Class Of Nonholonomic Systems Research Articles

Design of a Disturbance Rejection Controller for a Class of Nonholonomic Systems with Uncertainties

This study investigates the global output feedback stabilization problem for one type of the nonholonomic system with nonvanishing external disturbances. An extended state observer (ESO) is constructed in order to estimate the external disturbance and unmeasurable system states, in which the external disturbance term is seen as a general state. Thus, a new generalized error dynamic system is obtained. Accordingly, a disturbance rejection controller is designed by making use of the backstepping technique. A control law is given to ensure that all the signals in the closed-loop system are globally bounded, while the system states converge to an equilibrium point. The simulation example is proposed to verify that the control algorithm is effective.

Uncertain Nonholonomic Systems Control via Sampled-Data Output Feedback of Motor Robot With Two-Dimensional Z-States

Nonholonomic systems with uncertain nonlinearities are sufficiently important to research due to the numerous applications in the real world. It is imperative to find a sampled-data controller for nonholonomic systems due to their implementation within digital computers. It has been proven that under a lower-triangular growth condition, a class of nonholonomic system with a single z-state can be globally stabilized by a sampled-data output feedback controller whose observer and control laws are discrete-time and linear. In this paper, we will further extend the results to the two-dimensional z-states which is more challenging since the boundedness of the change of coordinates is not proved. To solve this problem, we firstly design a controller for the z-system, which can guarantee the boundedness of the change of coordinates after a certain time. From this, we can construct a globally stabilizing output feedback controller for nonholonomic systems. The examples and computer simulations were conducted to show the effectiveness of the proposed controllers for the two-dimensional z-states.

Terminal Sliding Mode Controller Tuned Using Evolutionary Algorithms for Finite-Time Robust Tracking Control in a Class of Nonholonomic Systems

This paper deals with utilizing a recursive singularity-free fast terminal sliding mode control method for finite-time robust tracking control in a class of nonholonomic systems described by an extended chained form. To enhance the performance of the proposed method, the constrained parameters in the controller are exactly tuned using evolutionary algorithms such that the tracking error reaches zero in a short time and without chattering. A comparative study is also presented among the applied evolutionary algorithms namely differential evolution, bat optimization, cuckoo optimization and bacterial foraging optimization. Applying the proposed design method leads to a considerable reduction in convergence time of the states as well as the chattering phenomenon. It is shown that the method is robust against disturbance in the input of the system. Numerical simulations for a well-known nonholonomic system, i.e., wheeled mobile robot demonstrate effective improvement in the results compared with conventional terminal sliding mode control method. DOI: http://dx.doi.org/10.5755/j01.itc.47.1.15031

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.

Control Design for a Class of Nonholonomic Systems Via Reference Vector Fields and Output Regulation

This paper presents procedural guidelines for the construction of discontinuous state feedback controllers for driftless, kinematic nonholonomic systems, with extensions to a class of dynamic nonholonomic systems with drift. Given an n-dimensional kinematic nonholonomic system subject to κ Pfaffian constraints, system states are partitioned into “leafwise” and “transverse,” based on the structure of the Pfaffian constraint matrix. A reference vector field F is defined as a function of the leafwise states only in a way that it is nonsingular everywhere except for a submanifold containing the origin. The induced decomposition of the configuration space, together with requiring the system vector field to be aligned with F, suggests choices for Lyapunov-like functions. The proposed approach recasts the original nonholonomic control problem as an output regulation problem, which although nontrivial, may admit solutions based on standard tools.

Widening the effect of Lie bracket motion: a semi-global approximation and control for nonholonomic systems using non-power series expansion

A nonlinear control system often has complicated input-to-state relationship, mainly due to its controllability structure in nonlinear sense. A difficult but challenging nature of such systems is that they can only be controlled using appropriate combination of periodic inputs, corresponding to the Lie brackets. However, the effect of so-called Lie bracket motion tends to be limited due to small choice of the input amplitudes. In this paper, focusing on a class of nonholonomic systems as typical examples, we propose to approximate the state displacement under periodic signals with larger amplitudes, and utilize the result to design periodic control input. The key of our approach is the use of suitable special function, such as the Bessel functions, for series expansion to predict the state displacement, as well as considering symmetry of the state space.

Nonlinear Superposition Formulas for Two Classes of Non-holonomic Systems

The aim of this paper is to apply the nonlinear superposition principle to some non-holonomic systems, in particular, those in chained and power forms, which are used to represent the kinematic equations of various non-holonomic wheeled vehicles. The existence of nonlinear superposition formulas is studied on the basis of Lie algebraic analysis. First, it is shown that nonlinear superposition formulas can be constructed using the knowledge of n + 1 particular solutions, using the affine structure of a system in chained form and the fact that a system in power form is diffeomorphic to a system in chained form. Secondly, using the notion of first integral, it is shown that only one particular solution is sufficient.

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.

Adaptive Output Feedback Stabilization of Nonholonomic Systems with Nonlinear Parameterization

This paper investigates the problem of adaptive output feedback stabilization for a class of nonholonomic systems with nonlinear parameterization and strong nonlinear drifts. A parameter separation technique is introduced to transform nonlinearly parameterized system into a linear-like parameterized system. Then, by using the integrator backstepping approach based on observer and parameter estimator, a constructive design procedure for output feedback adaptive control is given. And a switching strategy is developed to eliminate the phenomenon of uncontrollability. It is shown that, under some conditions, the proposed controller can guarantee that all the system states globally converge to the origin, while other signals remain bounded. An illustrative example is also provided to demonstrate the effectiveness of the proposed scheme.

Output Feedback Stabilization of Uncertain Nonholonomic Chained Systems

In this paper, output feedback stabilization problem of a class of nonholonomic systems in chained form with drift nonlinearity and unknown virtual control coefficients is considered. Observer-based output feedback design is developed when only partial system states are measurable. The control laws are developed using state scaling and backstepping techniques. The proposed control strategies can steer the system globally converge to the origin.

Global Finite-Time Output Feedback Stabilization for a Class of Uncertain Nonholonomic Systems

This paper investigates the problem of global finite-time stabilization by output feedback for a class of nonholonomic systems in chained form with uncertainties. By using backstepping recursive technique and the homogeneous domination approach, a constructive design procedure for output feedback control is given. 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.

Adaptive Stabilization for Nonholonomic Systems with Unknown Time Delays

This paper presents an adaptive control strategy for a class of nonholonomic systems in chained form with virtual control coefficients, nonlinear uncertainties, and unknown time delays. State scaling technique and backstepping recursive approach are applied to design a nonlinear state feedback controller, which can guarantee the stabilization of the closed-loop systems. The simulation results are provided to show the effectiveness of the proposed method.

Dirac Structures, Nonholonomic Systems and Reduction

The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.

On the governing equations of motion of nonholonomic systems on Riemannian manifolds

We propose a geometric approach to formulate the governing equations of motion for a class of nonholonomic systems on Riemannian manifolds. We first present a coordinate-free geometric formulation of the D’Alembert–Lagrange equation. Then by explicating this geometric formulation with respect to an arbitrary frame, we obtain the governing equations of motion in generalized form. The governing equations so obtained directly eliminate the dependent variations without using undetermined multipliers. As examples, we apply the formulation to a rigid body and a system with general first-order nonholonomic constraints; we also demonstrate their equivalences to the known results.

Nonholonomic system control via particle swarm optimization of a neural‐aided direct gradient descent control

AbstractIt is well known that the class of nonholonomic systems cannot be asymptotically stabilized by continuous static state feedback controls. It has been reported that the so‐called direct gradient descent control (DGDC) is able to stabilize nonholonomic systems. This article attempts to improve the performance of the DGDC by using neural network (NN) and particle swarm optimization (PSO). A control method is proposed by embedding an NN into the control law derived by the original DGDC. PSO is employed in order to search globally the parameters of the controller without requiring a redesign process of the parameters. To verify the method, the control problems of two typical nonholonomic systems, one being a wheeled mobile robot and the other a rotary crane system, are considered under constraints applied to the systems. Comparative performance tests are carried out, showing that the proposed approach outperforms the original method and a neurocontroller. Also, simulations show that the proposed method is able to control the systems effectively under the given constraints without the need of the redesign process. © 2011 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Adaptive output feedback control for uncertain nonholonomic chained systems

An adaptive output feedback control was proposed to deal with a class of nonholonomic systems in chained form with strong nonlinear disturbances and drift terms. The objective was to design adaptive nonlinear output feedback laws such that the closed-loop systems were globally asymptotically stable, while the estimated parameters remained bounded. The proposed systematic strategy combined input-state-scaling with backstepping technique. The adaptive output feedback controller was designed for a general case of uncertain chained system. Furthermore, one special case was considered. Simulation results demonstrate the effectiveness of the proposed controllers.

Adaptive stabilization of uncertain nonholonomic systems by output feedback

The adaptive output feedback control strategy is presented for a class of nonholonomic systems in chained form with nonlinearity uncertainties. A new observer and a filter are introduced for the states and parameter estimation. The proposed control strategies guarantee the convergence of the closed-loop system. The simulation example demonstrates the efficiency of the proposed method.

Design and analysis of a spherical mobile robot

A spherical mobile robot, rolling on a plane with the help of two internal rotors and working on the principle of conservation of angular momentum has recently been fabricated in our group. The robot is a classic nonholonomic system. Path planning algorithms exist in the literature for certain classes of nonholonomic systems like chained form systems, nilpotent systems and differentially flat systems. The model of this spherical mobile robot however, does not fall into any of these classes and hence these existing algorithms are rendered inapplicable to this system. The final objective is to make this robot as a testbed for feasible path planning and feedback control algorithms.

Neurocontroller with a genetic algorithm for nonholonomic systems: flying robot and four-wheel vehicle examples

This article considers intelligent control for a class of nonholonomic systems using a neurocontroller (NC) and a genetic algorithm (GA). First, we introduce the design of the NC with use of the GA, and then we apply the NC to control two typical examples of nonholonomic systems: a hopping robot in the flight phase and a four-wheel vehicle. In order to verify the effectiveness of the control system, the performance of the NC is investigated and also compared to that of the so-called direct gradient descent control (DGDC) approach, which is able to utilize a GA with the same examples in the comparison. Simulations show that the NC could achieve a competitive performance and control the nonholonomic systems effectively. Furthermore, the use of the NN and GA provide a straightforward solution for the problem without the need of the chained form conversion.

ＧＡ最適化による直接勾配降下制御器を用いた旋回クレーンの振れ止め制御

In this paper, we propose a control method for a rotary crane system using Direct Gradient Descent Control (DGDC) optimized by a genetic algorithm (GA). The rotary crane is known to be a class of nonholonomic system and the DGDC method is useful for the nonholonomic system control. However, the control performance of the DGDC strongly depends on the parameters of controller and the value of initial control inputs. Also, for usage of the DGDC, it is required to re-design iteratively the control parameters or the control inputs. We applied GA optimization to determine the sets of control parameters of the DGDC for the crane system. The parameters of the DGDC optimized by GA are not required to be re-designed. Simulation results show that the proposed method has higher control performance and has good robustness with noise and fluctuation of the initial states.