Systems In Chained Form Research Articles

Control strategy for fixed-time leader–follower consensus for multi-agent systems with chained-form dynamics

This paper is concerned with the fixed-time consensus problem of multiple chained-form systems under matched perturbations. In this study, the leader (which can be dynamic) only transmits its state and control input to its neighbors. For each agent, a decentralized observer is designed to estimate the leader state in a fixed-time. Contrary to finite-time schemes, the estimation of the settling time does not require the knowledge of the initial state, allowing a step-by-step design for the controller. A decentralized observer-based control protocol is proposed for each agent to solve the leader–follower consensus problem in a fixed-time. This paper ends with a numerical example showing the effectiveness of the proposed approach.

Regulation of nonholonomic systems: A smooth, time-invariant approach

In this paper we propose an energy pumping-and-damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity-based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive the state to zero or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time-invariant, state-feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher-order nonholonomic systems in chained form, a local stability result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.

Asymptotic Stabilization of Nonholonomic Robots Leveraging Singularity

Due to the nonholonomic constraints as well as the constraints on torque and power resources, it is challenging to design a controller to asymptotically stabilize a nonholonomic robot at a predefined pose. In this paper, a switched controller is introduced for the asymptotic stabilization of nonholonomic robots using singularity, which is deemed undesirable due to loss of controllability. The proposed controller is inspired by a new insight on the singularity set of the nonholonomic robot, i.e., the singularity set includes a subset that can be asymptotically stabilized. The proposed controller is applicable to chained form systems that make an important class of drift-less nonholonomic systems, especially for those robots with a differential-drive mechanism. Considering its simplicity and efficiency, our method has the potential to be used in practice.

Visual servoing of dynamic wheeled mobile robots with anti-interference finite-time controllers

PurposeThe finite-time visual servoing control problem is considered for dynamic wheeled mobile robots (WMRs) with unknown control direction and external disturbance.Design/methodology/approachBy using finite-time control method and switching design technique.FindingsFirst, the visual servoing kinematic WMR model is developed, which can be converted to the dynamic chained-form systems by using a state and input feedback transformation. Then, for two decoupled subsystems of the chained-form systems, according to the finite-time stability control theory, a discontinuous three-step switching control strategy is proposed in the presence of uncertain control coefficients and external disturbance.Originality/valueA class of discontinuous anti-interference control method has been presented for the dynamic nonholonomic systems.

Moving Target Tracking of Extended Nonholonomic Chained-Form Systems via Finite-Time Switching Control

A finite-time switching control scheme is presented for tracking a practical moving target of extended nonholonomic chained-form systems. Firstly, a dynamic output tracking error model is proposed combining moving target and extended nonholonomic chained-form systems. Secondly, two decoupled subsystems are considered for the tracking error systems, based on which the rigorous convergence and stability analysis are proposed by applying the finite-time stability control theory and switching design methods. Finally, the effectiveness of the proposed finite-time switching control approach is performed according to the further simulation results.

Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application

ABSTRACTThis paper studies the problem of finite-time stabilisation for a class of uncertain nonholonomic systems in chained form with output constraint. A nonlinear mapping is first introduced to transform the output-constrained system into a new unconstrained one. Then, by employing the adding a power integrator technique and switching control strategy, a state feedback controller is successfully constructed to render that the states of closed-loop system converge to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of finite-time parking a unicycle-type mobile robot is tackled. Simulation results are given to demonstrate the effectiveness of the proposed method.

Formation control for car-like mobile robots using front-wheel driving and steering

To solve the problem of front wheels being jammed due to the passive trajectory tracking of the conventional car-like robot in the leader–follower formation control, we propose a novel car-like robot with the integration of front-wheel driving and steering. We establish its kinematic model, then analyze its controllability via the method of chained form system, and design the trajectory-tracking controller via the backstepping method. Simulations and experimental results validate our algorithm. This novel car-like robot with the integration of front-wheel driving and steering system not only avoids the jamming in the formation motion, but also owes the advantages of compacter structure, lighter body, and lower energy consumption.

Robust Tube-Based Predictive Control for Visual Servoing of Constrained Differential-Drive Mobile Robots

This paper proposes a control strategy for the vision-based control problem of a nonholonomic constrained differential-drive mobile robots with bounded disturbance by using robust tube-based model predictive control (MPC) method. The proposed control strategy mainly consists of an ancillary state feedback controller and an MPC control for a nominal robotic system. First, the state-error kinematics of the nominal system is converted into a chained form system, and then its MPC optimization is computed to deal with a quadratic programming optimization problem by integrating a linear variable inequality-based primal-dual neural network (LVI-PDNN). Next, the gain scheduling of the ancillary state feedback is obtained via solving robust pole assignment using LVI-PDNN. An optimal state trajectory is thus generated for the nominal robotic system by the MPC without various uncertainties, the ancillary state feedback control forces the state variables to be constrained within an invariant designed tube. Finally, extensive experimental results on stabilization control of the nonholonomic mobile robot are provided to verify the effectiveness of the proposed robust tube-based MPC.

Finite‐time tracking control of uncertain nonholonomic systems by state and output feedback

SummaryThis paper studies the finite‐time tracking control of nonholonomic systems in chained form with parameter uncertainties, unknown output gains, and mismatched uncertainties. To achieve the finite‐time tracking control of uncertain nonholonomic systems, we propose 2 types of controllers by state and output feedback, respectively. Both of the proposed 2 types of controllers can achieve the finite‐time output tracking control of the nonholonomic systems even in the presence of mismatched uncertainties and/or unknown gains. The effectiveness of our proposed controllers are illustrated with simulation examples.

Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode

This article presents a robust stabilizing control for nonholonomic underwater systems that are affected by uncertainties. The methodology is based on adaptive integral sliding mode control. Firstly, the original underwater system is transformed in a way that the new system has uncertainties in matched form. A change of coordinates is carried out for this purpose, and the nonholonomic system is transformed into chained form system with matched uncertainties. Secondly, the chained form system with uncertainties is transformed into a special structure containing nominal part and some unknown terms through input transformation. The unknown terms are computed adaptively. Afterward, the transformed system is stabilized using integral sliding mode control. The stabilizing controller for the transformed system is constructed which consists of the nominal control plus some compensator control. The compensator controller and the adaptive laws are derived in a way that the derivative of a suitable Lyapunov function becomes strictly negative. Two different cases of perturbation are considered including the bounded uncertainty present in any single control input and the uncertainties present in the overall system model of the underwater vehicle. Finally, simulation results show the validity and correctness of the proposed controllers for both cases of nonholonomic underwater system affected by uncertainties.

Actuator Fault Compensation in Three Linked 2WD Mobile Robots Using Multiple Dynamic Controllers

The paper presents a new compensation control scheme to control three linked wheeled mobile robots with actuator failures. First, a configuration of three mobile robots with fixed link is described, and its kinematics and dynamics are modelled. Then, a multiple-model based control scheme is developed to compensate for actuator failures, consisting of a kinematic controller, multiple dynamic controllers and a control switching mechanism. The kinematic controller is based on the transformation of the considered kinematics into a chained-form system, after that the recursive technique is used to derive the kinematic control law, based on which, multiple dynamic controllers are designed considering all possible failure cases. From these dynamic controllers, an appropriate one is selected to generate the applied control signal by the control switching mechanism using multiple reconstruction dynamic signals to ensure desired system performance. Simulated fault scenarios are presented to illustrate the performance of the proposed approach.

Predictor-based stabilization for chained form systems with input time delay

Abstract This note addresses the stabilization problem of nonlinear chained-form systems with input time delay. We first employ the so-called σ-process transformation that renders the feedback system under a linear form. We introduce a particular transformation to convert the original system into a delay-free system. Finally, we apply a state feedback control, which guarantees a quasi-exponential stabilization to all the system states, which in turn converge exponentially to zero. Then we employ the so-called -type control to achieve a quasi-exponential stabilization of the subsequent system. A simulation example illustrated on the model of a wheeled mobile robot is provided to demonstrate the effectiveness of the proposed approach.

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

ABSTRACTThis paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

Finite-time tracking control for extended nonholonomic chained-form systems with parametric uncertainty and external disturbance

In this paper, the finite-time tracking control problem is discussed for extended nonholonomic chained-form systems with parametric uncertainty, unmodeled nonlinear dynamics and external uncertain time-varying disturbances. Two decoupled subsystems are considered, for which an anti-interference controller is proposed by combining finite-time stability control theory and chattering-free sliding-mode design strategy in the presence of the uncertainty, nonlinearity and perturbation. Moreover, for the corresponding closed-loop systems under the given control law, rigorous finite-time stability analysis is presented at the origin equilibrium point. Finally, the main conclusions are applied to the trajectory tracking control of dynamic nonholonomic mobile robots with visual servoing feedback, and the simulation results show the effectiveness of our control design approach.

Asymptotic Stabilization for a Class of Output-Constrained Nonholonomic Systems

Abstract: This paper addresses the problem of asymptotic stabilization for a class of nonholonomic systems in chained form with output constraint. A nonlinear mapping is first introduced to transform the output-constrained system into a new unconstrained one. Then, by employing the backstepping technique and switching control strategy, a state feedback controller is successfully constructed to guarantee that the states of closed-loop system are asymptotically regulated to zero without violation of the constraint. A simulation example is provided to demonstrate the effectiveness of the proposed method.

A strict Lyapunov function for non-holonomic systems under persistently-exciting controllers

Abstract: We study the stability of a non linear time-varying skew symmetric systems ẋ = A (t, x) x with particular structures that appear in the study problems of non holonomic systems in chained form as well as adaptive control systems. Roughly under the condition that each non diagonal element of A (t, x) is persistently exciting or uniform δ persistently exciting with respect x . Although some stability results are known in this area, our main contribution lies in the construction of Lyapunov functions that allows a computation of convergence rate estimates for the class of non linear systems under study.

Distributed trajectory tracking control for multiple nonholonomic mobile robots**This work was supported by Projects of Major International (Regional) Joint Research Program (No.61120106010), National Science Foundation for Distinguished Young Scholars of China (No.60925011), National Natural Science Foundation of China (No.61175112), Program for New Century Excellent Talents in University, and the Specialized Research Fund for the Doctoral Program of Higher Education of

Abstract In this paper, the distributed tracking problem for multiple nonholonomic mobile robots is investigated, in which the nonholonomic models are transformed into chained-form systems. By utilizing the dynamic oscillator strategy, the distributed controllers are constructed such that all the mobile robots’ trajectories converge to the desired reference asymptotically. One advantage of the chained-form system solution that we propose is that it requires no other variable transformations, which could help reducing the system’s complexity and broadening the proposed controller’s practical applications. Simulations are presented to show the effectiveness of the proposed control algorithms.

Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer

The consensus tracking problem of multiple nonholonomic high-order chained-form systems is considered in this paper. A finite-time observer-based distributed control strategy is proposed. At the first step, a distributed finite-time convergent observer is proposed for each agent to estimate the leader’s state in a finite time. Then, a finite-time tracking controller is designed to track the estimated state and the leader’s attitude in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback

This paper investigates the problem of finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. Comparing with the existing relevant literature, a distinguishing feature of the systems under investigation is that the x-subsystem is a feedforward-like rather than feedback-like system. This renders the existing control methods inapplicable to the control problems of the systems. A constructive design procedure for output feedback control is given. The designed controller renders that the states of closed-loop system are regulated to zero in a finite time. Two simulation examples are provided to illustrate the effectiveness of the proposed approach.