Passive acoustic monitoring (PAM) is a powerful tool for studying marine biodiversity, but large-scale analysis of underwater recordings is constrained by noise, overlapping signals, and limited labeled data. Here, we present a scalable, unsupervised contrastive learning framework for marine soundscapes. Using a large PAM dataset spanning multiple biogeographies, we show that the proposed approach organizes recordings into clusters with well-defined internal structure, as assessed using intrinsic clustering metrics and within-cluster similarity. The resulting clusters reveal recurring acoustic patterns that correspond to broad sound-source categories, including biological sounds such as fish calls and choruses, and anthropogenic sounds such as vessel noise, without explicitly enforcing these distinctions during training. Compared with established approaches, including cepstral features, variational autoencoders, and supervised pipelines, the proposed framework produces embeddings that support more compact and stable unsupervised clustering while preserving fine-scale acoustic variation beyond predefined species labels. By learning a shared representation across recordings from multiple sites and years, we examine the reproducibility of acoustic patterns across locations and identify both site-shared and site-specific sound signatures. Although the method is not designed to recover coarse species labels, it enables label-efficient analysis by reducing reliance on manual annotation and supporting exploratory characterization of complex marine soundscapes. Together, these results highlight multi-positive contrastive learning with a teacher network and acoustically informed augmentations as an effective strategy for scalable, discovery-driven analysis of passive acoustic monitoring data.

This paper proposes a new complex autoencoder suitable for learning spectrally efficient, constant envelope waveform coding. In contrast to prior work, we model the encoder output layer as a phase modulation layer with a complex exponential activation function. In addition, we model the decoder with a complex-valued feature detection layer that may be coherent or noncoherent. The complex topology leads to noncoherent waveform coding methods not obtained in prior studies. The paper provides a mathematical framework for training the proposed autoencoder along with illustrative examples that demonstrate its ability to learn improved spectral efficiency relative to traditional orthogonal and biorthogonal modulations.

Difficulty in analyzing deep learning systems is preventing association of its parameters and state outputs with elements that are derived from theoretic considerations. Medical and criminal justice communities are excited by the possibilities nevertheless reluctant to adopt machine learning for fear of errors and bias. There is also concern among educators that mystifying learning may have long-term adverse pedagogical implications on human learning. Deep learning techniques have not received enthusiastic attention in the realm of communication systems, either. This is in part due the effectiveness of traditional analytical solutions that render classification error rates larger that 10-3unacceptable. Understanding of deep networks for communications, and ability to perform comparison tests can be useful in developing scalable methods to understand them in more complex scenarios. This paper contributes a perspective and analysis with focus on Nyquist and non-Nyquist pulse shapes for bandlimited channels. It is hoped that this fundamental presentation motivates wider consideration of neural networks and deep learning for demodulation.

This paper presents a novel approach to categorize dolphin whistles into various types. Most accurate methods to identify dolphin whistles are tedious and not robust, especially in the presence of ocean noise. One of the biggest challenges of dolphin whistle extraction is the coexistence of short-time duration wide-band echo clicks with the whistles. In this research a subspace of select orientation parameters of the 2-D Gabor wavelet frames is utilized to enhance or suppress signals by their orientation. The result is a Gabor image that contains a noise free grayscale representation of the fundamental dolphin whistle which is resampled and fed into the Sparse Representation Classifier. The classifier uses the l1-norm to select a match. Experimental studies conducted demonstrate: (a) a robust technique based on the Gabor wavelet filters in extracting reliable call patterns, and (b) the superior performance of Sparse Representation Classifier for identifying dolphin whistles by their call type.

In this paper we consider the energy-efficient resource allocation that minimizes a general cost function of average user powers for small- or medium-scale wireless sensor networks, where the simple time-division multiple-access (TDMA) is adopted as the multiple access scheme. A class of so-called ß-fair cost functions is derived to balance the tradeoff between efficiency and fairness in energy-efficient designs. Based on such cost functions, optimal channel-adaptive resource allocation schemes are developed for both single-hop and multihop TDMA sensor networks. Relying on stochastic optimization tools, we further develop stochastic resource allocation schemes which are capable of dynamically learning the intended wireless channels and converging to the optimal benchmark without a priori knowledge of channel fading distribution function.

In this paper, we consider the energy-efficient resource allocation that minimizes a general cost function of average user powers in wireless networks. A class of so-called ß-fair cost functions is derived to balance the tradeoff between efficiency and fairness in energy-efficient designs. With these novel cost functions, optimal resource allocation schemes are developed for fading time-division multiple-access (TDMA) channels. Relying on stochastic approximation tools, we further develop the corresponding stochastic schemes which are capable of dynamically learning the intended wireless channels and converging to the optimal benchmark without a priori knowledge of fading distribution function.

Design and tuning a fuzzy logic controller (FLC) are usually done in two stages. In the first stage, the structure of a FLC is determined based on physical characteristics of the system. In the second stage, the parameters of the FLC are selected to optimize the performance of the system. The task of tuning FLCs can be performed by a number of methods such as adjusting control gains, changing membership functions, modifying control rules and varying control surfaces. A method for the design and tuning of FLCs through modifying their control surfaces is presented in this paper. The method can be summarized as follows. First, fuzzy control surfaces are modeled with Bezier functions. Shapes of the control surface are then adjusted through varying Bezier parameters. A genetic algorithm (GA) is used to search for the optimal set of parameters based on the control performance criteria. Simulation results on various control systems show the effectiveness of the proposed method.

This paper describes a multi-resolution pyramidal Gabor-eigenface (PGE) algorithm for face recognition. The PGE algorithm employs the eigenface method on the desirable Gabor facial features, which derive from the multi-resolution pyramidal Gabor wavelet (PGW) transform of face images in the spatial domain directly without a Fourier implementation. The use of eigenface method further reduces the redundancy of the images from PGW. The feasibility of the PGE algorithm has been successfully tested on face recognition using AT&T (formally Olivetti) face databases, which contain 400 face images of 40 subjects with variation in poses, facial expression, different viewing direction, and disguises. The effectiveness of the PGE algorithm is shown in terms of better accuracy, faster computational speed and much less computer memory amount.

A method for the self-calibration of a camera equipped robot manipulator is proposed in this paper. In this method, it is assumed only a scale, which is placed in the field of view of the camera, is known in the world coordinate system. It has been known from the computer vision field that, the extrinsic parameters of the camera along with its intrinsic parameters can be obtained up to a scale factor by using the corresponding points of objects in a natural environment from an image sequence. Now, if the camera is treated as the tool of the robot, one is then able to compute the corresponding robot pose directly from the camera extrinsic parameters once the scale factor is available. This scale factor, which changes from one camera pose to another, can be determined uniquely from the known scale. Another idea is the use of the factor method for pose estimation. The original factor method is sensitive to errors from image quantization, feature extraction, and model simplification. In order to make the factor method robust for robot pose estimation, a nonlinear least-squares algorithm is proposed in the paper. Issues relevant to this algorithm such as formulation of cost functions and selection of initial conditions are addressed. Once a sufficient number of robot poses at various measurement configurations are obtained using the proposed method, the estimation of actual link parameters of the robot becomes possible. Extensive simulations and experiment studies on a PUMA 560 robot reveal the convenience and effectiveness of the proposed self-calibration approach.

In most fuzzy logic controllers (FLCs), initial membership functions (MFs) are normally laid evenly all across the universes of discourse (UD) that represent fuzzy control inputs. However, for evenly distributed MFs, there exists a potential problem that may adversely affect the control performance; that is, if the actual inputs are not equally distributed, but instead concentrate within a certain interval that is only part of the entire input area, this will result in two negative effects. On one hand, the MFs staying in the dense-input area will not be sufficient to react precisely to the inputs, because these inputs are too close to each other compared to the MFs in this area. The same fuzzy control output could be triggered for several different inputs. On the other hand, some of the MFs assigned for the sparse-input area are "wasted". In this paper we argue that, if we arrange the placement of these MFs according to a statistical study of feedback errors in a closed-loop system, we can expect a better control performance. To this end, we introduce a new mechanism to modify the evenly distributed MFs with the help of a technique termed histogram equalization. The histogram of the errors is actually the spatial distribution of real-time errors of the control system. To illustrate the proposed MF modification approach, a computer simulation of a simple system that has a known mathematical model is first analyzed, leading to our understanding of how this histogram-based modification mechanism functions. We then apply this method to an experimental laser tracking system to demonstrate that in real-world applications, a better control performance can he obtained by using this proposed technique.

Investigates robot calibration with planar constraints, and in particular the conditions for the parameters of the robot kinematic model to be observable. Mainly multiple-plane constraints for robot calibration are considered. It is first shown that a single-plane constraint is normally not sufficient to calibrate a robot. It is also proven that by using a three-plane constraint, the constrained system is equivalent to an unconstrained point-measurement system under certain conditions. The significance of this observation is that one can use the three-plane constraint setup to successfully calibrate a robot. Simulations have been conducted to verify the theory presented in the paper.

The authors previously (1995) proposed an efficient method for tracking the eye movements. The proposed algorithm did not address the issue of compensating for head movements. Head movements are normally much slower than eye movements and can be compensated for using another tracking scheme for head position. In this paper, a hybrid method employing the two tracking schemes is developed. To this end, first a measurement model for the compensation of the head movement is formulated and then the overall tracking scheme is implemented by cascading two Kalman filters. The tracking of the iris movement is followed by the compensation of the head movement for each image frame. Experimental results are presented to demonstrate the accuracy aspects and the real-time applicability of the proposed approach.

In two previous papers, we proposed an iterative algorithm for robotic hand/eye calibration. We stated that the iterative algorithm has two distinct advantages over traditional linear approaches: it is less sensitive to noise and it can calibrate the hand/eye matrix by using only relative sensor position measurements. In this correspondence, we point out that although the iterative algorithm does not require direct measurement of the sensor relative rotation, it still needs the user to provide the same amount of sensor orientation information. We also explain why the accuracy performance of the iterative algorithm was not improved by the inclusion of rotation equations.

The problem investigated in this paper is an extension of the robotic hand/eye calibration problem. The system consists of a robot, a gimbal, and a three-dimensional (3D) sensor. It is assumed that the sensor, the gimbal, and the robot are calibrated in advance; therefore, their inaccuracy is negligible. The task is to determine the hand/eye matrix that relates the sensor coordinate frame to the first gimbal coordinate frame and the connection matrix that relates the last gimbal coordinate frame to the robot tool frame. The paper focuses on a special case of this problem. The robot is an x-y-z type and the gimbal has two rotary joints. Linear and iterative methods are presented, along with the discussion on issues such as solution uniqueness and parameter observability. Simulation and experimental results are presented to demonstrate the feasibility of the method.

Robotic hand/eye calibration is the process of identifying the fixed, yet unknown, position and orientation of a sensor mounted on the robot end-effector with respect to the robot hand coordinate frame. It is proven in this paper that in the case of camera-equipped electronic assembly robots, up to five parameters (three rotation and two position parameters) in the hand/eye matrix can be determined. However, it is shown that in order to measure relative poses of the hand-mounted sensor, one needs only to know these five parameters. Linear and iterative methods are proposed to estimate the five relevant parameters. Simulation and experimental studies confirm the effectiveness of the methods.

The problem investigated in this paper is an extension of the robotic hand/eye calibration problem. The system consists of a robot, a gimbal and a three dimensional sensor. The task is to determine the hand/eye matrix that relates the sensor coordinate frame to the first coordinate frame in the gimbal and the connection matrix that relates the first coordinate frame in the gimbal to the tool frame in the robot. The paper focuses on a special case of the mentioned problem. In this study, the robot is a x-y-z type and the gimbal has two rotary joints. Two solution methods, one of which is linear and another is nonlinear, are presented in this paper. Issues such as the uniqueness of the linear solution and the observability of error parameters are also investigated. Simulation and experimental results are given to demonstrate the feasibility of the method.

Widely used in manufacturing industry, coordinate measuring machines(CMM) are traditionally designed with a serial structure, which is composed of a serial chain of three mutually perpendicular prismatic joints to achieve three degrees of freedom in motion. There exist some shortcomings such as error accumulation and low stiffness in this kind of structure. This paper introduces a CMM with a parallel structure, which is more accurate and robust compared to the serial one, and studies some important issues in designing and developing this type of CMM, including the closed-form forward and inverse solutions, workspace analysis, and system calibration.

Self-calibration has the potential of: 1) removing the dependence on any external pose sensing information; 2) producing high accuracy measurement data over the entire workspace of the system with an extremely fast measurement rate; 3) being automated and completely noninvasive; 4) facilitating on-line accuracy compensation; and 5) being cost effective. A general framework is introduced in this paper for the self-calibration of parallel manipulators. The concept of creating forward and inverse measurement residuals by exploring conflicting information provided with redundant sensing is proposed. Some of these ideas have been widely used for robot calibration when robot end-effector poses are available. By this treatment, many existing kinematic parameter estimation techniques can be applied for the self-calibration of parallel mechanisms. It is illustrated through a case study, i.e. calibration of the Stewart platform, that with this framework the design of a suitable self-calibration system and the formulation of the relevant mathematical model become more systematic. A few principles important to the system self-calibration are also demonstrated through the case study. It is shown that by installing a number of redundant sensors on the Stewart platform, the system is able to perform self-calibration. The approach provides a tool for rapid and autonomous calibration of the parallel mechanism.

A single-stage linear method is devised in this paper to simultaneously fit rotation and translation (pose) parameters given two sets of three-dimensional (3-D) point measurements. The necessary and sufficient conditions for the unique solution of the pose determination problem are stated. The computational complexity of the new algorithm is similar to the existing linear algorithms. However it offers a mechanism to incorporate the reliability of measurements and a procedure to implement the estimation recursively. Applications of the technique include localization of a robot in its environment and real-time estimation of object motion based on computer vision.

A general numerical method is introduced in this paper for the self-calibration of parallel manipulators. The concept of creating inverse measurement residuals by exploring conflicting information provided with redundant sensing is generalized. A numerical kinematic analysis method is adopted to systematically compute the inverse measurement residuals. By this treatment, the design of a suitable self-calibration system became more systematic, and existing kinematic parameter estimation techniques can be applied for the self-calibration of parallel mechanisms. It is shown that by installing 2 or more redundant sensors on the Stewart platform, the system is able to perform self-calibration. It is possible to calibrate part of the system using a reduced number of redundant sensors; the identification algorithm converges rapidly; its accuracy performance is satisfactory; and the extension of the method to other parallel manipulators is straightforward.

A single-stage linear method is devised in this paper to simultaneously fit rotation and translation (pose) parameters given two sets of 3-D point measurements. The necessary and sufficient conditions for the unique solution of the pose determination problem are stated. The computational complexity of the new algorithm is similar to the existing linear algorithms. However it offers a mechanism to incorporate the reliability of measurements and a procedure to implement the estimation recursively. Applications of the technique include localization of a robot in its environment and real-time estimation of object motion based on computer vision.

In this paper, techniques developed in the science of genetic computing are applied to solve the problem of optimally selecting robot measurement configurations, which is an important element in successfully completing a robot calibration experiment. Genetic algorithms are customized for a type of robot measurement configuration selection problem in which the robot workspace constraints are defined in terms of robot joint limits. Simulation studies are conducted to examine the effectiveness of the genetic algorithms for the application.

Tsai's radial alignment constraint (RAC) method has been shown as a viable candidate for camera calibration. The solution procedure, however, will fail if the camera plane is parallel to the plane defined by a calibration board which is used to provide calibration data. Tsai also devised an algorithm that handled the exactly parallel case. In this paper, we show that by a slight modification of the RAC-based camera calibration method, the unknown parameters of the camera can still be calibrated even when the sensor plane is near-parallel to the camera calibration board. An application example of the proposed approach is the calibration of a selectively compliant assembly robot arm (SCARA) with a hand-mounted camera, where the extrinsic parameters need to be repeatedly calibrated to reconstruct robot end-effector poses at various robot measurement configurations.

This paper focuses on the accuracy enhancement of Stewart platforms through kinematic calibration. The calibration problem is formulated in terms of a measurement residual, which is the discrepancy between the measured leg length and the computed leg length. With this formulation, one is able to identify kinematic error parameters of the Stewart platform without the necessity of solving the forward kinematic problem, thus avoiding the numerical problems associated with the solution of the forward kinematic problem. The error parameters are basically the installation errors of the platform ball and U-joints as well as the leg length offsets. By this formulation, a concise differential error model with a well-structured identification Jacobian, which relates the pose measurement residual to the errors in the parameters of the platform, is derived. A measurement procedure that utilizes a single theodolite was devised to determine the poses of the platform. Experimental studies reveal that the proposed calibration method is effective in enhancing the accuracy performance of Stewart platforms.

Robot calibration is an effective and economical means for enhancing the accuracy performance of a robot manipulator through modification of its control software. This paper reports some research results by applying Lenz and Tsai's approach (1989) to calibrate a SCARA arm equipped with a hand-mounted camera. In order to measure robot poses, a new technique was employed to calibrate the camera at various robot configurations. The camera calibration technique is singularity free even when the image plane is nearly-parallel to the camera calibration board. Second, the modified complete and parametrically continuous (MCPC) model was used to describe the geometry of the SCARA arms because there is no model singularity in the MCPC model for this type of robots. Experimental studies were conducted to demonstrate the feasibility of the present approach for calibrating SCARA arms. Some practical recommendations are also made for robot users who need to calibrate SCARA arms.

In this correspondence, the single-scanline camera model proposed in the original paper (R. Horaud, R. Mohr and B. Lorecki, ibid., vol. 8, no. 1, p. 71-5, 1993) is modified to include a lens distortion coefficient. The authors say that, by this modification, the calibration approach presented will become more practical. The original authors accept that the improvement is sensible but say that the argument is not rigorous and suggest better approaches to some aspects.>

The solution method presented previously by us ( ibid. vol.9, no.2, p.174-85, 1993) employs the complete and parametrically continuous (CPC) model. In the first step of this approach, all CPC orientation parameters related to revolute joints, are sequentially determined. In the second step, CPC translation parameters, together with orientation parameters of prismatic joints, are simultaneously computed. While our approach eliminates propagation errors in the estimation of translation parameters, it has several drawbacks. In this paper we propose a modification to the linear approach of the previous method. This modification not only eliminates the two problems of the original method but also preserves the advantage of solving for the robot translation parameters simultaneously.

A popular configuration widely used in a variety of robotic applications is to mount a camera on the robot manipulator hand. Before performing a measurement task using such a system, both the camera and the robot need to be calibrated. In this paper, a procedure is developed for simultaneous calibration of a robot and a monocular camera. Unlike conventional approaches based on first calibrating the camera and then calibrating the robot, the algorithm solves for the kinematic parameters of the robot and camera in one stage, thus eliminating error propagation and improving noise sensitivity. Only two parameters are added to a robot calibration model to represent camera geometry. With this addition, different levels of calibration can be done under a unified framework. An error model relating-image measurement residuals to kinematic parameter deviations is derived. Simulation and experimental studies have been conducted to assess the effectiveness of the proposed procedure.>

Eye movement analysis is of importance in clinical studies and in research. Monitoring eye movements using video cameras has the advantage of being nonintrusive, inexpensive, and automated. The main objective of this paper is to propose an efficient approach for real-time eye feature tracking from a sequence of eye images. To this end, first we formulate a dynamic model for eye feature tracking, which relates the measurements from the eye images to the tracking parameters. In our model, the center of the iris is chosen as the tracking parameter vector and the gray level centroid of the eye is chosen as the measurement vector. In our procedure for evaluating the gray level centroid, the preprocessing step such as edge detection and curve fitting need to be performed only for the first frame of the image sequence. A discrete Kalman filter is then constructed for the recursive estimation of the eye features, while taking into account the measurement noise. Experimental results are presented to demonstrate the accuracy aspects and the real-time applicability of the proposed approach.

A self-calibration technique is proposed in this paper to estimate extrinsic parameters of a stereo camera system. This technique does not require external 3D measurements of precision calibration points. Furthermore, it is conceptually simple and easy to implement. It has applications in such areas as autonomous vehicle navigation, robotics and computer vision. The proposed approach relies solely on distance measurements of a fixed-length object, say a stick. While the object is moved in the 3D space, the image coordinates of the object end points are extracted from the image sequence. A cost function that relates unknown parameters to measurement residuals is formulated. A nonlinear least squares algorithm is then applied to compute the parameters by minimizing the cost function, using the measured image coordinates and the known length of the object. Simulation studies in this papers answer questions such as the number of iterations needed for the algorithm to converge, the number of measurements needed for a robust estimation, singularity cases, and noise sensitivities of the algorithm.>

Laser tracking systems based on interferometry have applications in robot and machine tool calibration. Relative distance measurements provided by laser interferometers have an extremely high resolution. However, accuracy errors of a coordinate measuring machine based on laser tracking are dominated by geometric errors in the tracking mirror system. Major geometric error sources include gimbal axis misalignments and mirror center offset. In this paper, a geometric model for a single-beam tracker is developed, in which a necessary and sufficient number of geometric parameters is used to represent these two types of error sources for arbitrary target positions. This model can be used for design, calibration and control of single-beam laser tracking measurement systems.>

Measuring robot positions and orientations is a crucial step in a robot calibration process. Off-line optimal selection of measurement configurations can significantly improve the accuracy of kinematic identification. Since the dimension of the parameter space is very large and the cost function is highly nonlinear, this selection process could be well beyond the capacity of today's computers if a global optimal solution is sought by an exhaustive search. On the other hand, gradient-based algorithms are often trapped into local minima. A simulated annealing (SA) approach is adopted in this paper to obtain optimal or near optimal measurement configurations for robot calibration. Simulated annealing is capable of overcoming local minimum points. It is also very convenient for the inclusion of joint travel limits. The SA algorithm is costly computationally; however, since optimal configuration selection can be performed off-line, this may not be a serious problem. To accelerate the convergence rate, a suitable cooling schedule is devised. Practical implementation considerations are discussed. Experimental results are presented to demonstrate the feasibility of the proposed approach.>

The paper presents a linear solution that allows a simultaneous computation of the transformations from robot world to robot base and from robot tool to robot flange coordinate frames. The flange frame is defined on the mounting surface of the end-effector. It is assumed that the robot geometry, i.e., the transformation from the robot base frame to the robot flange frame, is known with sufficient accuracy, and that robot end-effector poses are measured. The solution has applications to accurately locating a robot with respect to a reference frame, and a robot sensor with respect to a robot end-effector. The identification problem is cast as solving a system of homogeneous transformation equations of the form A/sub i/X=YB/sub i/,i=1, 2, ..., m. Quaternion algebra is applied to derive explicit linear solutions for X and Y provided that three robot pose measurements are available. Necessary and sufficient conditions for the uniqueness of the solution are stated. Computationally, the resulting solution algorithm is noniterative, fast and robust.>

This paper presents an approach for estimating motion from a stereo image sequence. First a stereo motion estimation model is derived using the direct dynamic motion estimation technique. The problem is then solved by applying a discrete Kalman filter that facilitates the use of a long stereo image sequence. Major issues in a motion estimation method are stereo matching, temporal matching, and noise sensitivity. In the proposed approach, owing to the use of temporal derivatives in the motion estimation model, temporal matching is not needed. The effort for stereo matching is kept to a minimum by the use of a parallel binocular configuration. Noise smoothing is achieved by the use of a sufficiently large number of measurement points and a long sequence of stereo images. Both simulation and experimental studies have been conducted to assess the effectiveness of the proposed approach.>

Hand/eye calibration is the process of identifying the unknown position and orientation of the camera frame with respect to the robot hand frame, when the camera is rigidly mounted on the robot hand. While computationally slightly more involved, one-stage iterative algorithms have two distinguished advantages over traditional two-stage linear approaches: 1) they are less sensitive to noise, and 2) they can handle cases in which the camera orientation information is not available. A more compact and lower dimensional identification Jacobian is derived. The Jacobian, which relates measurement residuals to pose error parameters of the unknown hand/eye transformation, is a crucial component of one-stage iterative algorithms. The derivation procedure for the new Jacobian is straightforward and simple, owing to an alternative mathematical formulation of the hand/eye calibration problem. Observability conditions of the pose error parameters in the unknown hand/eye transformation are also provided based on this identification Jacobian.>

A linear method for identifying the unknown kinematic parameters of a manipulator directly from the forward kinematic model is presented. The method requires the use of neither a nominal model nor a linearized error model of the robot. Such a solution is made possible by the use of a special robot kinematic modeling convention known as the complete and parametrically continuous (CPC) model, in which the independent CPC link parameters appear linearly in the system of equations to be solved, and the use of a particular sequence of robot pose measurements. The CPC orientation parameters of the revolute joints are first determined recursively under the condition that the pose measurements of the robot are taken while releasing each revolute joint one at a time and successively. The remaining CPC parameters are then computed in terms of the orientation parameters obtained earlier. Some practical issues related to kinematic parameter identification with the proposed approach are addressed through simulation studies.>

The problem of optimal design of robot accuracy compensators is addressed. Robot accuracy compensation requires that actual kinematic parameters of a robot be previously identified. Additive corrections of joint commands, including those at singular configurations, can be computed without solving the inverse kinematics problem for the actual robot. This is done by either the damped least-squares (DLS) algorithm or the linear quadratic regulator (LQR) algorithm, which is a recursive version of the DLS algorithm. The weight matrix in the performance index can be selected to achieve specific objectives, such as emphasizing end-effector's positioning accuracy over orientation accuracy or vice versa, or taking into account proximity to robot joint travel limits and singularity zones. The paper also compares the LQR and the DLS algorithms in terms of computational complexity, storage requirement, and programming convenience. Simulation results are provided to show the effectiveness of the algorithms.>

An iterative algorithm for calibration of a robotic hand-eye relationship is presented. The hand-eye calibration can be performed by solving a system of homogeneous transformation equations of the form A/sub i/X=XB/sub i/, where X is the unknown sensor position relative to the robot wrist, A/sub i/ is the ith robot motion, and B/sub i/ is the ith sensor motion. Unlike existing approaches, the algorithm presented solves the kinematic parameters of X in one stage, thus eliminating error propagation and improving noise sensitivity. Furthermore, with the iterative algorithm, the parameters of X can be computed even when the rotational part of B/sub i/ is unknown. This is important since position is easier to measure than orientation. Comparative simulation studies show that the performance of the iterative algorithm is usually better than that of noniterative two-stage algorithms, regardless of whether the orientation part of B/sub i/ is used or not. This paper also discusses the application of the proposed method to calibration of a tool mounted on a robot manipulator.>

A linear solution which allows a simultaneous computation of the transformations from robot world to robot base and from robot eye to robot hand coordinate frames, is reported in this paper. It is assumed that the robot geometry, which is the transformation from the robot base frame to the robot flange frame, is accurately known, and that robot hand positions and orientations in world coordinates are measured. The solution has applications in accurate locating of the robot with respect to a reference frame, and of the robot sensor with respect to the robot end-effector. The identification problem is cast as the solution of a system of homogeneous transformation equations of the form A iX = Y Bi, i = 1, 2, ..., m. Quaternion algebra is applied to derive explicit linear solutions for X and Y provided that three robot pose measurements are available. Necessary and sufficient conditions for the uniqueness of the solution are stated. Computationally, the solution is noniterative, fast and robust. Simulation studies reveal that the method is a viable candidate for robot/world and eyehand calibration.

A noise tolerant algorithm for calibration of wrist-mounted robotic sensors is presented. The sensor-wrist calibration can be performed by solving a system of homogeneous transformation equations of the form AiX = XBi, where X is the unknown sensor position relative to the robot wrist, Ai is the ith robot motion, and B; is the ith sensor motion [l-41. A Jacobian relating the measurement residual errors to pose errors of the unknown matrix X is derived. Based on this relationship, X can be iteratively solved. Unlike existing approaches, the algorithm presented here solves kinematic parameters of X in one stage, thus eliminating error propagations and improving noise sensitivities. Moreover, with the proposed algorithm, the parameters of X are observable even when the rotation part of 11; is unknown. This is important in practice since position is easier to measure than orientation. Comparative simulation studies show that the accuracy performance of the iterative algorithm is, in general, better than that of noniterative twostage algorithms, regardless whether the orientation part of Bi is used. The approach presented in this paper also has wide applications for wrist-mounted tool calibration.

In the above-named work (ibid., vol.7, p.877-8, (Dec. 1991)), H. Zhuang and Z. S. Roth point out that a particular solution can be simplified by using quaternions to represent rotations. While it is true that this approach gives rise to an algorithm more efficient than the one considered, the commenter argues that it is incorrect to claim that a unique solution for R/sub X/ exists if and only if the axes of rotation of R/sub A1/ and R/sub A2/ are nonzero (theorem 1 of the original work). A counterexample is presented to prove this point. In replying, Zhuang and Roth note the error in the original work and provide an analysis leading to the revision of their original theorem 1.>

A kinematic modeling convention for robot manipulators is proposed. The kinematic model is named for its completeness and parametric continuity (CPC) properties. Parametric continuity of the CPC model is achieved by adopting a singularity-free line representation consisting of four line parameters. Completeness is achieved through adding two link parameters to allow arbitrary placement of link coordinate frames. The transformations from the world frame to the base frame and from the last link frame to the tool frame can be modeled with the same modeling convention used for internal link transformations. Since all the redundant parameters in the CPC model can be systematically eliminated, a linearized robot error model can be constructed in which all error parameters are independent and span the entire geometric error space. The focus is on model construction, mappings between the CPC model and the Denavit-Hartenberg model, the study of the model properties, and its application to robot kinematic calibration.>

A closed form solution for the unknown kinematic parameters of a robot manipulator obtained directly from the forward kinematic model is described. The method requires the use of neither a nominal model nor a linearized error model of the robot. Such a solution is possible because of (1) the use of a special robot kinematic modeling convention, namely the CPC model, and (2) the use of a particular sequence of robot pose measurements. The CPC orientational parameters of the revolute joints are determined recursively under the condition that the pose measurements of the robot are taken while moving the revolute joints one at a time and successively. The remaining CPC parameters are then computed in terms of the orientational parameters obtained earlier.>

The commenters point out that the derivation of the closed-form solution to the homogeneous transform equation AX=XB by Y.C. Shiu and S. Ahmad (see ibid., vol.5, no.1, p.16-27, Feb.1989), although containing many useful ideas, is somewhat lengthy. It can be presented much more compactly using quaternion algebra. Direct benefits of such an approach are presented. In their reply, Shiu and Ahmad admit that the commenters' method has significant advantages over the original solution for the rotational part. However, it does not provide the geometric insight that the solution for AX=XB has a rotational degree of freedom about k/sub A/ (the axes of rotation of A). The solution to the translational part of X discussed in the original paper is not affected by this discussion since its computation is not dependent on how the rotational part is computed.>

A kinematic modeling convention for robot manipulators is proposed. The kinematic model has complete and parametrically continuous (CPC) properties. The parametric continuity of the CPC model is achieved by adopting a singularity-free line representation. Completeness is achieved through adding two link parameters which allow arbitrary placement of link coordinate frames. The transformation from the base frame to the world frame and from the tool frame to the last link frame can be modeled with the same convention as that used for internal link transformations. These parameters make the CPC model particularly useful for robot calibration.>

The design of a kinematic accuracy compensator for a robot manipulator by using linear optimal control theory is discussed. The method is based on the assumption that either the actual kinematic parameters of the robot have been previously identified or that the pose errors of the manipulator can be measured online. A general mathematical framework is used, so that any linearized error model derived from the corresponding kinematic model can be used to construct an effective robot accuracy compensator. The additive corrections of joint commands are found by a linear quadratic regulator algorithm without explicitly solving the inverse kinematic problem for the actual robot. The weighting matrix and coefficients in the cost function can be chosen systematically to achieve specific objectives. It the poses of the manipulator can be measured online, a parameter identification phase of the robot calibration process can be eliminated, thus avoiding the need to identify all the error sources. A simplified algorithm is presented that accelerates significantly the process speed, making it suitable for real-time applications.>