Systems In Chained Form Research Articles

Predefined-time VFO control design for unicycle-like mobile robots

The paper presents a predefined-time Vector-Field-Orientation (VFO) control law for unicycle-like nonholonomic mobile robots. We consider a set-point control problem in the presence of strict time constraints, which has to guarantee satisfaction of a prescribed upper bound of the settling time for the configuration errors. The control law is based on the VFO methodology, which is characterized by non-oscillatory and well-predictable time evolution of transient states for unicycle-like robots. A formal stability analysis based on the Lyapunov theory is provided for the closed-loop dynamics. Then, the results of extensive numerical simulations as well as experimental tests illustrate the resultant control performance where time constraints are considered. The proposed approach is compared with an alternative predefined-time stabilizer, recently introduced for nonholonomic chained-form systems.

Adaptive Multiple-Surface Sliding Mode Control of Nonholonomic Systems With Matched and Unmatched Uncertainties

The problem of stabilizing a class of nonholonomic systems in chained form affected by both matched and unmatched uncertainties is addressed in this paper. The proposed design methodology is based on a discontinuous transformation of the perturbed nonholonomic system to which an adaptive multiple-surface sliding mode technique is applied. The generation of a sliding mode allows to eliminate the effect of matched uncertainties, while a suitable function approximation technique enables to deal with the residual uncertainties, which are unmatched. The control problem is solved by choosing a particular sliding manifold upon which a second order sliding mode is enforced via a continuous control with discontinuous derivative. A positive feature of the present proposal, apart from the fact of being capable of dealing with the presence of both matched and unmatched uncertainties, is that no knowledge of the bounds of the unmatched uncertainty terms is required. Moreover, the fact of producing a continuous control makes the proposed approach particularly appropriate in nonholonomic applications, such as those of mechanical nature.

Improved Finite-Time Disturbance Observer-Based Control of Networked Nonholonomic High-Order Chained-Form Systems

This article investigates the finite-time leader–follower tracking problem for consensus control of nonholonomic MASs with chained-form dynamics under unknown time-varying disturbances. First, a finite-time distributed observer, consisting of the tangent hyperbolic function with an induced high gain effect, is constructed to estimate the leader’s information both quickly and accurately for each follower leading to communication loop avoidance. Besides, to cope with the adverse impact resulting from external disturbances, a finite-time disturbance observer is developed to provide accurate estimations of unknown terms within a finite time. A finite-time backstepping control scheme with a fast convergence rate is then proposed for each follower based on estimated disturbances to track the estimated states of the leader. Regardless of how close or how far away from the equilibrium point the follower states are, this method accelerates the convergence rate. An approximation technique using piecewise functions is also employed to bring the upper estimate of the convergence time closer to its real value. Finally, the efficiency of the presented control protocol is verified by some simulations on a number of connected wheeled mobile robots under external disturbances.

Finite-Time Discontinuous Control of Nonholonomic Chained-Form Systems

A finite-time discontinuous control method is proposed for controlling nonholonomic chained-form systems. Through a general discontinuous coordinate transformation, the nonholonomic system is transformed into two decoupled subsystems that are independently stabilized with control laws. Sufficient conditions for the existence of decoupled subsystems and finite-time convergence of system states are given. Furthermore, the finite-time discontinuous control laws are proposed to ensure that the system states reach the equilibrium in a finite time. Simulation results are presented to demonstrate the effectiveness and advantages of the proposed approach.

Event-triggered tracking control for a class of nonholonomic systems in chained form

Event-triggered tracking control for a class of nonholonomic systems in chained form

Fixed-Time Consensus Tracking for Multi-Agent Systems With a Nonholomonic Dynamics

In this article, we investigate the control strategy of fixed-time leader-following consensus for chained-form systems with matched disturbances. A new decentralized observer is designed under a directed topology to estimate the leader state in a fixed time for each follower. Then, a novel control protocol is developed to track the estimated leader state in a prescribed finite time. Different from existing results, the bound we derive for the setting time does not depend on the initial conditions even in the presence of matching perturbations. Moreover, the chattering phenomenon of control output is effectively reduced as signum function gets smaller in the proposed method.

Prescribed-time control of high-order nonholonomic systems in chained form by time-varying feedback

In this paper, the prescribed-time control problem for a class of high-order nonholonomic systems is investigated. With the aid of a novel state transformation, the nonholonomic systems are decoupled. Further, a time-varying high-gain feedback controller is constructed by backstepping. It is shown that the proposed control law can achieve the prescribed-time convergence for high-order nonholonomic systems and the controller is bounded. Numerical examples verify the effectiveness of the method proposed in this paper.

A time-scale transformation approach to prescribed-time stabilisation of non-holonomic systems with inputs quantisation

This article addresses the problem of global stabilisation using state feedback for a kind of uncertain non-holonomic systems in chained form. Two distinct characteristics of this study are that the considered system suffers from the input-quantised actuator, and the system states are expected to converge to zero in prescribed finite time. To address these, a time-scale transformation, that can change the original stabilisation into the finite-time stabilisation of the transformed one, is first introduced. Then, under the new framework of equivalent transformation, a quantised state feedback controller that achieves of the performance requirements is developed with the aid of the recursive technique. Finally, simulation results of a unicycle-type mobile robot are provided to confirm the efficacy of the proposed approach.

Robust finite-time stabilisation of an arbitrary-order nonholonomic system in chained form

We present a robust finite-time stabilising algorithm for an arbitrary-order nonholonomic system in chained form. The state feedback is locally bounded, homogeneous and discontinuous. Its design follows from a generalised circle criterion based on the theory of homogeneous Lyapunov functions and a two-stage homogeneity-preserving strategy proposed by Nakamura.

Bounded Observer-Based Consensus Algorithm for Robust Finite-Time Tracking Control of Multiple Nonholonomic Chained-Form Systems

This article is concerned with the leader–follower consensus tracking problem for multiagent systems with nonholonomic high-order chained-form dynamics subject to external disturbances. A novel distributed and bounded observer is first developed for each follower to estimate the leader information in a finite time. Then, a bounded fast terminal sliding-mode control protocol is constructed for each follower to track the estimated leader's states leading to the fast convergence performance as well as strong robustness. Contrary to some existing finite-time consensus tracking schemes, the control input constraint is taken into account by utilizing hyperbolic tangent saturation function to reduce the risk of the actuator saturation. Moreover, an approximation-based technique is introduced to reduce the conservatism of the upper bound of convergence time. Finally, some simulations for a set of wheeled mobile robots are carried out to demonstrate the efficiency of the proposed control algorithm.

Linear Algebra Based Control: Application to a second order chained form system

Control of underactuated systems with non-holonomic constraints has been an issue of interest in recent years. These systems are hard to control because their linearization makes them uncontrollable and current approaches generally involve complex calculations. In this manuscript, a controller for trajectory tracking and positioning for a second-order chained form system using a simple approach based on linear algebra is proposed. The control law is formulated by setting two of the six variables trajectories, while the other four are calculated assuming the equations system has an exact solution, and ensuring the error tends to zero. The stability of the proposed control system is demonstrated through the Khalil Lemma, and simulations show the performance of the controller.

Predefined-time leader-following consensus for nonholonomic chained-form multiagent dynamic systems

ABSTRACT In addition to stability and accuracy, rapidity is another important index of the performance of control systems. The current fixed time design cannot meet the requirement for rapidity. The design to meet this requirement must be such that the settling time can be given in advance, that is, the so-called predefined-time design. This paper deals with the predefined-time consensus problem for a class of nonholonomic chained-form multiagent dynamic systems with unknown disturbances. First, a distributed observer for each follower is investigated such that the leader state can be estimated by the followers in a predefined time. Based on this observer, a switching consensus tracking controller is proposed to ensure that the tracking errors converge to zero within a predefined time. Compared with the existing finite-time and fixed-time schemes, the upper bound of the settling time is an directly tunable control parameter, and the settling time can be easily tuned by the control parameter. The stability of the closed-loop system is proved by the Lyapunov method. A simulation example of wheeled mobile robots is performed to demonstrate the effectiveness of the proposed controllers.

Smooth, time‐invariant regulation of nonholonomic systems via energy pumping‐and‐damping

SummaryIn this article 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 to zero the state 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 convergence result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided.

Control Based on Linear Algebra for Trajectory Tracking and Positioning of Second-Order Chained Form System

The development of controllers for underactuated systems with nonholonomic constraints has been a topic of significant interest for many researchers in recent years. These systems are hard to control because their linearization transform them into uncontrollable systems. The proposed approaches involve the use of a permanent excitation in the reference trajectory; coordinate transformation; discontinuities; or complex calculations. This paper proposes the design of the controller of the second-order chained form system for trajectory tracking by using a simpler approach based on linear algebra. Up to the present time, no controllers based on this approach have been designed for that system. The control problem is solved by setting two of the three systems variables as a reference, while the remaining variable is calculated imposing the condition that the equations system has an exact solution to ensure that tracking errors go to zero. The stability of the proposed controller is theoretically demonstrated, and simulations results show a suitable control system performance. Also, no coordinate transformation is necessary.

Reduced order finite time observers and output feedback for time-varying nonlinear systems

We provide finite time reduced order observers for a class of nonlinear time-varying continuous-time systems. We use the observers to design globally asymptotically stabilizing output feedback controls. We illustrate our work in tracking dynamics for a nonholonomic system in chained form.

Barrier Lyapunov functions-based fixed-time stabilization of nonholonomic systems with unmatched uncertainties and time-varying output constraints

The fixed-time stabilization problem is addressed in this paper for a kind of nonholonomic systems in chained form with unmatched uncertainties and time-varying output constraints. A novel tan-type barrier Lyapunov function is introduced to deal with time-varying output constraints. Under the unified framework of the considered system with and without output constraints, a state feedback controller is designed with the aid of adding a power integrator technique and switching control strategy. It is shown that the suggested controller ensures the states of closed-loop system to zero in a given fixed time without disobeying the constraints. Finally, simulation results are given to confirm the efficacy of the presented control scheme.

Fixed-time output tracking control for extended nonholonomic chained-form systems with state observers

This paper deals with the fixed-time tracking control problem of extended nonholonomic chained-form systems with state observers. According to the structure characteristic of such chained-form systems, two subsystems are considered to design controllers, respectively. First of all, using the fixed-time control theory, a controller is proposed to make the first tracking error subsystem converge to zero in bounded time independent initial state. Second, a state observer is proposed to estimate the unmeasurable states of the second subsystem. And the precise state estimation can be presented from the observer within finite time; moreover, the upper bound of time is a constant independent on the initial estimation error. Third, a fixed-time controller is designed to drive all states of the second chained-form subsystem to zero within pre-calculated time. Finally, the effectiveness of the proposed control scheme is validated by simulation results.

Constrained Trajectory Planning for Second-Order Chained Form Systems Using Time Polynomials

This paper deals with time polynomial based trajectory planning for differentially flat affine dynamical systems that can be written as a chain of second-order controlled subsystems. An analytical approach is proposed to account for state and input constraints by adjusting the standard third-order time polynomial based considerations. For a point-to-point motion planning problem the constraints are met by properly selecting the time of motion value or/and initial or final values of some of the state variables. As an illustrative example trajectory planning for a 3-DoF Delta pick and place robot is considered.

Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems

Convergence rate is an important performance index in consensus control. Yet, most of the existing results can only achieve asymptotic consensus, or finite-time consensus whose settling time is contingent on initial conditions. This paper studies the robust fixed-time consensus tracking control problem for high-order nonholonomic chained-form systems subject to unknown parameters and nonlinear uncertainties. By using the modified power integrator method, we propose a new robust fixed-time consensus tracking algorithm, with which the consensus tracking can be achieved in a fixed time independent of initial conditions even in the presence of uncertainties. An observer-based fixed-time consensus tracking algorithm is also developed as an alternative method to overcome the communication loop problem. Lyapunov analysis shows the fixed-time stability of the closed-loop system. An application to multiple wheeled mobile robots is presented.