N-degrees Of Freedom Research Articles

Immersion and invariance disturbance observer-based nonlinear discrete-time control for fully actuated mechanical systems

This paper addresses the attenuation problem of input disturbances in the control of fully actuated mechanical systems in the discrete-time setting. Firstly, a discrete-time disturbance estimator design with immersion and invariance (I&I) approach is presented for the n-degrees of freedom (DOF) fully actuated mechanical systems. Then, a discrete-time combined feedback linearising and backstepping control is established that this controller uses the estimated disturbance information. Global asymptotic stability of the estimator and local asymptotic stability of the entire closed-loop system in an arbitrarily large compact set are shown utilising the Lyapunov stability theory. In order to show the effectiveness of the proposed composite observer-based discrete-time control method, it is applied to the 3-DOF robotic manipulator. Performance of proposed direct discrete-time combined feedback linearising and backstepping controller with discrete-time I&I observer is compared with a direct discrete-time conventional second-order sliding mode controller with another discrete-time nonlinear disturbance observer via simulations. The superior performance of the proposed method is demonstrated with simulation results.

Adaptive Neural Network Control of Underwater Robotic Manipulators Tuned by a Genetic Algorithm

This paper describes a novel approach for the control of underwater robots that can handle uncertainties and disturbance problems, which are commonly met in underwater environments. The considered system is an underwater manipulator with n-degrees of freedom. The approximation capability of an adaptive neural network is exploited to estimate uncertainties in system dynamics. Drag and lift forces are considered as an external disturbance, and a disturbance observer approach which has been proved to be effective with on-land robotic systems, is applied to compensate for it. The objective of the controller designed is to track a desired trajectory. To find the optimal gain parameters of this controller, a classical Genetic Algorithm is employed. Extensive simulation studies carried out on a two degrees of freedom manipulator indicate the efficacy of the proposed approach, proving that the disturbance observer originally developed for on-land systems can also be used effectively for underwater robotic systems. Finally, the performance of the proposed controller, tuned by the Genetic Algorithm is compared with that of a controller, tuned manually. The results show that the reliance on a well-known classic Genetic Algorithm for the tuning of the controller parameters not only saves time, but also provides better values of the parameters.

Instability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom under the existence of a single resonance and an invariant ray

In this paper we prove the instability of one equilibrium point in an autonomous Hamiltonian system with n-degrees of freedom under two assumptions: the first is the existence of a single resonance of order s (without resonance of lower order, but it could exist resonance of greater order); and the second is the existence of an invariant ray solution of the truncated Hamiltonian system up to order s. Application of our main result to the satellite problem is considered.

Procedures to determine the principal directions of kinematic performance in serial robots

SUMMARYAssume that the end-effector of a serial mechanism with n-degrees of freedom arrives at the position p0, where it can change arbitrarily the direction of its movement. The physical conditions imply that this change in direction also alters its velocity. The kinematic performance ellipse represents the velocities according to the new direction of the system, and thus solving the problem of which direction will correspond to a maximum or minimum (principal directions) magnitude of the corresponding velocity. In this paper, a new procedure to calculate these principal directions is presented and contrasted with two of the most common procedures employed in the field. All three procedures are considered in some detail, in order to understand their underlying concepts and, therefore, gain a deeper understanding of the physical situation. They are all proved in standard examples.

Instability of Equilibrium Solutions of Hamiltonian Systems with n-Degrees of Freedom Under the Existence of Multiple Resonances and an Application to the Spatial Satellite Problem

In this paper, we prove the instability of one equilibrium point in a Hamiltonian system with n-degrees of freedom under two assumptions: the first is the existence of multiple resonance of odd order s (without resonance of lower order) but with the possible existence of resonance of higher order; and the second is the existence of an invariant ray solution of the truncated Hamiltonian system up to order s. It is shown that in the case of resonance without interaction, the necessary conditions for instability have important simplifications with respect to the general case. Examples in three, four and six degrees of freedom are given. An application of our main result to the spatial satellite problem is considered.

Stability of equilibrium solutions of Hamiltonian systems with n-degrees of freedom and single resonance in the critical case

In this paper we give new results for the stability of one equilibrium solution of an autonomous analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom. Our Main Theorem generalizes several results existing in the literature and mainly we give information in the critical cases (i.e., the condition of stability and instability is not fulfilled). In particular, our Main Theorem provides necessary and sufficient conditions for stability of the equilibrium solutions under the existence of a single resonance. Using analogous tools used in the Main Theorem for the critical case, we study the stability or instability of degenerate equilibrium points in Hamiltonian systems with one degree of freedom. We apply our results to the stability of Hamiltonians of the type of cosmological models as in planar as in the spatial case.

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions.

Non-existence of KAM torus

Given an integrable Hamiltonian h 0 with n-degrees of freedom and a Diophantine frequency ω, then, arbitrarily close to h 0 in the C r topology with r < 2n, there exists an analytical Hamiltonian h e with no KAM torus of rotation vector ω. In contrast with it, KAM tori exist if perturbations are small in C r topology with r > 2n.

Stability of Equilibrium Solutions of Autonomous and Periodic Hamiltonian Systems with n-Degrees of Freedom in the Case of Single Resonance

This paper concerns with the study of the stability of an equilibrium solution of an analytic Hamiltonian system in a neighborhood of the equilibrium point with n-degrees of freedom, in the autonomous and periodic case under the presence of a single resonance. Our Main Theorem generalizes several results existing in the literature and we also give a geometrical interpretation of the hypotheses involved there. In particular, our Main Theorem provides necessary and sufficient conditions for the stability of the equilibrium solutions under the existence of a single resonance, depending on the coefficients of the Hamiltonian function.

Online fuzzy logic control for tipover avoidance of autonomous redundant mobile manipulators

A redundant mobile manipulator composed of a three-wheeled non-holonomic mobile platform and a N-degrees of freedom (DOF) onboard manipulator is investigated in this paper. Redundancy for such a robot is exploited to avoid tipover via online adjusting self-motions. The dynamic model is established and a new tipover criterion is proposed considering inertia, gravity and acceleration. An online fuzzy logic (FL) self-motion planner and a robust adaptive controller are presented to prevent the robot from tipover without affecting the end-effector's motion tasks. Real experiments for a redundant mobile manipulator demonstrate that the proposed algorithm is effective.

Analysis of dynamic response of prey-predator system with nonliner diffusion-reaction equations by using superposition

A method for calculating the dynamic response of the diffusion-reaction system with prey and predator model is proposed by using superposition of normal modes. For this kind of nonlinear equation with N-Degrees of Freedom (DOF) discretized by finite element method (FEM), mode superposition is used to evaluate the transient process of the system subjected to initial conditions. For the calculation of the generalized coordinates in vectors of superposition, the fourth-order Runge-Kutta method is employed to solve the ordinary differential equations of the N-DOF system. The results obtained are compared with those by three-step explicit FEM. Two of methods can predict the oscillation phenomena in prey and predator in two-dimensional space.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and a four output differential systems and their applications including all-wheel drive vehicles, universal robotic grippers and multi-spindle nut runners.

AN EFFICIENT COMPUTATIONAL SCHEME FOR THE VIBRATION ANALYSIS OF HIGH TENSION CABLE NETS

An approach base on group theory is described for calculating the eigenvalues and hence natural circular frequencies of vibration of cable nets consisting of two families of high tensioned cables, each cable lying in a vertical plane, and with the projections of cables on the horizontal plane comprising two perpendicular sets of lines. The cable net systems are assumed to have ndegrees of freedom in the form of vertical motions of masses concentrated at the cable intersections. After briefly outlining the linear cable net theory that forms the basis for the illustration of the proposed group-theoretic approach, those concepts of symmetry groups and representation theory that are fundamental to the present development are summarized. The actual computational scheme is then outlined, followed by a step-by-step illustration of the proposed procedure, the proposed method makes use of the full symmetry of the cable network in a systematic and highly efficient manner: the problem is decomposed into mutually independent subspaces spanned by symmetry adapted variables, for which the required eigenvalues are simply obtained through the solution of a small number of polynomial equations each of degree a fraction of n(instead of through the solution of a single polynomial equations of degree n, as yielded by a conventional analysis), resulting is substantial simplifications in the computation of the natural frequencies of vibration of the cable network. Once eigenvalues have been obtained, calculation of the system eigenvector components is carried out on the basis of parent subspaces of the eigenvalues, with mode shapes of the cable net following through a relatively trivial final step.

Anthropomorphous robot and kinematics model in general form

In this paper is represented a model of anthropomorphous robot with "the biomechanical pairs". This is the general received various kinds of robot, because from here can be received various kinds of robots as the particular cases. Accordingly, the kinematics model of the robot is also represented in general form. The proposed algorithm for solving inverse problem for the anthromorphous robot with n-degrees of freedom allows to receive analytical forms for the control parameters.

Fuzzy control of a manipulator using an actuator and multibrakes

This paper is concerned with the control of a manipulator with n-degrees of freedom by one actuator and n − 1 brakes using fuzzy inference. All the links of the manipulator are excited by a motor placed on the base link, and the excitation torque is successively transmitted through each link from the base link until the final link. The brakes on the joints act at identical frequency with different phases, and the phases of timing on the brakes are controlled by fuzzy inference such that all the joint angles of links are followed to the desired trajectories. The effectiveness of the proposed method is illustrated by a simple example.

Sliding mode control for gradient tracking and robot navigation using artificial potential fields

This paper introduces a sliding mode control strategy for tracking the gradient of an artificial potential field. The control methodology is applicable to fully actuated holonomic robotic systems with n-degrees of freedom. The controller yields exact tracking of the gradient lines and is invariant with respect to parametric uncertainty and disturbances in system dynamics. A detailed case study for mobile robots introduces the equilibrium point placement method for designing harmonic planar potential fields for circular obstacle security zones. Diffeomorph mappings can be utilized for more complex obstacle security zones. The gradient of the harmonic potential field is shown to always lead away from the obstacle security zone and to continuously approach the goal point.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fuzzy control of a manipulator using the switching motion of brakes

A method of controlling a manipulator with n-degrees of freedom by one actuator and n — 1 brakes using fuzzy inference is described. The manipulator is reduced to have two-degrees of freedom because n — 2 brakes are applied, so that the switching time of the brakes and the torque of the actuator are obtained. The manipulator is assumed to have uncertainty in the model and fuzzy control is determined by learning the dynamic response of the manipulator. The effectiveness of the proposed method is illustrated by a simple example.

Model reference control and identification of robotic manipulators under uncertainty

The robotic manipulator is considered in terms of an open kinetic chain with n-degrees of freedom, with nonlinear and nonlinearizable characteristics and couplings, and with uncertain but bounded values of system parameters. The chain is powered by n-actuators and effected by a pay-load which is unknown but within a known band. The objective is to reach for a moving target and avoid moving obstacle. It is specified in terms of a dynamic model to be followed. The well known linear model-reference adaptive control technique is extended to the nonlinear case at hand and used to stabilize the manipulator about the model, at the same time on-line identifying the uncertain parameters and the payload. The method is similar to the self-tuning control which is used in manufacturing when high speed must be combined with high accuracy and not-too-high requirements on sensors (reducing the number of transducers and reading time) as well as broadening the functional abilities of the actuators. The identification uses nonlinear identifier (predictor) system which also stabilizes the resultant response of the manipulator and itself about the desired dynamic model. Algorithms for the adaptive laws in both control and identification are provided. Numerical simulation illustrates the results.

Modal subspaces and normal mode vibrations

Trajectories of non-linear conservative systems having n-degrees of freedom can be identified with the motions of a unit mass in an n-dimensional Euclidean space under a force derivable from a potential function. Normal modes of vibrations of such systems have been defined and discussed by R.M. Rosenberg and others. This paper deals with special classes of motions of the system for which the trajectories of the unit mass remain in subspaces of the Euclidean n-space; these are called modal subspaces. Using the symmetry and other properties of the potential function, methods are developed to find these modal subspaces and to systematically reduce the dimensions of the modal subspaces. In many cases, this procedure leads to finding one-dimensional modal subspaces which represent normal modes of vibration. The methods determine the modes geometrically without having to integrate the differential equations. Examples are given to demonstrate the applications.

Theory of Self-Excited Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—1

Self-excited chatter, an instability of the cutting process in combination with the machine structure, is a basic performance limitation of a machine tool. A theory is developed which permits calculation of borderlines of stability for a structure having n-degrees of freedom and assuming no dynamics in the cutting process. Harmonic solutions of the system characteristic equation are found using a special chart, and the resulting data are used to plot a stability chart. However, an infinite number of such stability charts exists for a given machine because the structure dynamics vary with cutting-force orientation. This fact makes a simpler index of chatter performance desirable. A simple stability criterion is proposed which states that the directional cutting stiffness must be less than one half the minimum directional dynamic stiffness of the structure for each force orientation to assure chatter-free performance at all spindle speeds. Thus chatter-free performance can be fundamentally identified with adequate structural dynamic stiffness for all cutting-force orientations. Such a broad requirement for dynamic stiffness is difficult to meet in the design stage since structural characteristics are not easily predicted and controlled. Machine testing with continual improvements in the structure to increase dynamic stiffness is currently the best way to combat chatter.