Joint Error Research Articles

Transmission Error of Modular Robotic Joint

This paper deals with the accuracy problem of a type of joint module with two rotary degrees of freedom used in a modular robot system. The error investigation concentrates on its differential gear mechanism. By dividing the gearing error into the gear transmission error due to effective eccentricity and the lost motion error due to effective backlash, errors in two output angles (i. e., joint angles) are modeled based on the engaging principle of two bevel gears. Effective eccentricity due to the tolerances in the bearing system is then determined using the geometry between the bearing and the bevel gear. By taking into account the random nature of tolerances, stochastic characteristics of the output angles' errors are calculated under the assumption that eccentricity is distributed uniformly within a circle of tolerance. On the basis of the above stochastic error formulas, an optimal method and a simplified method are proposed for allocating the tolerances. In this paper, the concrete structure of the modular joint is examined to illustrate error estimation and tolerance allocation. Finally some conclusions are drawn for improving the accuracy of this type of modular joint.

On the optimum tolerances of structural parameters and kinematic parameters of robit manipulators

The paper presents a matrix form of the positional and orientational erros of the end-effector of manipulators. By using the matrix theory, the paper reaches a conclusion that if the output kinematic errors of a manipulator are minimum, the aberrations of its structural parameters and the kinematic errors in robot joints must be the components of the eigenvector related to the least eigenvalue of the Jacobian. According to this conclusion, the method for choosing the optimum tolerances of structural parameters and kinematic parameters is also given in the paper. A numerical example of a six DOF manipulator is presented.

Robust control of robot arms including motor dynamics

A state model that incorporates robot arm dynamics together with joint actuator dynamics is formulated as a nominally linear uncertain system. The uncertainty is matched and it is shown to be bounded by a cubic expression of the norm of the joint errors. A nonlinear robust feedback controller is then derived which guarantees global ultimate boundedness of the actual system trajectories. Computer simulations are performed on a model of the PUMA 560 robot arm and the results have verified the feasibility of our controller with excellent trajectory tracking performance.

The dynamics of adjustment in deviations from covered interest parity in the Euromarket: evidence from matched daily data

The speed of adjustment of deviations from covered interest parity is considered. A data set is used which is composed of daily observations in the Euromarket for five currencies, in which careful attention was paid to the timing of observations. As the forward exchange discount and the nominal interest differential for each of these currencies contain a unit root, error correction models were constructed which model the adjustment of these variables. The results show that although a joint error correction representation exists between the forward exchange discount and the nominal interest differential, the lags are short enough to be consistent with rapid adjustment to equilibrium.

Local joint control in cooperating manipulator systems - force distribution and global stability

SUMMARYAlmost all industrial robot applications in use today are controlled using a control law that is simple and computationally efficient, local joint error feedback. When two or more open chain manipulators cooperate to manipulate the same object - such as in mechanical grippers, walking machines, and cooperating manipulator systems - closed kinematic chain, redundantly actuated mechanisms are formed. Control approaches for this type of system focus on the more computationally intensive computed torque or inverse plant control laws, due to the concern over instability caused by the unspecified distribution of control forces in the redundant actuator space, and due to the constrained motion caused by the closed kinematic chains.

Stochastic error propagation in robot arms

Static error propagation in positioning robot arms has been extensively analyzed based on linearized error propagation models. These models are used for robot design and calibration. Most results were calculated using normally distributed errors in the different robot joints and links. In reality not all joints and links errors are normally distributed, and a mix of suitable symmetric and nonsymmetric probability distributions should be used in the error propagation model. The paper presents the general model for propagating errors with different distributions applicable to any system whose model can be linearized. Numerical examples are given for a general beta distribution of errors, and for a mix of symmetric and nonsymmetric distributions. Within the work-volume, the different configurations that a robot arm may attain during its life span can be expressed by a probability distribution. The paper includes the analysis of the effect of this distribution on the position error of the end-effector.

Compensation of Robot joint variables using special Jacobian matrices

In dealing with an industrial manipulator, the end-effector accuracy is a major concern. The positioning of the end effector is determined by the controller that utilizes the data from a closed-form kinematic inversion. The closed-form inversion uses nominal, i.e., manufacturer specified, values of link lengths, twists, and offsets. Due to manufacturing tolerances, set-up, and usage, these nominal parameters may be inaccurate. If the nominal parameters contain built-in error values, the closed-form kinematic inversion will yield incorrect joint values, and the actual end-effector position will deviate from its desired position. One may use a parameter identification method to identify the position-independent error parameter values. This article assumes that this has been done and it presents an iterative compensation algorithm (ICA) through which the identified position-independent parameter error values may be used to correct the joint values obtained through the closed-form kinematic inversion. The Denavit and Hartenberg (D-H) parameters (θsαa) are used to model the given M-jointed manipulator, and a set of four special Jacobian matrices (Jθ, Js, Jα, and Ja) are formulated. The iterative compensation algorithm allows one to determine the M unknown position-dependent joint error values by using these four special Jacobian matrices. The improvements obtained through the use of the compensation algorithm will be presented for regular trajectories, as well as when the robot nears certain singularity conditions. Since it is important to know a priori a definite number of iterations that must be performed, the level of compensation after a fixed number of iterations is also studied. Through the presentation of numerous examples, it is shown that the proposed compensation algorithm is simple and straightforward to implement, and it increases the end-effector accuracy.

A joint signature encryption and error correction public-key cryptosystem based on algebraic coding theory

A joint signature, entyption and error correction public-key cryptosystem is presented based on an NP-completeness problem—the decoding problem of general linear codes in algebraic coding theory.

New Robot Adaptive Control Strategies Through Nonholonomic Transformations

The design problem of model-based adaptive control of robots with unknown parameters is considered. By intro ducing a nonholonomic transformation of the error dynamics, a general class of adaptive algorithms is obtained, which includes some previously derived results as special cases. The algorithms can be implemented through fast recursive schemes such as the Newton-Euler formulation without requiring excessive feedback gains. By setting certain terms, it is also possible to obtain an exponential convergence of the joint errors.

An observer for flexible joint robots

The problem of state observation of robots that have elastic joints is discussed. Outputs are assumed to be the global link coordinates and their time derivatives, and a nonlinear observer is proposed which asymptotically reconstructs all the robot state variables. The dynamic behaviour of the observation algorithm is illustrated by simulation tests referred to a manipulator with three revolute elastic joints. To verify the observer robustness, the previous simulation tests were repeated by using the same observer, designed for a nominal payload of 5 kg, and actual robot payloads of 0 and 10 kg. The differences with respect to the nominal case are not appreciable. However, the steady-state joint errors, which were about 10/sup -6/ rad in the nominal case, became about 10/sup -4/ rad.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Tolerance Volume Due to Joint Variable Errors in Robots

The locational uncertainty of a manipulator is largely due to the errors of the joint variables. But these errors cannot be easily compensated for because they are dependent on the operation (i.e., robot-configuration). Motivated by the need to conduct precision engineering and the intellectual curiosity of geometric uncertainty, the probabilistic tolerance volume due to joint errors is investigated. By defining the locational uncertainty in Cartesian space as a tolerance volume, the investigation focuses on the automatic generation of the tolerance volume from a given confidence level. For this purpose, the linear mapping form Δq space to Δd space through Jacobian matrix is analyzed probabilistically. Probabilistic approach is advantageous since the tolerance volume by the deterministic approach is found to be unnecessarily large. With the assumption of normality of joint variables, this paper begins with the computation of the confidence level for a given tolerance volume. A fast analytic procedure, which gives a considerable time-reduction compared to the commonly used Monte-Carlo simulation, is presented. Based on the monotonic relation between confidence level and tolerance volume, the procedure is used to generate the tolerance volume covering the desired confidence level. The scheme is tested with the six degrees-of-freedom Stanford manipulator and shows a significant (more than 5 times) reduction in the size of the tolerance volume with a 0.3 percent probability of error.

Position Errors Due to Clearances in Journal Bearings

The positional errors due to clearances in journal bearings intended to approximate revolute joints are analyzed. Equations are presented which relate joint geometry, external loads, and errors. The paper treats the case common in serial chain manipulators where the revolute joint’s nominal rotational angle is controlled, and it is desired to determine the errors that result from the clearances.

Determination of elastodynamic errors in joints of industrial robots

SUMMARYThis paper presents a method for automatic forming and solving dynamic equations of motion of manipulator with elastic joints and rigid segments. For the minimal configuration of a cylindrical manipulator the numerical integration of these equations is performed, and vibrations in the joints are obtained as dynamic errors with respect to the prescribed trajectory.

Computer-aided joint error analysis of robots

Various definitions of task-space tolerances, using geometric pseudoenvelopes, are introduced, and new approaches to "direct" and "inverse" joint-error analysis of robots are formulated. These error analyses lead to the development of a "feasible joint-tolerance domain" concept for use in computer-aided design of robots.

Distribution-free and link-free estimation for the sample selection model

Abstract The prevalent estimation methods for the sample selection model rely heavily on parametric assumptions and are sensitive to departures from the underlying parametric assumptions [see, e.g., Goldberger (1983)]. We propose an alternative estimation method, the corrected maximum likelihood estimate, which is consistent for the slope vector in the outcome equation up to a multiplicative scalar, even through the parametric model on which the estimate is based might be misspecified. As an important corollary, it follows from our result that Olsen's (1980) corrected ordinary least squares estimate is consistent if the outcome equation is linear, without requiring Olsen's assumptions on the joint error distribution.

An analytical quadratic model for the geometric error of a machine tool

Abstract In the analysis of geometric error of a machine, errors (especially angular errors) of a joint (axis) are assumed to remain constant with movement along the joint. The assumption, as actual measurements indicate, is not justifiable. Substantial variations can be observed. In this paper an analytical model for the prediction of geometric error of a machine tool is presented. Unlike previously proposed models, this model allows for the variation of errors along the machine's joints (axes). The model, developed using rigid body kinematics, relates the error vector at a point in the machine tool work space to the coordinates of that point by the dimensional and form errors of the individual links and joints of the machine's kinematic scheme. Shape and joint transforms are developed for inaccurate machine elements. An expression is developed for the case where the individual joint errors vary linearly with movement along the joint (or axis). The expression is quadratic. A comparison, made between the errors predicted by the model which allows for variation of individual errors and one that does not, indicates that the higher order terms of the expression make significant contributions to the predicted error. Finally, a method for estimating the coefficients of the model from the error obtained on a workpiece is proposed.

On bounding the errors in three Runge-Kutta type formulations

Total error bounds are established for three of the Runge—Kutta type numerical integration formulas. These are (a) the Heun third-order formula, (b) the Kutta—Simpson three-eighths formula, and (c) the Kutta—Simpson one-third formula. For (a) and (b), it is established that when analyzing for equations of the sort y′(x) = ƒ(x,y), the total error at any step i is of the form | E i | ≤ E(e ihM − 1)/(e hm − 1) where h is the step size and E and M are certain constants. It is found that a system of two equations, y′(x) = ƒ(x, y, z) and z′( g) = ( g)( x, y, z), have a joint error given by max (| E i |, | D i |) ≤ E(e 2 ihM − 1)/(e 2 hM − 1) when analyzed by method (c). In addition to error bounds, conditions under which the ith step result is valid are derived for each procedure.

Let Them Eat Cake: A Note on Comparing Alternative Models of the Demand for Medical Care

This article comments on the Rand econometric approach to estimating and testing models of the demand for medical care as typified in Duan et al. (1983). The Rand methodology is contrasted with more mainstream econometric approaches to similar empirical problems as developed in the sample selection literature. It is shown that despite Rand's claim, their approach requires some fairly unusual assumptions on the model joint error distribution and functional form. Alternatively, their model likelihood functions may be interpreted as being nested in more general sample selection model likelihood functions with easily testable parameter restrictions.

Compensation in time-dispersion properties of cascaded multimode fibres

Time-dispersion effects in cascaded multimode fibres are investigated. The well known compensation behaviour between index profiles having opposite deviations from the optimum is demonstrated through a new very simple theoretical approach. The effects of possible joint errors are also taken into account.

Joint encryption and error correction schemes

Joint encryption and error correction schemes