The measurement of dynamic forces within spacecraft sources is critical for safeguarding mission accuracy and stable operation. Two major challenges impede accurate measurement of dynamic forces from large sources: the severe nonlinearity of platforms; leading to inaccuracies in traditional methods; and the explosion of redundant sensor combinations, lowering optimization efficiency. To address these issues, this article proposes an intelligent framework that synergistically integrates the genetic algorithm with adaptive-learning-rate-based back propagation (GAARBP) and Bayesian optimization (BO). The GAARBP module addresses the nonlinear input-output mapping problem of the platform, and enhances the efficiency and accuracy of model training through adaptive learning rate adjustment. The BO module employs a blockwise Matérn kernel function tailored for sensors on horizontal and vertical planes to construct a Gaussian process surrogate model, alongside an expected improvement-based acquisition function for efficient optimization. These two modules operate in a closed loop, wherein GAARBP provides accurate fitting errors to guide BO’s selection, and BO feeds back optimal sensors to enhance GAARBP’s model training. Experimental results show that the framework achieves higher measurement accuracy (error: 2.28%) and superior decoupling performance (error: 1.13%), sufficient to satisfy the measurement requirements of large vibration sources in spacecraft. Moreover, compared with conventional methods (exhaustive search, D-optimization, particle swarm optimization, etc.), the proposed framework selects the best sensor combination more effectively for the optimization problem of six sensors selected from 24, with outcomes that are virtually globally optimal. This article offers a novel, effective approach to synergistically solving nonlinear dynamic force measurement and sensor optimization in complex environments. It thereby promotes the intelligent advancement of testing technologies in these fields.

Collaborative robots often exhibit limited absolute accuracy despite high repeatability, necessitating cost-effective calibration solutions. This paper presents a novel sensor-free self-calibration method for collaborative robots using position and distance constraints. A tri-sphere end-effector with precision balls and magnetic holders enables repeatable Tool Center Point (TCP) positioning (<0.01mm) through hand-guiding, where the three-sphere configuration crucially enhances the orientation calibration accuracy compared to a single-sphere approach. The proposed device eliminates expensive external sensors while establishing geometric constraints through workspace-wide TCP engagements. By analyzing relative position/distance errors between multiple configurations, the method identifies kinematic parameters via a Local Product of Exponential (Local POE) based error model. Experiments demonstrated a 91.7% position error reduction (7.98mm to 0.66mm) and 69.6% orientation improvement (0.0069rad to 0.0021rad), achieving comparable accuracy to laser-tracker methods at <1% device cost. This approach offers a low-cost, mechanically robust solution for enhancing collaborative robot accuracy in industrial applications.

This paper proposes an innovative virtual chain-based kinematic calibration for the 4PPa-2PaR parallel manipulators with subchain architectures. Conventional calibration methods for such architectures suffer from inherent limitations due to coupled parameter constraints and restricted solution spaces caused by joint displacement and structural parameter dependencies. The presented methodology introduces three fundamental advancements: (1) a novel parameter assignment strategy enabling independent joint/link parameter definition across different kinematic chains, (2) systematic transformation of constrained optimization into an unconstrained one, and (3) significant expansion of error parameter solution space through virtual chain modeling. Comparative experiment on the physical prototype demonstrate improvements in both orientation and position accuracy compared to existing methods.

Flexible joints are the integral drive and control components for manipulators in interaction applications. Ensuring optimal performance while implementing torque control is crucial to maintaining stability during interactions. However, the system is susceptible to numerous disturbances, such as motor inaccuracies, nonlinearity caused by friction, and hysteresis. These disturbances are distributed across the motor-side, reduction gear, and load-side, leading to limitations in system performance, including response speed and steady-state accuracy. This paper proposes a disturbance compensation method combined with dual torque sensors and an improved disturbance observer (DOB). Two torque sensors are installed on the fixed side and load-side, respectively. These sensors are utilized to measure the load-side disturbances without considering accuracy models. Furthermore, an improved DOB is designed based on one of the torque sensors to estimate the motor-side disturbances. The disturbance compensator and feedback controller are introduced as the control algorithms for the flexible joint to achieve high-precision torque control. The robust stability of the proposed method is analyzed. Finally, several comparative experiments are conducted under various conditions. The results demonstrate that the proposed method enhances torque control performances and backdrivability compared with the traditional methods. Note to Practitioners—Generally, lots of nonlinear disturbances in the flexible joint system are distributed across low-speed/high-torque and high-speed/low-torque ports. These disturbances will lead to limitations in torque control performance. To address the problem above, this paper focuses on integrating dual torque sensors with an improved DOB. Specifically, two torque sensors are installed on the fixed side of the reduction gear and load-side, respectively. This enables the real-time measurement and calculation of load-side disturbances. On the other hand, considering the torque sensor mounted at the fixed side and motor-side model, an improved DOB is designed to estimate the motor-side disturbances. Subsequently, the closed-loop control architecture is designed based on the torque sensor attached to the load. The complex modeling process can be reduced by installing and applying torque sensors. The model and parameter errors are not considered, and the torque control performance is improved. The research outcome of this paper provides an effective approach that can be used to achieve stable and rapid torque tracking, as well as effortless human-robot interaction. The proposed method still has good torque tracking performance in the case of a large load.

For conventional linear-in-parameter (LIP) dynamic model of industrial robots, redundant terms in multivariate polynomials (MVPs) are strongly coupled and more difficult to eliminate than the redundant parameters. In this work, by analyzing the mapping from linearized chain kinematics to Lagrange dynamics, the linear-in-multivariate-polynomial (LI-MVP) model is formed. Subsequently, a bilinearized dynamics is derived in both LI-MVP and LIP formulations, so that redundant MVPs and inertial parameters are concurrently eliminated. In addition, all the MVPs are encoded into a numeric matrix within a monoid, where a binary operation is defined to replace symbolic Kronecker products for efficient derivation of LI-MVP model. Eventually, by rearranging the encoded matrix with respect to total degrees of variate, the symbolic LIP model is directly restored with decoded MVPs in Horner forms, which can further reduce the number of multiplications during torque computation. Simulations and experiments on serial industrial robots in both model derivation and torque calculation demonstrate the effectiveness of proposed methods.

Most bioinspired cable-driven continuum robots (CDCRs) usually employ a flexible backbone to realize the continuous deflection. For the CDCR to merely produce bending motions, its flexible backbone has to be designed with low bending stiffness but high tensile and torsion stiffness. In this article, a pattern-based design approach is employed for the flexible backbone, which adopts rectangle-shaped patterns inspired by elastic couplings. As it is rather difficult to derive accurate analytical stiffness models for such a pattern-based backbone structure with large nonlinear deflections, a novel data-driven stiffness modeling approach is proposed. The Gaussian process regression method is employed to train the stiffness model with respect to structure parameters of the backbone, while the dataset is generated through a commercial finite element analysis software package. To narrow the distribution of the training data and make the predicated stiffness values always positive, the natural logarithm transformation is utilized for data preprocessing, which significantly increases the accuracy of prediction results. The average errors of the bending, tensile, and torsion stiffness between simulation results and predicted results converge to 1.88%, 2.33%, and 2.11%, respectively. The particle swarm optimization algorithm is employed for the structure parameter optimization based on the data-driven stiffness model. The stiffness errors of the optimized flexible backbone between simulation results and experimental results are 5.19%, 19.09%, and 5.38%, respectively. Experimental results show that the average position repeatability and orientation repeatability of a CDCR are 0.8822 mm and 0.0046 rad and the CDCR can carry the 500 g payload.

Feature selection is challenging in high-dimensional and small-sample data, particularly in industrial informatics with diverse noise sources. The information entropy of feature noise is included in mutual information of a label and noise-corrupted features, which can be removed to increase classification accuracy. In this article, we propose a robust feature selection method by eliminating feature noise in the relevance measure. Feature noise is modeled as a zero-mean censored normal distribution, so its entropy is determined by solving the variance equation based on the maximum entropy principle. Then, a noisy channel for feature transmission is proposed to extract class-relevant noise component. Furthermore, a noise-free mutual information metric is developed by removing noise entropy within mutual information. Eventually, a novel criterion is proposed by maximizing relevance based on noise-free mutual information while minimizing redundancy. Experimental results confirm the effectiveness of our approach on datasets from various industrial sectors.

It remains a challenge to improve the accuracy of impedance rendering while ensuring stability under strong impacts during human-robot interaction. In this work, we aim to render the desired impedance for the flexible joint under an admittance control scheme with prescribed performance function (PPF). Specially, Gaussian kernels are introduced as the slack terms for PPF, so that the control stability can be maintained in the presence of abrupt external torques. Meanwhile, a narrower error envelope is yielded when such torques are absent, which also improves the fidelity of the desired impedance model. To achieve the prescribed tracking performance of the inner position loop, a two-stage backstepping control is proposed by defining two first-order composite error surfaces bridged by a second-order dynamic surface. This promulgates the minimum number of backstepping stages under the available state feedback, thus avoiding “explosion of terms.” In addition, dual-adaptive neural networks are incorporated into the backstepping control to compensate for the matched and unmatched disturbances. Real-time experiments are conducted to validate the appeal of the proposed method.

Industrial robots and collaborative robots are widely employed in industry and are progressively being utilized to assist individuals in their daily routines. To improve their absolute accuracy, self-calibration methods using portable local measurement devices are cost-effective solutions. However, compared with the conventional external calibration methods, self-calibration methods employing two configurations as a calibration sample introduce more non-kinematic errors to the robot. Therefore, noise reduction is significantly necessary in self-calibration. A novel Piecewise-weighted Random Sample Consensus (RANSAC) method is proposed in this paper. Instead of choosing an optimal model with all inliers, the proposed method employs a general weight considering both the sample and hypothesis model qualities to generate a new model with Weighted Least Square (WLS) method. Besides, the proposed method turns the target of finding an uncontaminated set of inliers into the training of the proper weight coefficient for WLS, which not only improves the accuracy but also greatly enhances the speed. The self-calibration experiment on a 6 degree-of-freedom(DOF) robot CR10 shows that the accuracy of the proposed Piecewise-weighted RANSAC method makes a 27.7% accuracy improvement from that employing Least Square method, a 20.0% accuracy improvement from that employing standard RANSAC method, and a 5.5% accuracy improvement from that employing LO-RANSAC method. Besides, the proposed method is also over 10.9 times faster than the standard RANSAC method and 18.6 times faster than the LO-RANSAC method.

The unit dual quaternion (UDQ)-based product-of-exponential (POE) formula has achieved efficient kinematic calibration for serial manipulators. However, due to the presence of unknown passive joint displacements, it is difficult to directly establish explicit forward kinematic models for parallel manipulators (PMs). This forms a barrier to subsequent error modeling and compensation. This work establishes a novel UDQ-based forward kinematic model for a PM by utilizing constraints on the identical pose of the moving platform across all its chains. Furthermore, the adjoint transformation of UDQ's twist is derived for PM's error modeling. Notably, an index matrix is introduced to achieve a unified representation of active or passive joint displacement. Thereby, this UDQ-based kinematic error modeling method is applicable to general PMs. In addition, an error compensation method is proposed for a PM using the UDQ-based local POE formula, which incorporates the developed forward kinematic model to adjust active joint displacements. The proposed method offers significant runtime savings compared to the traditional homogeneous-transformation-matrix-based POE formula due to the compact data structure and reduced arithmetic operations.

This paper proposes an improved stability observer to obtain the interaction state in real-time for physical human-robot-environment interaction (pHREI). Firstly, a stability observer is designed to effectively avoid the misjudgment caused by the phase advance or delay of the filter. Then, the variable admittance control algorithm is designed according to the value of the observer. Finally, a comparative experiment is carried out. The results show that the proposed method can effectively reduce the oscillation when the operator drags the robot into contact with the environment.

Various optimal control and system designs involve searching for a feedback gain matrix with structural constraints. As an alternative solution, the parameter space methods map the constraints from the state space to another extended state-input space, in which an equivalent optimization problem is solved. However, to further extend its applications, there are still some issues need to be addressed, such as the limited type of structural constraints, the marginally stable solutions, and the low computation efficiency. In this article, we aim to make this method applicable to a class of structural constraints for some elements in the gain matrix being zero or with intrarow and intracolumn constraints. To address such structured control problem, we propose a procedure to transform the original system to an extended system with the decentralized feedback matrix. From here, the mapping rules to the parameter space are given for the decentralized feedback matrix with both intrarow and intracolumn constraints. To avoid oscillatory closed-loop dynamics, we include the closed-loop dominant pole constraints during optimization. In addition, to improve the computation efficiency during optimization, we revise the cutting plane logic, which allows adding multiple linear constraints within a single iteration. Simulation examples demonstrate the effectiveness of the proposed method.

Removing the parameter redundancy in the kinematic error model does improve the robustness of parameter identification. However, this does not help much on saving the calculation time on the error compensation process, which is closely related to the data structure used for representing rigid-body motion. Compared with the homogenous transformation matrix (HTM), the unit dual quaternion (UDQ) can describe the rigid-body motion in term of an array with eight entries, thus it is a conducive data structure for efficient kinematic computation. In this article, the exponential and logarithm mappings of an UDQ are defined explicitly so that the relationship between finite and instantaneous motions is set up under the exponential coordinate. Thereafter, by defining the adjoint operator of UDQ to transform the twist under different frames, the linearized kinematic error models are built with the local product-of-exponentials (POE) formula. This facilitates the upcoming parameter identification and error compensation processes. Especially, the counts of elementary operations are evaluated throughout the compensation processes, which shows the number of arithmetic operations are greatly reduced compared with using the POE formula based on the HTM. Additionally, the simple data structure in term of 1-D arrays saves the data dispatch time when performing adjoint operations. These make the developed model suitable for calibration of the articulated robot with a long sequence of trajectories. Experiments on a 6-degree-of-freedom industrial robot validate the effectiveness of the proposed approach.

Off-line programming of the polishing tool trajectory for complex workpieces is challenging due to the nontrivial material removal model and the polishing accuracy requirement. Current tool trajectory planning methods are mainly developed for some simple surfaces but cannot handle the increasingly complicated industrial parts, such as the wheel hubs. This article first develops a numerical contact mechanics model for the point-sampled complex workpieces. The contact pressure distribution and the material removal depths on the workpiece point cloud can be predicted efficiently. A novel high-priority subregion searching algorithm is developed to track the most-worth-polishing workpiece points. By selecting the path pattern as direction-parallel, the path direction, tool dwell times, and the path spacings inside each extracted subregion are optimized to minimize the deviation from the desired material removal depths. The effectiveness of the proposed method is verified by performing disk polishing simulations on workpieces with different shapes. A robotic polishing experiment is also conducted on a wheel hub. Both simulation and experimental results show that reasonable tool trajectories can be generated on the workpiece, and the desired material removal depths can be achieved. Note to Practitioners—In robotic polishing industries, it is crucial to plan the tool trajectory (tool path and feed velocity) to achieve desired material removal depths on the workpiece surface, which means high surface quality. In this article, a model-based tool trajectory planning method for robotic polishing of complex surfaces that are represented by the point cloud form is presented. The advantage of using the point cloud is that workpiece surfaces with varying curvatures and complex features, e.g., grooves and holes, need not be expressed explicitly. The proposed method generates high-priority subregions according to the updated material removal distribution dynamically. In this work, the polishing path pattern is chosen as direction-parallel. Based on an efficient numerical contact mechanics and material removal model, the path locations and the tool dwell times inside each subregion are optimized to minimize the deviation between the actual and the desired material removal depths. When the desired material removal depths are attained in an extracted subregion, the algorithm finds the next high-priority subregion until the whole workpiece is well polished. The trajectory planning method can be integrated into an industrial robot with the force-control module. Future work is to integrate the roughness model into the tool trajectory planning method.

In a multiwire slicer, it is very crucial to keep wire sending smooth and tension constant to guarantee the quality of silicon wafers. Since the wire sending status has impact on the wire tension, it needs to be controlled to be smooth enough first. The measurement of the wire sending state is based on the two tensometers near the wire sending point and the tension adjusting unit, respectively. The measuring principle is given in detail. The smooth wire sending control is realized through a position adjusting unit. To achieve good control performance, the wire sending state is divided into several sections, and a novel feedforward multiconditioned P controller is designed. After the smooth wire sending controller is designed, the factors related to the wire tension vibration are analyzed deeply, and then, a self-tuning fuzzy controller is proposed. The parameters of the controller can be tuned according to the wire moving velocity. To show the validity of the proposed method, experiments on real platform are well conducted.

The ten papers in this special section aim gather the latest research and development works on design, sensing, and intelligent control of robotics and mechatronics systems resulting from the emerging information sharing and design technologies.

The industrial robot usually has high repeatability but relatively lower accuracy. Therefore, error compensation plays a pivotal role in many industrial robotic applications with high accuracy requirement. In this paper, we present a novel computational method that utilizes a hybrid model that consists of Local Product-Of-Exponential (POE) and Gaussian Process Regression (GPR) to compensate the positioning errors of the industrial robotic manipulator for high accuracy industrial robotic applications. Specifically in the proposed method, the Local POE calibration method is first applied to calibrate the robot forward kinematic model to reduce the geometric error. Then the GPR is applied to learn the inverse kinematic model to further compensate the residual error in task space. We also demonstrate the robustness and effectiveness of our proposed method by showing the reduction of norm pose error by up to 37.2%, compared to the existing methods with multiple datasets.

A new four degrees-of-freedom (DOF) parallel manipulator that can produce 3-DOF translations and 1-DOF rotation (3T1R), has been proposed in this paper. It has two identical limbs connected to the moving platform through passive revolute joints, and each limb has two identical branches driven by a pair of base mounted collinear prismatic joints. Due to such a unique “4-2-1” kinematic structure, the 4-DOF parallel manipulator has the advantages of simple kinematics, large workspace, high speed, and high positioning accuracy. These advantages make it an appropriate candidate for high-speed and high-precision pick-and-place operations. To validate the proposed parallel manipulator design, mobility analysis is conducted based on the screw theory. Other critical design analysis issues, such as displacement, singularity, and workspace analyses, have been addressed in details.

Robot calibration is critical for industrial robot applications that require high accuracy. This paper presents a novel calibration method that utilizes Product-Of-Exponential (POE) and Gaussian Process (GP) regression to compensate for both geometric and non-geometric errors within the robot manipulator. Effects of a payload at the end-effector is also considered in the GP regression model in order to further improve robot positioning accuracy in the task space. Simulation and experimental results demonstrate the effectiveness of the proposed method. The experimental results show that the proposed method reduces norm pose error by 65.5% and 50.2% on average compared to conventional base-tool calibration and POE calibration respectively.

This paper analyzes the influences of displacement sensor noise on the power amplifiers of active magnetic bearing systems in both current and voltage control schemes. An effective evaluation index has been proposed to guarantee that the comparison is meaningful and fair enough to both control schemes. In addition, an appropriate controller is designed for each control scheme, while each controller is capable of dealing with both linear and nonlinear plants. Three significant findings are obtained through a thorough computer simulation. Firstly, using the proposed evaluation index, the maximum displacement response values are almost identical for the two control schemes, when the same unit pulse of external disturbance force signal is inputted; secondly, the current control scheme is more sensible to the noise; and lastly, the power amplifier in voltage control scheme has better noise suppression capability than current control scheme.

This paper studies the dynamic response of a high-speed ball-screw drive in a machine tool feed system. The Timoshenko beam theory is employed to model the rotating screw, while the nut is modeled as a lumped moving mass subjected to an external force resolved into three mutually perpendicular components. The dynamic model of the ball-screw drive is formulated based on the assumed mode method. To study the deformation characteristics of the ball-screw drive with different constrains, the dynamic equations are solved by using the fourth order Runge-Kutta method. In this paper, the moving mass and force effect are taken into consideration synchronously, and the relative velocity relationship of screw and nut is studied as well. The results show that the pitch of the screw, which determines the relative speeds of the rotating beam with respect to the moving excitation, have strong influences on the lateral deformation. Major factors affecting the ball-screw drive deformation are identified to illustrate its vibration performance.

A manipulator with variable stiffness allows the manipulator to adjust its stiffness to fulfill different task requirements. In this paper, a cable-driven manipulator with the ability to significantly regulate its stiffness through tension manipulation is introduced. Variable stiffness is achieved by attaching a novel variable stiffness device along each driving cable, in which the stiffness of the device is a function the cable tension. As cable-driven manipulator has actuation redundancy, the tension distribution can be manipulated even at a stationary pose. Such property allows the cable-driven manipulator to adjust the stiffness of each variable stiffness device, thereby changing the stiffness of the manipulator. The design and analysis of the variable stiffness device is presented. The variable stiffness device uses commercial torsion springs, and has a compact and light-weight design. Experimental and simulation results verified that cable-driven manipulator with such variable stiffness devices is able to achieve significant stiffness regulation.

This paper addresses the kinematic calibration issues for a 7-DOF cable-driven humanoid arm in order to improve its motion control accuracy. The proposed 7-DOF humanoid arm has a hybrid parallel-serial kinematic structure, which consists of three serially connected parallel cable-driven modules, i.e., a 3-DOF shoulder module, a 1-DOF elbow module, and a 3-DOF wrist module. Due to the unique arm design features such as hybrid parallel-serial structure, modular configuration, and redundant sensors, an integrated two-level self-calibration method is proposed in this work. The first level of self-calibration, termed as the central linkage mechanism calibration, is to identify the kinematics errors existed in the 7-DOF central linkage mechanism based on its self-motion capability. The second level of calibration, termed as the cable-driven module calibration, is to identify the kinematics errors existed in each of the parallel cable-driven modules based on its sensing redundancy. To simplify the formulation of the calibration algorithms, the error model of the serial central linkage mechanism is derived from its forward kinematics, in which the Products-Of-Exponential (POE) formula is employed, while the error models of the parallel cable-driven modules are derived from their inverse kinematics. The simulation and experimental results have shown that the proposed self-calibration algorithms can effectively improve the accuracy of the 7-DOF cable-driven humanoid arm.

Industrial robotic manipulators have excellent repeatability while accuracy is significantly poorer. Numerous error sources in the robotic workcell contributes to the accuracy problem. Modeling and identification of all the errors to achieve the required levels of accuracy may be difficult. To resolve the accuracy issues, a sensor based indirect error compensation approach is proposed in this paper where the errors are compensated online via measurements of the work object. The sensor captures a point cloud of the work object and with the CAD model of the work object, the actual relative pose of the sensor frame and work object frame can be established via a point cloud registration. Once this relationship has been established, the robot will be able to move the tool accurately relative to the work object frame near the point of compensation. A data pre-processing technique is proposed to reduce computation time and prevent a local minima solution during point cloud registration. A simulation study is presented to illustrate the effectiveness of the proposed solution.

A flexure-based parallel manipulator (FPM) is a closed-loop compliant mechanism in which the moving platform is connected to the base through a number of flexural legs. Utilizing parallel-kinematics configurations and flexure joints, the FPMs can achieve extremely high motion resolution and accuracy. In this work, we focus on the analysis and design of a 3-DOF (θx- θy- Z) zero-torsion FPM for nano-alignment applications. Among various possible zero-torsion parallel kinematics configurations, it is identified that the 3-legged Prismatic-Prismatic-Spherical (3PPS) is a suitable candidate. Based on the concept of instantaneous rotation, the critical kinematic design issues, such as displacement and workspace analyses, are addressed. With these analysis algorithms, the major kinematic parameters are readily determined to meet the task requirements. To achieve a large workspace, beam-based flexure joints are employed in the FPM design. As the beam based Universal (U) flexure joints are able to accommodate the required passive prismatic and spherical motions, each flexure PPS leg can be replaced by a simple flexure PU leg. A research prototype of the 3-DOF 3PU FPM has been developed, which achieves position and orientation resolutions of 20 nm and 0.05 arcsecond throughout a workspace of 5° × 5° × 5 mm, respectively.

This paper presents the design of a novel 4-DOF (x-y-θx-θy) flexure-based system used for coaxial alignment. The movable head (a rigid rod) of the system is suspended with two monolithic flexural mechanisms constructed with leaf flexures. To achieve the required x-y-θx-θymotion, the leaf-type flexures are specially arranged in such a configuration that is compliant in the specified axes but stiff in other axes. The leaf flexures are initially designed based on the linear models of the flexible beam deflection and then improved through FEA simulations. A system prototype was built with the flexural mechanisms. It demonstrates superior motion performances in the x and y axes as well as the angular axes. The prototype has been successfully applied in the coaxial alignment of the capillary machining.

Thermally induced deformation has become more of a concern for precision machines as accuracy is getting more stringent. Unlike other indirect drives which are possible to isolate or place rotating motors, which are heat sources, away from the working area. A linear motor is a direct drive system which is heat source and placed near to the working area. Therefore, this thermal effect characteristic study is conducted here to find out the effect of heat that is transferred and dissipated around the working area, causing unwanted deformation. The surface area joining the linear motor coil to the application carriage is large. It will be inaccurate to assume a constant temperature or heat flux through the entire surface. The temperature of the surface is different for different location and time. Experiments are conducted to investigate the surface temperature and heat flux profile in different application processes. Finally, the result of this investigation can define the heat source accurately so that a further study could develop a prediction scheme for the deformation of the carriage. This finding can be applied to error budgeting for machine design stages.

Stable and clear video imaging system is crucial in various industry applications for monitoring and remote control purposes. Severe vibrations across full spectrum frequencies are inevitable in many industrial operations resulting in shaky and unclear images. It may reduce the response time for operator and also affect the throughput during the production or monitoring process. On the other hand, commercially available cameras with built-in image stabilization functions may not be sufficient to overcome this problem since they only deal with camera shaking at small magnitude. To stabilize images captured under sever and full spectrum vibration condition, a vibration suppression system was developed. The system consists of a passive vibration mechanism and a digital image stabilization technique. The eddy current damper inside the passive vibration mechanism reduces high frequency vibration, while the digital image stabilization shifts the image for low frequency vibration elimination. Trial results have demonstrated the effectiveness of the system's capability to cover full vibration spectrum. However, it is also found that it needs to increase the degree-of-freedom (DOF) for this mechanism in the future instead of only single DOF.

This paper presents a new intuitive method for robot tool path teaching in Augmented Reality (AR) environment. Conventional industrial robot teaching method is long known to be either tedious or require a highly accurate virtual representation of robot work cell. Our method targets to provide the user with a fast and easy way of programming an industrial robot for useful tasks in a safe environment. In our system, a human robot interaction (HRI) system has been designed by fusing information from a camera and a laser ranger finder. The video images provide visual information to the user to operate the system, whereas the laser range finder captures the Cartesian information of the user intended robot working paths and trajectories. Furthermore, an AR environment has been designed where the virtual tool is superimposed onto the live video. The user simply needs to point and click on the image of the workpiece to generate the tool path. User can also adjust virtual tool orientation and simulate the tool trajectory in the AR environment, thus simplifying the robot teaching task. The proposed system has been tested for robot laser welding application. It is intuitive as no prior knowledge of robotic control is required in order to use our system. Most importantly, the system is safe and the user does not need to be physically close to the robot during path teaching.

This paper presents the modeling and control of a Flexure-Based Electromagnetic Linear Actuator (FELA) that is employed as a high-precision imprinting actuator of a desktop hot-embossing imprinter. In this work, a systematic approach of obtaining the unknown physical parameters of FELA is presented. Subsequently, these parameters are used to design two model-based PID controllers that allow the FELA to perform high-precision positioning tasks and direct-force imprinting tasks respectively. As the imprinting tasks require the FELA to operate in both position and direct-force control modes, two types of control strategies are explored and their competency of enabling the FELA to perform such tasks are investigated. Lastly, the selected control strategy is implemented on the FELA to assist the hot-embossing imprinter in fabricating micro-channels on polymer substrates via a hot-embossing process.

Cable-driven parallel manipulators (CDPMs) are a special class of parallel manipulators that are driven by cables instead of rigid links. Due to the unilateral property of the cables, all the driving cables in a fully-constrained CDPM must always maintain positive tension. As a result, tension analysis is the most essential issue for these CDPMs. By drawing upon the mathematical theory from convex analysis, a sufficient and necessary tension-closure condition is proposed in this paper. The key point of this tension-closure condition is to construct a critical vector that must be positively expressed by the tension vectors associated with the driving cables. It has been verified that such a tension-closure condition is general enough to cater for CDPMs with different numbers of cables and DOFs. Using the tension-closure condition, a computationally efficient algorithm is developed for the tension-closure pose analysis of CDPMs, in which only a limited set of deterministic linear equation systems need to be resolved. This algorithm has been employed for the tension-closure workspace analysis of CDPMs and verified by a number of computational examples. The computational time required by the proposed algorithm is always shorter as compared to other existing algorithms.

Modern industries, e.g., semiconductor packaging, imposes increasing stringent requirement on equipment with very high acceleration and high precision. Traditionally, arm linkage and drive mechanism are first designed followed by control design. The integrated design method is proposed as a preferable technique of the traditional one. In this paper, a general framework of the integrated design method for a point-to-point control is presented. The dynamic model for a flexible planar two-link manipulator is derived by the finite element method. The PD control strategy is applied in the closed-loop system. The structural parameters and control parameters are optimized simultaneously by solving the integrated design problem. The differential evolution (DE) technique, a global optimization technique, is used to solve the optimal design problem. A simulation shows the integrated design method gives improved system performance.

This paper presents a ball-joint-like three-degree-of-freedom (3-DOF) permanent magnet (PM) spherical actuator which features a ball-shaped rotor with multiple PM poles and a spherical iron stator with air-core coils. Torque output of this PM spherical actuator is formulated analytically. Based on the torque model, simulation result of the actuator torque variation is presented. In addition, the effect of the stator iron on the torque output is evaluated.

This paper presents the kinematic calibration of a novel 7-degree-of-freedom (DOF) cable-driven robotic arm (CDRA), aimed at improving its absolute positioning accuracy. This CDRA consists of three 'self-calibrated' cable-driven parallel mechanism (CDPM) modules. In order to account for any kinematic errors that might arise when assembling the individual CDPMs, a calibration model is formulated based on the local product-of-exponential formula and the measurement residues in the tool-tip frame poses. An iterative least-squares algorithm is employed to identify the errors in the fixed transformation frames of the sequentially assembled 'self- calibrated' CDPM modules. Both computer simulations and experimental studies were carried out to verify the robustness and effectiveness of the proposed calibration algorithm. From the experimental studies, errors in the fixed kinematic transformation frames were precisely recovered after a minimum of 15 pose measurements.

This paper presents the joint centre self-identification of a novel cable-driven anthropocentric shoulder rehabilitator. For such a wearable rehabilitator, identification of joint centre is critical for kinematic modeling, path planning and motion control. However, the shoulder joint centre location is unknown when a user wears this rehabilitator and it differs among users. These complicate the initial patient preparatory. A joint centre self-identification model is formulated based on the differential change in the cable end-point distance. A computationally effective algorithm is employed to identify the shoulder joint centre. It does not require any external measurement devices because of the redundant actuation scheme in the cable-driven shoulder rehabilitator. In order to verify the effectiveness and robustness of the proposed algorithm, we conducted computer simulation studies. In the simulation example, although large errors (up to plusmn50mm) had been injected into the initial estimates, the joint centre was always accurately identified within four to five iterations.

This paper presents a novel flexural-based nano-positioning actuator that has a positioning accuracy of 10 nm (limited by encoder resolution) throughout a range of 3 mm. A new dual-magnet configuration is introduced to enhance this electromagnetically driven actuator in achieving 60 N/Amp in a compact configuration. In addition, a constant and evenly distributed magnetic flux density is obtained throughout 11 mm of air gap. A new mathematical model is presented to accurately predict the behavior of magnetic field within the effective air gap of this configuration. Complete analytical models for this actuator's electromagnetic drive and flexural-bearing support element are presented. Lastly, a prototype of this actuator is developed for validating the established analytical models and verifying the claimed capabilities.

This paper presents a large-displacement and decoupled AYZ-flexure parallel mechanism (FPM) using typical large-displacement prismatic joints, and a nonlinear modeling method for these prismatic joints is proposed. The monolithic prismatic joints using notch hinges have large motion range of more than 1 mm, hence, the assembled XYZ-stage is large-displacement. Since the prismatic joints have small parasitic motion error and are orthogonally combined in parallel, the XYZ-stage can achieve the three decoupled translational motions. Exact stiffness and dynamics models are given using the proposed modeling method. The comparison between the proposed method and the classical pseudo-rigid-body (PRB) method is done to the example of the XYZ-stage. Finally, the experiments are conducted to verify the proposed XYZ-stage and the comparison between two methods

Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-dimensional space, it is difficult to quantify and qualify it. Most of the literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a finite-partition approach of the special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of special orthogonal group SO(3) and Ropf3. It is known that the SO(3) is homeomorphic to a solid ball D3with antipodal points identified while the geometry of Ropf3can be regarded as a cuboid. Furthermore, the solid ball and the cuboid can be parametrically and proportionally partitioned into a number of elements. Therefore, a basis volume element of SE(3) is the product of a basis volume element of Ropf3and a basis volume element of SO(3), which is the product of a basis volume element of D3and its associated integration measure. By this way, the integration of the complete 6-D workspace volume become the simple summation of the basis volume elements of SE(3). Two global performance indices, i.e., workspace volume ratio (Wr) and global condition index (GCI)., are defined over the complete 6-D workspace. An optimization algorithm is developed for a 3RPlowbarPS parallel manipulator to illustrate the effectiveness of the finite-partition approach. As a result, the workspace optimization method is valid although it is computationally intensive

This paper presents a design concept of spherical actuators including a ball-shaped rotor with two layers of permanent-magnet (PM) poles and a spherical-shell-like stator with two layers of circumferential air-core coils. Corresponding to the poles configuration, the torque model of the spherical actuator has been derived. The magnetic field as well as torque output have been compared with that of spherical actuator with single-layer PM-pole configuration. This generic torque modeling method can be extended for spherical actuators with multi-layer PM&coil poles which can achieve high motion resolution as well as large working range

Workspace analysis and optimization is a critical issue in robot manipulator design. For a cable-driven parallel manipulator (CDPM), due to the unilateral driving properties of the cables, maintaining positive cable tension is essential to maneuver the moving platform. As a result, its workspaces are always determined and characterized by the tension status of its driving cables. It has been realized that the tension factor (TF) reflecting the relative tension distribution among the driving cables is an appropriate measure to evaluate the quality of force closure for CDPMs. However, in a fully restrained CDPM, since redundant cables are employed to drive the moving platform, the TF values are not unique even for a particular moving platform pose. Therefore, how to obtain the optimal TF value so as to generate an optimized workspace becomes the major subject of this paper. It is proved that the optimal TF value can be efficiently determined through a linear optimization approach, although it is essentially a nonlinear optimization problem. Subsequently, a global tension index is proposed to evaluate the quality of the entire workspace, which is achieved by integrating the local TF values (i.e., the optimal TF values at every moving platform poses) over the workspace. Computation examples are provided to demonstrate the effectiveness of the proposed algorithms

A new three-limb, six-degree-of-freedom (DOF) parallel manipulator (PM), termed a selectively actuated PM (SA-PM), is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion, depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture completely decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. Singularity analysis shows that the SA-PM is an isotropic translation PM when all the actuators are in linear mode. Because of the decoupled motion structure, a decomposition method is applied for both the displacement analysis and dimension optimization. With the index of maximal workspace satisfying given global conditioning requirements, the geometrical parameters are optimized. As a result, the translational workspace is a cube, and the orientation workspace is nearly unlimited.

Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a finite partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for finite partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D/sup 3/ of radius /spl pi/ with antipodal points identified. A novel partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D/sup 3/ of radius /spl pi/, into finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the partition scheme and also reduce the computation efforts, as the elements in the same partition layer (along the radial direction) have the same integration measure. The effectiveness of the partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this partition scheme.

An actuator with 3-DOF spherical motion is developed based on layered arrangement of stator coils and rotor poles. Due to the use of air-core coils and permanent magnet poles, the torque model of the actuator cannot be obtained by traditional coenergy approach. This paper describes a generic torque modeling method based on Lorentz force law. The closed-form solution of the torque model is derived from the scalar potentials of the magnetic field. Experimental study on the torque model is carried out. A comparison between the closed-form solution and the experimental result shows that the proposed torque model is valid and can be used for real-time control.

A cable-driven parallel mechanism (CDPM) possesses a number of promising advantages over the conventional rigid-link mechanisms, such as simple and light-weight mechanical structure, high-loading capacity, and large workspace. However, the formulations and results obtained for the rigid-link mechanisms cannot be directly applied to CDPMs due to the unilateral property of cables. For a CDPM, cable tensions appear to be the most important part in analyzing kinetostatic issues such as stability, workspace, stiffness, etc. This paper mainly focuses on the tension analysis issue. The equilibrium constraints such as force-closure condition, feasible wrench condition and wrench set condition are addressed. Generic analysis approaches based on dimension reduction techniques, which are successfully implemented through computationally effective recursive algorithms, are proposed.

This paper has proposed a design concept of a spherical actuator including a ball-shaped rotor with a full circle of permanent-magnet (PM) poles and a spherical-shell like stator with two layers of circumferential air-core coils. One key feature of this design is parameterization of the PM pole, which benefits the design optimization of the spherical actuator greatly. According to the magnetic field model, the variation of flux density with respect to PM-pole parameters can be revealed. Therefore, these parameters can be appropriately chosen to achieve a high magnetic flux density. Another advantage of this design is the singularity-free, which is verified within the workspace with torque model and condition numbers.

Based on the local product-of-exponentials (POE) formula, this paper proposes an effective approach to solve the inverse displacement analysis for a class of modular 3-legged parallel robots by Paden-Kahan sub-problems. Since passive joint displacements can be solved together with solving active joint, so that the solved passive joint displacements can be regarded as guess solution to calculate forward kinematics by traditional numerical solution method. Through comparing with traditional iterative numerical solution method, proposed approach can evidently improve computation efficiency for forward kinematics. The effectiveness of the proposed approach has been demonstrated by machining demonstrations with online motion monitoring for a workpiece with spherical surface.

A parallel manipulator (PM) based on 3-limb design termed a selectively actuated parallel manipulator (SA-PM) is proposed. The end-effector of the manipulator can produce 3-DOF spherical motion, 3-DOF translation, 3-DOF hybrid motion, or complete 6-DOF spatial motion depending on the types of the actuation (rotary or linear) chosen for the actuators. The manipulator architecture decouples translation and rotation of the end-effector for individual control. The structure synthesis of SA-PM is achieved using the line geometry. A Lego model of the SA-PM is built for the constructibility and preliminary study. Singularity analysis of the SA-PM based on geometry is presented for all actuation schemes to facilitate the kinematic design of the manipulator. Because of the decoupled motion, the SA-PM has a great potential for high precision motion alignment and assembly, especially in micro- or nano-motion stage design.

A cable-driven parallel manipulator (CDPM) possesses a number of promising advantages over the conventional rigid-link manipulators, such as the simple and lightweight mechanical structure, high-loading capacity, and large reachable workspace. However, due to the unilateral driving capability of the flexible cables, most of the well-developed modelling and analysis methods for conventional rigid-link mechanisms cannot be directly applied to CDPM. This paper focuses on the kinematics and singularity analysis of a specific type of CDPM, i.e., a completely restrained planar CDPM. Following an analytical approach, the forward displacement analysis leads to solve a fourth order polynomial equation. Hence, the solutions can be determined efficiently in symbolic forms. To verify the effectiveness of this method, a computation example is provided, in which four real solutions are found out. It is realized the Jacobian-based singularity analysis, where all cables are treated as rigid links, is incomplete for the CDPM. Based on the concept of the instantaneous center and taking into account the cable-tension condition, a new geometrical singularity analysis method is proposed, which is able to effectively identify all forward singularity configurations for a completely restrained planar CDPM.

The design of a new six-degree-of-freedom (6-DOF) parallel-kinematics machine (PKM) has been proposed. Different from the conventional Stewart-Gough platform which has six extensible legs, the new PKM employs three identical RPRS legs to support the moving platform. Since all joint axes, excluding the three spherical joints at the leg ends, are parallel to each other and perpendicular to the base plane, this 6-DOF PKM presents a promising platform structure with decoupled-motion architecture (DMA) such that translation in a horizontal plane and rotation about a vertical axis are driven by the three active revolute joints, while translation in the vertical direction and rotation about horizontal axes are driven by the three active prismatic joints. As a result, this 6-DOF 3RPRS PKM with DMA has simple kinematics, large cylindrical reachable workspace, and high stiffness in the vertical direction. These features make it appropriate for light machining and heavy parts assembly tasks. Because of the DMA, a projection technique is employed for its kinematics analysis. By projecting the manipulator onto horizontal directions and vertical planes, the kinematics issues such as the displacement, singularity, and workspace analysis are significantly simplified.

This paper presents a numerical technique for path planning inside the workspace of parallel manipulators avoiding singularity. A generic numerical algorithm for generating the reachable workspace of parallel manipulators is described. The singularity points are determined inside the workspace. These points are grouped into several clusters and modeled as obstacles. Subsequently, a path planning algorithm is used to find an optimal path avoiding these obstacle. If any singularity point lies on or very close to the path, the path is restructured to avoid the singularity point by a local routing method based on Grassmann's line geometry. The path planning algorithm is uniformly applicable to parallel manipulators with any combinations of revolute and prismatic joints. An example is demonstrated for the effectiveness of the algorithm.

A joystick-based interactive motion control approach is proposed for modular reconfigurable manipulators. Based on the product-of-exponentials (POE) formula, the velocity models as well as the incremental displacement models have been formulated for both serial manipulators (with arbitrary configurations and DOFs) and a class of three-legged parallel manipulators. As a result, two different control modes, i.e., the velocity control mode and the incremental displacement control mode, have been developed. A user-friendly GUI has also been developed, which can display the joystick input, the actual joint angles, and the end-effector pose simultaneously. A 6-DOF serial modular robot and a 6-DOF 3RPRS parallel robot have demonstrated the effectiveness of this approach.

Based on the numerical inverse kinematic algorithm developed for modular robots, this paper presents a new control method, termed joint angle increment redistribution, which makes that the maximum allowable joint rates of a redundant robot can be specifically defined according to the internal and external constrains such as joints, tasks, and environments. For example, if some joints have failures and need to be locked, the corresponding joint angle increments can be redistributed to be zero or very small values. The proposed approach can be readily used for online fault-tolerant control of redundant robots. It also makes the optimal control with multiple performance criteria easy. The effectiveness of the proposed algorithms has been demonstrated by a 7-DOF serial modular robot for the avoidance of joint angle limits.

This paper presents a numerical algorithm for the analysis of reachable workspace and singularity representation of three-legged parallel manipulators. After finding out the approximate maximum workspace, a radial and equal area discretization is done. Then, a multitasking search is performed to determine the exact workspace boundary. The volume of the workspace is determined easily by a numerical integration method. Any void inside the workspace is found out. information about its position and stretch is determined and singularity curves inside the workspace is also drawn. A three-legged modular parallel manipulator is considered to demonstrate the effectiveness of the algorithm and found to work quite satisfactorily. The model is based on Product-of-Exponential scheme of formulation and, hence, the algorithm is uniformly applicable to any combinations of revolute and prismatic joints in the configuration of the leg.

In this paper, we propose a novel design of a hybrid 6-DOF parallel-serial manipulator. It consists of a 3-DOF planar parallel platform (lower part) and a 3-DOF serial robot arm (upper part). Benefiting from the hybrid kinematic structure, the manipulator possesses compromised performance between the serial robot and the parallel one, e.g., larger reachable and dexterous workspace (comparing with a parallel robot), and higher rigidity and loading capacity (comparing with a serial robot). It order to rapidly deploy the system, the modularity design concept is employed in the system development. Based on the modular and symmetric design, the symbolic closed-form solutions for both forward and inverse displacement analysis are derived, which are great helps for the motion planning, computer simulation, and on-line control of the hybrid manipulator. Computation examples are provided to verify the proposed kinematic analysis algorithms.

A parallel robot, due to its closed-loop structure, normally has two Jacobian matrices: the inverse and forward Jacobian matrices. Conventional methods for singularity analysis of planar parallel robots are based on analysis of the ranks of the two Jacobian matrices. The inverse singularity has been well studied as the inverse Jacobian matrix always has a simple diagonal form. However, the forward singularity analysis is somehow complicated, partially because some essential geometric relations may be occulted in the formulation of the forward Jacobian matrix. This paper focuses on the forward singularity analysis of a class of 3-RRR planar parallel robots with various actuation schemes. A simple geometric approach based on the concept of instantaneous center is proposed. By analyzing the instantaneous mobility of the moving platform when all the active joints are locked, the necessary and sufficient geometrical conditions for the forward singularity configurations are readily identified. It has been shown that this simple geometrical approach can be employed for singularity analysis of various planar parallel robots and mechanisms.

Focusing on the instantaneous velocities of passive joints, a formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Since only four 3/spl times/3 matrices need to be analyzed, the complexity of singularity analysis is significantly, reduced. Using the product-of-exponentials (POE) formula, the kinematic equations possess well-defined algebraic structures so that the instantaneous kinematics and singularity analysis algorithms can be readily and systematically formulated. Three types of singularities, i.e. the forward, inverse, and combined singularities, have been identified. A unified condition for various singularities is proposed. Significant geometric conditions are also presented for identifying singularity configurations that require simple computations.

An instantaneous kinematics and singularity analysis of a class of three-legged, 6-DOF parallel manipulators are addressed. The kinematic relation between the actuator joint rates and end-effector velocity is established using twist annihilators. Then the singularity analysis is performed using the concepts of reciprocal screw and Grassmann line geometry. The instantaneous kinematics model derived using the product-of-exponential formulation, is uniform to any combination of revolute and prismatic joints in the leg. It is shown that reciprocal screws can be easily constructed by using twist annihilators. Based on the line geometry, the geometric conditions are proposed to identify each of the case of singularity configurations for the considered class of parallel manipulators. These geometric conditions are simple and thus, the singularity configurations are readily conceived.

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace of the mobile platform. Singularity analysis become important in design, motion planning, and control of parallel robots. Focusing on the instantaneous velocities of passive joints, a new formulation approach is proposed for the instantaneous kinematics and singularity analysis of a class of three-legged parallel robots. Excluding the passive spherical joints at the leg ends, the number of 1-dof passive joints in a three-legged, 6-DOF, parallel robot is three, which is only half of the number of active joints (six). Consequently, the complexity of the singularity analysis is significantly reduced because only four 3/spl times/3 matrices need to be analyzed. Using the product-of-exponential formula, the kinematic equations possess well-defined algebraic structures so that the instantaneous kinematics and singularity analysis algorithms can be readily and systematically formulated. Three types singularities, i.e., the forward, inverse, and combined singularities, have been identified. A unified condition for various singularities is proposed. Significant geometric conditions are also presented for identifying singularity configurations that requires simple computations.

The paper focuses on the kinematic control of redundant modular robots for trajectory tracing. Based on the geometric numerical inverse kinematic algorithm developed for modular robots, a new online control method is presented. In this method, the inverse kinematic solution can be optimized through constructing a weighted matrix. Following this approach, some fundamental interpolation algorithms are proposed for Cartesian space (task space) control of redundant modular robots. The effectiveness of the proposed algorithms has been experimentally demonstrated by a 7-DOF serial modular robot that performs a pick-and-place task with the avoidance of joint angle limits.

A modular parallel robotic system consists of a collection of individual standard units that can be assembled into various robot configurations for a diversity of task requirements. This paper is focused on the design and kinematic analysis of modular reconfigurable parallel robots. A set of fundamental modules is considered. A local frame representation of the product-of-exponentials (POE) formula, i.e., the local POE formula, is employed for the kinematic analysis of modular parallel robots. Two forward displacement analysis algorithms and a workspace visualization scheme are presented for a class of 3-leg modular parallel robots. Computation examples are also given to demonstrate the effectiveness of the proposed algorithms. The kinematic formulation shows that the local POE formula is a systematic and well-structured method for the kinematic analysis of parallel robots.

Inverse kinematics solutions of a reconfigurable robot system built upon a collection of standardized components are difficult to obtain because of its varying configuration. This paper addresses the formulation of a generic numerical inverse kinematics model and automatic generation of the model for arbitrary robot geometry including serial type and branching type geometry. Both revolute and prismatic types of joints are considered. The inverse kinematics is obtained through the differential kinematics equations based on the product-of-exponential formulas. The Newton-Raphson iteration method is employed for the solution. The automated model generation is accomplished through the introduction of assembly incidence matrix representation of a modular robot assembly configuration and the related accessibility matrix and path matrix. Examples of the inverse kinematics solutions for different types of modular robots are given to demonstrate the applicability and effectiveness of the proposed algorithm.

Manual derivation of the dynamic model of a modular robot is almost impossible because it may have very different geometries and DOFs through module reconfiguration. This paper presents an algorithm to automatically generate the closed-form equation of motion of a modular robot from a kinematic graph based representation of the assembly configuration. We consider modular robots with the more general branching geometry. The formulation of the dynamic model is started with recursive Newton-Euler algorithm. The generalized velocity, acceleration, and forces are expressed in terms of linear operations on se(3), the Lie algebra of the Euclidean group SE(3). Based on the equivalence relationship between the recursive formulation and the closed-form Lagrangian formulation, we use the accessibility matrix of the kinematic graph to assist the construction of the closed-form equation of motion of a modular robot. Applications of the closed-form dynamic model of a branching robot are in robot design, calibration, and motion optimization.

A modular reconfigurable robot system is a collection of individual link and joint components that can be assembled into different robot geometries for specific tasks requirements. However, the machining tolerance and assembly errors at the module interconnections may affect the positioning accuracy of the end-effector. Based on the product-of-exponentials formula and recursive forward dyad kinematics, this paper describes a novel kinematic calibration algorithm for modular robots. The error correction parameters are assumed to be in the relative initial positions of the dyads. A six-parameter calibration method is derived on the ground of a linear superposition principle and differential transformation theory. An iterative least square algorithm is employed for the calibration solution. A simulation example of calibrating a three-module manipulator is demonstrated. The result has shown that the average positioning accuracy of the end-effector increases two orders of magnitudes after the calibration.

A modular robotic system consists of standardized joint and link units that can be assembled into a number of different kinematic configurations. This paper describes the design and kinematic issues of a newly developed modular robot aimed for assembly tasks. All modules are designed as cubic units. There are connecting interfaces, termed connecting ports, on all faces of the cubes so that different kinematic configurations can be achieved by just re-connecting the modules into different ports. A graph based representation scheme, termed assembly incidence matrices (AIM), is employed to indicate the ever changing configurations. The dyad kinematics based on product-of-exponentials formula is introduced. Using dyad kinematics along with a graph traversing algorithm, the authors are able to derive forward kinematics for a modular robot with specific configuration automatically. This formulation can be applied to modular robots with hybrid geometries and is demonstrated by a 3-DOF serial modular robot example.