracking performance improves with preview, primarily due to the far-viewpoint response, which allows humans to cancel their own and the controlled element's lags, without additional control activity. The near-viewpoint response yields better target tracking at higher frequencies, but requires substantially more control activity. The control-theoretic approach adopted in this paper provides unique quantitative insights into human use of preview, which can help to explain human behavior observed in other preview control tasks, like driving.

Distributed Continuous-Time Convex Optimization With Time-Varying Cost Functions

In this paper, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems. Control algorithms are designed for the cases of single-integrator and double-integrator dynamics. Two discontinuous algorithms based on the signum function are proposed to solve the problem in each case. Then in the case of double-integrator dynamics, two continuous algorithms based on, respectively, a time-varying and a fixed boundary layer are proposed as continuous approximations of the signum function. Also, to account for inter-agent collision for physical agents, a distributed convex optimization problem with swarm tracking behavior is introduced for both single-integrator and double-integrator dynamics.