Double Integrator Research Articles

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.

Barrier lyapunov function-based homogeneous fixed-time controller design for a double integrator system

This study proposes a controller design for the fixed-time stabilisation of a double integrator system (DIS), taking into account both output and state constraints. The controller combines Barrier Lyapunov Function (BLF)-based control method with homogeneous fixed-time controllers to provide faster convergence, eliminate the singularity of BLF-based fixed-time control algorithms, and guarantee precise convergence to the origin while maintaining the constraints. Three different cases including output constraint, output and state constraints, and fixed-time extended-state observer-based control for the disturbed DIS are studied. Several sets of simulations are carried out and comparisons are made with several finite-time and fixed-time controllers. In addition, the proposed control system is applied to the lateral control of an autonomous vehicle. Simulation results outline faster convergence, faster response, less sensitivity to sensor noise, more capability in disturbance rejection, and more accurate positioning compared to previous control systems.

Model adaptive reference tracking control for uncertain robotic manipulators with input disturbance

AbstractThis article presents a simple approach for designing a linear adaptive controller, employing the model reference systems concept, to enable the tracking of uncertain robotic manipulators under the influence of input disturbances. The combined impact of model uncertainties and matched disturbances on the robot's behavior is considered as a total matched disturbance, attributed to a double integral system. Subsequently, a novel linear disturbance estimator, augmented by a feed‐forward correction term, is employed to estimate this lumped disturbance within the double integrator system. As a result of this procedure, the requisite adaptive law, based on the model reference system, is formulated for the nominal control parameter instead of arbitrary free‐parameter selections. The effectiveness of the proposed approach is theoretically justified and further supported by its application in the analysis of an active magnetic bearing system.

Global practical stabilization of the double integrator system with an imperfect sensor and subject to a bounded disturbance

This paper is concerned with global practical stabilization of the double integrator system with an imperfect sensor and subject to an additive bounded output disturbance. The imperfect sensor nonlinearity possesses the nonlinear characteristics of saturation and dead zone. Because of the presence of output dead zone and the additive disturbance, the states cannot be expected to driven into an arbitrarily small neighborhood of the origin. To solve the global practical stabilization problem, we proposes a low gain-based linear dynamic output feedback law, under which the first state enters and remains in a bounded set whose size is depended on the bound of disturbance and the range of dead zone and the second state enters and remains in a pre-specified arbitrarily small set, both in finite time. Simulation results illustrate the effectiveness of our proposed control method.

Explicit flatness-based MPC design for indoor nano-quadcopter position tracking

Due to the nonlinearities and operational constraints of quadcopters, Model Predictive Control (MPC) encounters the requirement of high computational power. This problem may prove impractical, especially for hardware-limited setups. By removing the need for online solvers, Explicit MPC (ExMPC) stands out as a strong candidate. Yet, the formulation was usually hindered by the system's nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for quadcopter position stabilisation. With the former issue, the system is exactly linearised into a concatenation of three double integrators. For the latter, with a suitable characterisation of the new convoluted constraints, the stabilising ExMPC can be computed for each double integrator separately. The controller is validated via simulations and experiments on a nanodrone platform. The proposed scheme provides similar performance and theoretical guarantees to the up-to-date nonlinear MPC solutions but with notably less computational effort, allowing scalability in a centralised manner.

Infeasible and Critically Feasible Optimal Control

AbstractWe consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple bounds. When the intersection of these two sets is empty, typically because the bounds on the control variables are too tight, the problem becomes infeasible. In this paper, we prove that, under a controllability assumption, the “best approximation” optimal control minimizing the distance (and thus finding the “gap”) between the two sets is of bang–bang type, with the “gap function” playing the role of a switching function. The critically feasible control solution (the case when one has the smallest control bound for which the problem is feasible) is also shown to be of bang–bang type. We present the full analytical solution for the critically feasible problem involving the (simple but rich enough) double integrator. We illustrate the overall results numerically on various challenging example problems.

A Distributed Model Predictive Control Strategy for Constrained Multi-Agent Systems: The Uncertain Target Capturing Scenario

In this paper, a distributed control architecture is presented for addressing the target capturing problem of a multi-agent system whose dynamics is described by double integrator models subject to bounded disturbance effects. Starting from novel kinematic models used as reference trajectories, the aim consists in driving the multi-agent system within the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">containment</i> region without entering the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">distancing</i> one and, whenever necessary, there remaining confined. The underlying control problem has been tackled by means of model predictive control arguments. In particular, two different distributed strategies have been developed, and adequately switched to each other, in order to guarantee constraint satisfaction within the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">capturing</i> region despite any disturbance realization. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a methodological solution for dealing with the capturing problem for multi-agent systems operating in uncertain environments where the target is defined by the ring resulting from the distancing and containment ellipsoids. Differently from the existing literature, the proposed approach combines into a unique framework properties coming from potential fields theory and distributed model predictive control philosophy. It is interesting to put in light that the underlying control strategy allows the users to face surveillance and rescue operations, to cite a few, in computational affordable way due to the required memory resources because most of computations can be straightforwardly moved in the off-line phase.

Global Exponential Stabilization and Global Lp Performance of a Saturated Double Integrator

Global Exponential Stabilization and Global <i>L_p </i> Performance of a Saturated Double Integrator

Quasi Time-Fuel Optimal Control Strategy for Dynamic Target Tracking

Time and fuel balance is an important topic in the dynamic tracking problem of unmanned systems. In this paper, we propose a quasi time-fuel optimal control strategy (QTFOC) to solve the dynamic tracking problem of a double integrator system, which is capable of multi-target switching tracking tasks, such as the multi-target strike of weapons and the rapid multi-target grabbing of robots on industrial assembly lines. Compared with the previous optimal control algorithms, the proposed controller retains the time-fuel optimal characteristic when switching among multiple dynamic targets, and overcomes the high-frequency oscillation problem by incorporating local linear control region and two nonlinear buffer areas. That is, when switching among multiple dynamic targets, the proposed control strategy enables the corresponding system to achieve desired transient performance and satisfactory steady-state performance simultaneously. In addition, the asymmetry of friction load is further explored, which affects the dynamic performance of the actual system. Extensive experiments based on the visual tracking turntable demonstrate the superiority and feasibility of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of multi-target switching tracking, such as the multi-target strike of weapons with vision sensors and the rapid multi-target grabbing of robots on industrial assembly lines. In recent years, various algorithms have been developed for trajectory planning and tracking. However, it is still challenging for unmanned servo system to capture dynamic targets quickly due to the constrains of motion performance, energy, and computational power. In order to reduce the computational burden and obtain ideal response under various physical constraints, a quasi time-fuel optimal control strategy (QTFOC) with analytical solutions is proposed in this paper. First, the static target is extended to the dynamic target by further investigating the traditional time-fuel optimal control theory for double integrator system. Second, to deal with the oscillation problem caused by system disturbances, we incorporate buffer areas and local linear control region into the control algorithm, which makes the system more robust. Third, the system performance is further improved by analyzing the frictional load asymmetry. This algorithm requires small computational resources and can be implemented directly on microcontrollers such as STM32. The experimental results demonstrate the superiority of our proposed method in handling the multi-target switching tracking problem, which can also adjust the response speed weight, making the unmanned system perform better under different operating conditions. Furthermore, the proposed QTFOC can be extended to other unmanned systems, such as trajectory planning and motion control for unmanned vehicles and bionic robots.

Global Asymptotic Stabilization of the Double Integrator System with Output Saturation

Global Asymptotic Stabilization of the Double Integrator System with Output Saturation

Emergent Hypotrochoidal and Epitrochoidal Formations in a Swarm of Agents

This paper proposes a decentralised controller for a swarm of agents that generates hypotrochoidal and epitrochoidal curves in 3D space. The dynamics of the agents is modelled as a double integrator where the control input, i.e. the acceleration profile, contains two terms that account for the interactions between the agents in terms of position and velocity, respectively. The term related to the interaction between velocities is weighted by a skew-symmetric matrix responsible for coupling the velocities displacements. Such a matrix defines an axis of rotation centred on the centroid of the swarm, around which the swarm organises itself to generate the desired trajectories, which can be selected by properly setting two free parameters of the model. In particular, the motion of each agent is analysed by separating its dynamics along the rotation axis from that in the perpendicular plane. It is shown that the agents achieve consensus or periodic motion along the axis of rotation while performing the desired evolutions in the perpendicular plane. Numerical simulations are presented to illustrate the proposed framework.

Theoretical Experiments on Road Profile Data Analysis using Filter Combinations

Identification of road profiles is needed to provide the input of automotive simulation and endurance testing. The analysis with estimation methods is mostly done to identify road profiles. The main goal of analysis methods is to obtain the data of vertical displacements due to road profile measurement. The acceleration data is obtained from measuring road profile by using 4 sensors of accelerometer placed on each car wheel. The measuring data is converted to be vertical displacement data by using a "double integrator", however, it is not easy to get accurate results since the signal obtained carries a lot of noise and it is necessary to design the right filter reduce the noise. In this study, the signal filtering methods reducing the noise were used Fast Fourier Transform (FFT) and Kalman Filter (KF) combination. Experiments were carried out by combining Fast Fourier Transform and Kalman Filters using an input signal with unit (volt) in the time domain. In addition, this research focused on preparing the survey data that has been obtained by eliminating the noise to convert becoming the displacement input data for providing the loads of automotive simulation testing.

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

Fuzzy state feedback with double integrator and anti-windup for the Van de Vusse reaction

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.

A Three-Phase Synchronization Algorithm Based on a Modified DSOGI with Adjustable Re-Filtering

The precise calculation of phase angle, voltage magnitude and frequency is crucial for the effective control of power electronic inverters connected to an electrical power system. The phase-locked loop (PLL) is a commonly employed method for measuring these variables. Nevertheless, the reliability of this measurement is influenced by transient events in the electrical power system and varies depending on the nature of the event and the specific design of the PLL. Notably, PLLs utilizing the double second-order generalized integrator are widely adopted for power converter synchronization purposes. This article proposes a three-phase PLL, which is based on the single-phase version previously reported by the authors. The proposed PLL, based on an alternative integrator approach, allows a fine adjustment of the tolerance to disturbances in the input voltage thanks to a second feedback gain in its pre-filter. It is reasonable to anticipate that the three-phase PLL will exhibit similar strengths to the single-phase version; however, in the three-phase case, an additional integrator is involved in pre-filtering the quadrature signals, and the double integrator is not employed as the quadrature signal generator. The performance of the proposed PLL is assessed by comparing it to other PLLs based on the second-order integrator, using a processor-in-the-loop approach.

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.

On the fixed-time extinction based nonlinear control and systems decomposition: applications to bilinear systems

This paper deals with new criteria of the fixed-time extinction of nonlinear dynamical systems. We show, by comparison principal, that Gronwall-like integral inequalities leading to the extinction of the energy system in fixed-time; this helps us to build fixed-time stabilizing feedback laws for bilinear control systems in Hilbert space. In addition, in order to relax some existing results on the fixed-time stability of systems by Lyapunov function, we prove that the decomposition of the system into two subsystems so that one is finite-time stable and the other is polynomially stable, leads to fixed-time extinction of the whole system. Our results are applied to the double integrator where new fixed-time stabilizing feedbacks, with various aspects, are constructed.

One New Property of a Class of Linear Time-Optimal Control Problems

The following paper deals with a new property of linear time-optimal control problems with real eigenvalues of the system. This property unveils the possibility of synthesizing the time-optimal control without describing the switching hyper-surfaces. Furthermore, the novel technique offers an alternative solution to the classic example of the time-optimal control of a double integrator system.

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.

Improved Performance for PMSM Sensorless Control Based on the LADRC Controller, ESO-Type Observer, DO-Type Observer, and RL-TD3 Agent

Starting from the fact that in sensorless control systems of the Permanent Magnet Synchronous Motor (PMSM), the load torque can have short and significant variations, this paper presents the sensorless control of a PMSM based on a Linear Adaptive Disturbance Rejection Controller (LADRC) type controller. Essentially, the successful operation of the LADRC controller to achieve PMSM rotor speed control performance depends on a good estimation of the disturbances acting on the system. Traditionally, an Extended State Observer (ESO) is used to make such an estimate. In this paper, it is proposed to use a Disturbance Observer (DO) to estimate the external disturbances, and after their rejection, the LADRC controller ensures an equivalent global behavior of the control system with an ideal double integrator, thus increasing ease in achieving the desired control performance. Control structures and Matlab/Simulink implementation of the PMSM sensorless control system based on the LADRC controller with an ESO-/DO-type observer are presented, as is its use in tandem with a Reinforcement Learning Twin-Delayed Deep Deterministic Policy Gradient (RL-TD3) specially trained agent that provides correction signals for more accurate estimation of external disturbances and hence improved control performance. To optimize the gain value of the DO-type observer, a computational intelligence algorithm such as the Ant Colony Algorithm (ACO) is used. Qualitatively superior performance is achieved by using LADRC with the RL-TD3 agent control structure in terms of parametric robustness, response time, and steady-state error. In addition, by calculating the fractal dimension (DF) of the controlled signal and the PMSM rotor speed, it is found that the higher the DF, the better the performance of the control system. The validation of the superiority of the proposed control structures is carried out by means of numerical simulations in the Matlab/Simulink environment.