Nonholonomic Systems In Chained Form Research Articles

Predefined-time stabilisation of a class of nonholonomic systems

ABSTRACT This paper deals with the predefined-time stabilisation problem for a class of uncertain chained-form nonholonomic systems. Based on a novel generalised Lyapunov-like characterisation of predefined-time stability, new predefined-time controllers are introduced for a class of first and second order systems with matched perturbations. Contrary to existing finite-time and fixed-time schemes, an upper bound of the settling time is an easily tuneable control parameter. Then, these results for first and second order systems are used to design a switching strategy, which guarantees the predefined-time stability of the closed-loop system. The switching time and the settling-time can be easily tuned according to the control parameters. A benchmark example is presented to show the effectiveness of the proposed method.

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.

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.

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.

Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode

This paper proposes a novel recursive terminal sliding mode structure for tracking control of third-order chained–form nonholonomic systems in the presence of the unknown external disturbances. Finite-time convergence of the disturbance approximation error is guaranteed using the designed disturbance observer. Under the proposed terminal sliding model tracking control technique, the finite-time convergence of the states of the closed-loop system is guaranteed via Lyapunov analysis. A new reaching control law is proposed to guarantee the existence of the sliding mode around the recursive TSM surface in a finite-time. Simulation results are illustrated on a benchmark example of third-order chained-form nonholonomic systems: a wheeled mobile robot. The results demonstrate that the proposed control technique achieves promising tracking performance for nonholonomic systems.

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 of nth-order chained-form non-holonomic systems in the presence of disturbances

This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.

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.

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.

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.

Finite‐time state‐feedback stabilisation of non‐holonomic systems with low‐order non‐linearities

This study investigates the problem of finite-time stabilisation by state feedback for a class of non-holonomic systems in chained form with low-order non-linearities, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state-feedback controller is successfully constructed. Together with a novel switching control strategy, the designed controller guarantees 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.

Fast terminal sliding mode tracking of non‐holonomic systems with exponential decay rate

In this study, a recursive singularity-free, fast terminal sliding mode control method, which is able to avoid the possible singularity during the control phase, is applied for a finite-time tracking control of a class of non-holonomic systems. The reaching control law is proposed to guarantee the existence of the sliding mode around the fast terminal sliding surface and zero-tracking errors are achieved in finite time with an exponential decay rate. Simulation results are illustrated on three benchmark examples of chained-form non-holonomic systems: a wheeled mobile robot, an under-actuated rigid body and a front-wheel-drive car. The results demonstrate that the proposed control law achieves favourable tracking performance for non-holonomic systems.

Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method

This paper presents a new recursive terminal sliding mode strategy for tracking control of disturbed chained-form nonholonomic systems whose reference targets are allowed to converge to zero in finite time with an exponential rate. By introducing time-varying coordinate transformation and designing a novel control law, the existence of the sliding mode around the terminal sliding surface is guaranteed. Simulation results are applied on two benchmark examples of chained-form nonholonomic systems: a wheeled mobile robot and an underactuated rigid body. The simulation results show the efficiency of the proposed method in the presence of external disturbances.

Global Finite-Time Partial Stabilization for a Class of Nonholonomic Mobile Robots Subject to Input Saturation

In this paper, the global finite-time partial stabilization problem is discussed for a class of nonholonomic mobile wheeled robots with continuous pure state feedback and subject to input saturation. Firstly, for the mobile robot kinematic model, a “3 inputs, 2 chains, 1 generator” nonholonomic chained form systems can be obtained by using a state and input transformation. The continuous, saturated pure state feedback control law is proposed such that the special chained form systems can be stabilized to zero (except an angle variable) in a finite time, i.e., finite-time partial stabilization. Secondly, the rigorous stability analysis of the corresponding closed-loop system is presented by applying Lyapunov theorem combined with the finite-time control theory, and the angle variable can be proved to converge to a constant, moreover, its convergent limit may be accurately estimated in advance. Finally, the simulation results show the correctness and the validity of the proposed controller not only for the chained system but also for the original mobile robots system.

Consensus of multiple nonholonomic chained form systems

Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.

Global Stabilization of Nonholonomic Chained Form Systems with Input Delay

This paper investigates the global stabilization problem for a class of nonholonomic systems in chained form with input delay. A particular transformation is introduced to convert the original time-delay system into a delay-free form. Then, by using input-state-scaling technique and the method of sliding mode control, a constructive design procedure for state feedback control is given, which can guarantee that all the system states globally asymptotically converge to the origin. An illustrative example is also provided to demonstrate the effectiveness of the proposed scheme.

Finite-time Stabilization for Nonholonomic Chained Form Systems with Communication Delay

In this paper, the problem of finite-time stabilization is developed for nonholonomic chained form systems with communication delay in the input. The finite-time control laws are presented by utilizing the switching control strategy and the theory of finite-time stability, which can make the states of the nonholonomic chained form systems to converge from any non-equilibrium state to the equilibrium or a given point in a finite time. Finally, the simulation results show the effectiveness of the proposed control approach.

Adaptive Stabilization for a Class of Stochastic Nonlinearly Parameterized Nonholonomic Systems with Unknown Control Coefficients

AbstractThis paper investigates the problem of adaptive state feedback stabilization for a class of stochastic nonlinearly parameterized nonholonomic systems in chained form with unknown control coefficients. By defining two new unknown parameters whose dynamic updating laws are properly chosen and also by skilfully using the parameter separation, input‐state‐scaling, and integrator backstepping techniques, an adaptive state feedback controller is successfully designed, which guarantees that the closed‐loop system is asymptotically stabilized in probability. A simulation example is provided to illustrate the effectiveness of the proposed approach.