We present the design and implementation of a quadrotor tail-sitter Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicle (UAV). The VTOL UAV combines the advantage of a quadrotor, vertical take-off and landing and hovering at a stationary point, with that of a fixed-wing, efficient level flight. We describe our vehicle design with special considerations on fully autonomous operation in a real outdoor environment where the wind is present. The designed quadrotor tail-sitter UAV has insignificant vibration level and achieves stable hovering and landing performance when a cross wind is present. Wind tunnel test is conducted to characterize the full envelope aerodynamics of the aircraft, based on which a flight controller is designed, implemented and tested. MATLAB simulation is presented and shows that our vehicle can achieve a continuous transition from hover flight to level flight. Finally, both indoor and outdoor flight experiments are conducted to verify the performance of our vehicle and the designed controller.

We present a hierarchical control approach that can be used to fulfill autonomous flight, including vertical takeoff, landing, hovering, transition, and level flight, of a quadrotor tail-sitter vertical takeoff and landing unmanned aerial vehicle (VTOL UAV). A unified attitude controller, together with a moment allocation scheme between elevons and motor differential thrust, is developed for all flight modes. A comparison study via real flight tests is performed to verify the effectiveness of using elevons in addition to motor differential thrust. With the well-designed switch scheme proposed in this paper, the aircraft can transit between different flight modes with negligible altitude drop or gain. Intensive flight tests have been performed to verify the effectiveness of the proposed control approach in both manual and fully autonomous flight mode.

This paper presents a unified control framework for controlling a quadrotor tail-sitter UAV. The most salient feature of this framework is its capability of uniformly treating the hovering and forward flight, and enabling continuous transition between these two modes, depending on the commanded velocity. The key part of this framework is a nonlinear solver that solves for the proper attitude and thrust that produces the required acceleration set by the position controller in an online fashion. The planned attitude and thrust are then achieved by an inner attitude controller that is global asymptotically stable. To characterize the aircraft aerodynamics, a full envelope wind tunnel test is performed on the full-scale quadrotor tail-sitter UAV. In addition to planning the attitude and thrust required by the position controller, this framework can also be used to analyze the UAV's equilibrium state (trimmed condition), especially when wind gust is present. Finally, simulation results are presented to verify the controller's capacity, and experiments are conducted to show the attitude controller's performance.

The product of exponential model based robot calibration approach eliminates parameter discontinuity and simplifies coordinate frame setup, but demands extra effort to normalize twist coordinates and differentiate parameter-varying exponential maps. In this paper, we show that such an endeavor can be exempted by respecting the nonlinear geometry of the joint axis configuration space (ACS), the set of all possible axis locations. We analyze the geometry of the ACS models for prismatic and revolute joints, and treat the errors as Adjoint transformations on joint twists. We propose a novel robot kinematic calibration algorithm based on the ACS and Adjoint error model. It is geometrically intuitive, computationally efficient, and can easily handle additional assumptions on joint axes relations. We present a comparative study with simulations and experiments to show that our algorithm outperforms the existing ones in various aspects.

Just as the 3-D Euclidean space can be inverted through any of its points, the special Euclidean group SE(3) admits an inversion symmetry through any of its elements and is known to be a symmetric space. In this paper, we show that the symmetric submanifolds of SE(3) can be systematically exploited to study the kinematics of a variety of kinesiological and mechanical systems and, therefore, have many potential applications in robot kinematics. Unlike Lie subgroups of SE(3), symmetric submanifolds inherit distinct geometric properties from inversion symmetry. They can be generated by kinematic chains with symmetric joint twists. The main contribution of this paper is: 1) to give a complete classification of symmetric submanifolds of SE(3); 2) to investigate their geometric properties for robotics applications; and 3) to develop a generic method for synthesizing their kinematic chains.

We present an autonomous quadrotor system that is able to perform high precision landing on small platform in both indoor and outdoor environment. Its taking off and landing processes are fully autonomous. We use vision sensor to detect the landing platform, and the vision measurement is enhanced by IMU with SRUKF based sensor fusion method. All computation are done real-time and on-board. We implement the system and carry a series of experiments under various environmental conditions. The experiment results confirm the robustness and precision of our system in real use cases.

This paper presents a novel quadrotor UAV attitude control algorithm to realize complex acrobatic UAV maneuvers. A nonlinear dynamic model based on the exponential coordinates parametrization of rotation is proposed. By analysing the model using Lie Group and Lie Algebra theory, cascaded linear PID controllers are designed. To further improve the controller performance, PID controllers are augmented with smith predictor and rotational trajectory planner. The experiments conducted on a real quadrotor show that our control algorithm surpasses most known quadrotor controllers.

In this paper, we first analyze the identifiability of POE based Adjoint error approach. By carefully examining the linear dependence between calibration Jacobian columns, it is proved that joint offsets and Adjoint errors cannot be identified simultaneously, and the maximum dimension of identifiable parameters is 4r + 2t + 6. Some more scenarios are considered to augment the Adjoint error approach. To satisfy the constraints on joint relations, constrained method and projection method are proposed. Moreover, we present the identifiability of reduction ratios and joint pitches. Simulations of a 6 Degree-of-Freedom robot and a SCARA robot are given to illustrate and compare our methods. It shows that the constrained method can handle such situations effectively and yields better results.

In this paper, we conduct a comparative study of three well known robot kinematic calibration algorithms, namely the Denavit-Hartenberg (DH) parameter algorithm, the product of exponentials (POE) algorithm, and the local POE (LPOE) algorithm. To cope with distinct formulations associated to different algorithms, we propose a unified geometric framework which is based on POE kinematics and a novel Adjoint error model. The Adjoint error model offers us an extremely efficient way to benchmark the aforesaid calibration algorithms, and also compare them to a novel calibration algorithm based on the Adjoint error model.

In this paper, we propose a novel inertial-assisted visual odometry system intended for low-cost micro aerial vehicles (MAVs). The system sensor assembly consists of two downward-facing cameras and an inertial measurement unit (IMU) with three-axis accelerometers/gyroscopes. Real-time implementation of the system is enabled by a low-cost embedded system via two important features: firstly, simple pixel-level algorithms are integrated in a low-end FPGA and accelerated via pipeline and combinational logic techniques; secondly, a fast yaw-and-translation estimation algorithm works well with a novel outlier rejection scheme based on probabilistic predetermined operations rather than hypothesis testing iterations. We illustrate the performance of our system by hovering a MAV in a GPS-denied environment. Its feasibility and robustness is also illustrated in complex outdoor environments.

Optimal design is an inevitable step for parallel manipulators. The formulated optimal design problems are generally constrained, nonlinear, multimodal, and even without closed-form analytical expressions. Numerical optimization algorithms are thus applied to solve the problems. However, the optimization algorithms are usually chosen ad arbitrium. This paper aims to provide a guideline to choose algorithms for optimal design problems. Typical algorithms, the sequential quadratic programming (SQP) with multiple initial points, the controlled random search (CRS), the genetic algorithm (GA), the differential evolution (DE), and the particle swarm optimization (PSO), are investigated in detail for their convergence performances by using two canonical design examples, the Delta robot and the Gough-Stewart platform. It is shown that SQP with multiple initial points can be efficient for simple design problems, while DE and PSO perform effectively and steadily for all design problems. CRS can be used to generate good initial points since it exhibits excellent convergence evolution in the starting period.

This paper aims to develop a new kinematic model, the exponential submanifolds (EXPSs) eΩwith Ω a subspace of se(3) (the Lie algebra of the special Euclidean group SE(3)), for mechanism analysis and synthesis. The EXPSs provide perfect models for many global motion types appearing in the past mechanisms, robotics and kinesiology literatures which cannot be modeled as the well known Lie subgroups or their product. We derive in this paper both the sufficient and necessary conditions on Ω such that eΩis an EXPS, and geometric properties of the EXPS for mechanism analysis and synthesis.

In this paper, we present an experimental evaluation of the Cartesian stiffness of a novel parallel wrist under redundant and antagonistic actuation. The mechanism in consideration is Omni-Wrist V (OW5), a two degrees-of-freedom (DoF) parallel mechanism redundantly actuated by three subchains. We first give a brief review of its kineto-statics and derive its reduced Cartesian stiffness model. To illustrate the stiffness enhancement of OW5 under redundant and antagonistic actuation, its Cartesian stiffness is measured and evaluated under four control schemes: the non-redundant control, the minimum 2-norm torque control without or with redundant encoder, and the antagonistic actuation control. Measurement data are represented using stiffness matrices and stiffness ellipses. Our study offers a quick quantitative evaluation of stiffness enhancement of OW5 under redundant and antagonistic actuation.

A novel class of spatial four degree-of-freedom Schönflies-motion parallel manipulators with four identical subchains is presented. Their features are that each serial subchain undergoes the pure Schönflies motion without redundant joints. The parallel mechanisms possess the simplest topology and are suitable for pick-and-place operations. Kinematic analysis of the 4-PRPaR parallel manipulator, including its inverse and forward kinematics, singularity, and workspace, is discussed in detail. The analysis shows that the moving platform and the base must be in dissimilar dimension for good manipulability performance. The optimal design of the parallel manipulator is formulated as a multiobjective optimization problem. A novel performance index characterizing the approximation of the generated workspace to the prescribed regular workspace, the regular workspace share, is proposed to serve as one of the design objectives. The other objective is the global condition index, which measures the manipulability. The multiobjective optimization problem provides multiple optimal solutions for choice. Simulation verifies that the designed parallel manipulator can approximate the prescribed regular workspace with good condition index.

ICP (Iterative Closest Point) algorithm plays an important role in sequential scan matching SLAM. In the algorithm, closest point searching is the well-recognized speed bottleneck. We realize that a searching-friendly structure already exists in the raw data sequence from range acquisition device, and the acquisition order, which we called sensor order, is naturally derived from sensor working mechanism. We show that considering these geometric relations, the searching space could be greatly reduced and can lead to an efficient 3D sequential scan matching algorithm.

Due to the effect of joint clearance and component flexibility ( joint or link), a parallel kinematic manipulator (PKM), with proposed motion type G ⊂ SE(3), may have undesirable (or uncompensatible) pose error beyond G at the end-effector, which would cause severe accuracy performance degeneration of the PKM. As such phenomenons have been discovered and verified in many researches, we proposed a new performance index, called “Type Error”, which could be applied to evaluate such undesirable errors. Specifically with this index, the largest translational/rotational pose error could be quantized and the worst case over the designed workspace can be predicted. A three-step method for general application is presented in details by case study of three kinds of translational PKM.

This paper presents the unscented Kalman filter (UKF) with reduced simplex sigma-point for the navigation system in a small scale unmanned helicopter. UKF is widely applied to nonlinear systems. However, the disadvantage of traditional UKF is the high computational cost caused by the unscented transformation step. The computational cost is proportional to the number of the constructed sigma-points. Therefore a reduced simplex sigma-point selection is proposed to be practically applied for the sensor fusion on the unmanned helicopter. The simulation and experimental results verify the computational load reduction.

In this paper, we identify a class of structurally distinguished machines, called quotient kinematics machines (QKM). A QKM realizes a motion task, typically characterized by a subgroup G of rigid transformation group SE(3), through coordinated motion of two mechanisms called modules. One is referred to as a subgroup module H and the other a complementary or quotient module G/H of H in G. Since QKM can retain both large workspace/rotation range of SKMs and speed/accuracy of PKMs by appropriate choice of modules, it is often implemented in high end machine design for semiconductor die/wire-bonding and 5-axis machining, etc. To promote QKM technology beyond occasional studies and applications, we use differential geometric techniques to develop a rigorous and precise treatment of QKMs, including: (i) modeling and analysis of QKMs; (ii) classification and synthesis of QKMs; (iii) PKM realization of quotient modules.

The advantages of tilt-and-torsion angles in analysis of zero-torsion parallel kinematics machines (PKM) have been reported by several literatures. However, geometric properties of tilt-and-torsion angles are not completely understood and fully utilized in synthesis of novel zero-torsion PKMs. In this paper, we study geometric properties of the so called zero-torsion motion types via differential geometry of Lie groups. We show that zero-torsion motion types admit simple representations under canonical coordinates of the first kind of the special Euclidean group SE(3). Using the proposed representation, we give a classification of zero-torsion PKMs. The synthesis condition for several well known zero-torsion PKMs are correctly identified. We will conduct type synthesis of zero-torsion PKMs in a separate paper.

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.

In mechanism and machine design, the notion of serial kinematics machine (SKM), parallel kinematics machine (PKM) and hybrid kinematics machine (HKM) is well understood. In this paper, we introduce a fourth type of kinematics machine, known as quotient kinematics machine(QKM). A QKM generating a subgroup motion G consists of two mechanisms (or motion modules) acting in unison, one synthesizing a subgroup H of G, and another that of a complement of G/H. Apparently, the two motion modules of a QKM have simpler kinematic structures than that of a SKM, PKM or HKM with the same motion type G, and thus is expected to have performance advantages in terms of stiffness (speed and accuracy), modularity and etc, over its SKM/PKM/HKM counterparts. The formulation of the QKM concept and its analysis and synthesis are considered in this paper.

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform.

Finger gait is necessarily needed in order to relocate fingers of the robotic hand when a dextrous manipulation task cannot be accomplished only by the rolling and sliding motions of the fingers. In this paper, a novel modeling framework for the multifingered manipulation with finger gaits is proposed. Through classifying the fingers into grasping fingers and free fingers, an alternate representation of a grasp is introduced. With the consideration of both its discrete and continuous characteristics, the kinematics model of a fingered manipulation with finger gaits is formulated into a hybrid automaton. Finally, simulation results verify the validity of the proposed modeling framework.

In view of the successful application of planar parallelogram in the Delta robot and its variants, we are interested to investigate mechanisms consisting of spatial parallelograms. The spatial parallelogram, denoted by Pscra*, is a 2-SS (S stands for a spherical joint) parallel mechanism having identical length for opposite links. We show that a 3-PPscra* mechanism is generically undergoes 3-dimensional purely translational motion. Based on the 3-PPscra* topology, an integrated optimal design on both architecture and geometry design is carried out. Using the formulation of maximizing effective cubic workspace, the Orthopod, which has three orthogonally arranged linear joint axes, is found to be the best in our settings. A prototype machine of the Orthopod is thus designed and manufactured.

To avoid deteriorating the mechanism's performance, joint clearance can be eliminated by preloading the pairing elements of the joint. However, this paper proves rigorously that in the real world, the unavoidable assembly and manufacturing errors will cause overconstrained parallel manipulators to lose degree of freedoms, or even unable to be assembled if they are composed of purely clearance-free pairs (e.g., preloaded pairs). Introducing joint clearance is an essential and efficient way for the correct functioning and easy assembly of overconstrained parallel manipulators.

Due to the joint clearance, parallel manipulators always exhibit some position and orientation errors at the mobile platform. This paper aims to provide a systematic framework for the error analysis problem of general parallel mechanisms influenced by the joint clearance. A novel and efficient method is proposed to evaluate the maximal pose errors of general spatial parallel manipulators with joint clearance.

Under a whole hand grasp, it may not be possible to generate grasping forces in all directions. Thus, the traditional techniques developed based on fingertip contacts is inadequate. In this paper, we decompose the contact force space into four orthogonal subspaces, each with a clear physical interpretation. Based on linear matrix inequalities (LMI's) representations of grasping constraints, we address and formulate the active force closure and the active grasp feasibility problems as LMI feasibility problems. Combining the effects of both active and passive forces, we propose a new cost index for the whole hand grasping force optimization problem. We further simply the force optimization problem for a whole hand grasp, which is active force closure.

A robotic hand may change its grasp status and relocate some of its fingers in order to perform a large scale manipulation. Such a strategy is called a finger gait. In this paper, a randomized manipulation planning algorithm is proposed to solving the finger gait planning problem. One of the most used finger gaiting primitives, finger substitution, is introduced. Because of its discrete-continuous characteristics, the kinematics model of a finger substitution is formulated into a hybrid automaton. Considering the discrete and continuous topology of the automaton, both the discrete metric and continuous metric are defined on the state space. An improved RRT based planner is proposed to find a feasible finger substitution. Finally, simulation results verify the validity of the proposed finger gait planner.

Mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group${\rm SE}(3)$, we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of${\rm SE}(3)$and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.

Since the tracking error does not truly reflect product quality, the contouring error is introduced in the dynamic control of parallel machining systems. For real-time computation reason, the contouring error is approximated by the distance from the actual position to the tangent plane of the desired contour at the corresponding desired position, i.e., the error in normal direction. By attaching a moving task frame to each point on a desired trajectory, the tracking error is decomposed into tangential error and normal error. By the transformation introduced by the task frame, we obtain error dynamics in the task frame. The error dynamics is decoupled into error dynamics in tangential and normal directions by applying the computed torque control and choosing appropriate system matrices. Simulation shows that a larger bandwidth of the normal dynamics leads to smaller contouring error given fixed natural frequency for the tangential dynamics. By a comparison with the PD control in the world frame, the task space based contouring control exhibits much better performance in contouring accuracy

A novel 3-DoF purely translational parallel mechanism, the Orthotripod, is proposed. It is a variant of the tripod based parallel machine and has a similar architecture to the Orthoglide. In order to reduce the number of passive joints and remove the effect of ease of abrasion of revolute joints, spherical joints are applied in the parallelogram. A mathematic mobility analysis shows the mechanism is indeed 3-DoF purely translational. We optimally design the Orthotripod and the tripod based parallel machine by maximizing the well-conditioned workspace. The optimized Orthotripod possesses a nearly ball-shaped workspace and has much better kinematic performance than the optimized tripod based parallel mechanism. The proposed mechanism is adaptable for machine tool applications

Type synthesis of low (3-5) degree of freedom (Dof) spatial parallel manipulators is well documented in literature. Recent approaches such as proposed in J.M. Herve and F. Sparacino (1991) - Z. Huang and Q.C. Li (2003) showed some systematic design capability, but did not develop an equally effective means to check for prescribed finite motion. In this paper, we studied the finite motion set of parallel manipulators from a general input-affine nonlinear system viewpoint. Differential geometry tools for controllability (reachability) analysis of nonlinear system on a differential manifold are utilized together with lie group theory. Our techniques are shown to be effective by applying to a systematic type synthesis method proposed in M. Jian, et al. (2005) and W. Yuanqing, et al. (2005)

In tasks of grasping and manipulation, the hand sometimes uses not only fingertips but also fingers' inner links and the palm to achieve more robust grasp. This kind of grasp is called whole hand grasp, or power grasp. One property of whole hand grasp is that the hand may not be able to generate grasping forces in any directions, so previous fingertip grasping analysis is no longer suitable for whole hand grasp. In this paper, concepts of active force and passive force are introduced. With these concepts, the contact force space is decomposed into four orthogonal subspaces. Considering the roles of both active force and passive force, a new cost index is proposed for the whole hand grasping force optimization, which is then reformulated into a convex optimization problem involving LMIs. Finally, numerical example and simulation results verify the validity and performance of our formulation of the problem with that new proposed cost index

Large-scale motion of the grasped object is one of the tasks, which is involved in practical dextrous manipulation of multifingered robotic hand. When the large-scale motion can not be accomplished only by rolling and sliding of the finger, finger gaiting, or regrasping, is used. In this paper, two primitives of finger gaits are introduced. Based on the characteristic of finger gaits, we model finger gaits as a hybrid automaton. Finally, we do simulations on a three fingered hand to verify the validity of our model

In this paper we concentrate on contouring control for surface machining. The object of the motion control system is tracking the spatial curve lying on the surface. Observing that the contour error can be approximated by the tracking error (projected to the normal subspace of the surface), we propose a new design procedure based on the geometrical properties of the curves and surfaces. Essentially the controllers look ahead using the information provided by the curvature of the curves and surfaces. The simulation results show the efficiency of the design method

In this paper, the desired performance of the mechanical system is specified in terms of contouring error instead of traditional method which specifies a task as a desired timed trajectory tracking problem. By defining the task frame, a simplified contouring error model is obtained through projecting tracking error to this new frame. Then a novel adaptive contouring controller is developed directly in the task frame to handle bounded external disturbances and system model uncertainties while maintaining superior contouring tracking performance. The algorithm effectively exploit the the structure of manipulator dynamics to reduce the computation complexity. Experimental results on an AC motor driven X-Y table demonstrate the merit of significant improvement of the proposed controller for increasing contouring accuracy compared with other conventional control algorithms.

This paper proposes to optimally design a parallel machine based on multiple criteria. Many criteria, workspace, condition number, accuracy, stiffness, maximum velocity, and maximum force, are considered. The optimal design problem is proposed as to find a set of design parameters such that (a) the Cartesian workspace generated by the resulting manipulator contains a prescribed workspace; (b) the resulting manipulator possesses a good condition number at each points in the prescribed workspace; (c) the resulting manipulator possesses good performance on accuracy, stiffness, velocity/force transmission factor. By some manipulations, the requirements on the latter four criteria are reduced to constraints on singular values of the kinematic Jacobian. A trade-off must be made since there're opposite requirements among those four criteria. The singular values of kinematic Jacobian are limited in a given interval to guarantee good properties. All the requirement are finally reduced to polynomial inequalities with respect to design parameters. The optimal design problem is transformed into a Max-Det optimization problem that can be ef ficiently solved. The Orthoglide is used as an example to demonstrate the procedure.

This paper presents a rigorous and precise geometric theory for the analysis and synthesis of sub-6 DoF parallel manipulators. We give a rigorous definition for the parallel manipulator synthesis problem, and introduce a general method for specifying the corresponding subchains which will result in the desired parallel manipulator. Following this, a procedure for solving the parallel manipulator synthesis problem is proposed when the set of desired end-effector motions is in the form of Lie subgroup or a regular submanifold of SE(3). Numerous examples are used to illustrate the generality and effectiveness of the proposed synthesis method.

Motivated by the work of Herve and his coworkers, this paper presents a rigorous and precise geometric theory for the synthesis and analysis of sub-6 DoF serial manipulator subchains. First, we review the basic properties of the Special Euclidean group SE(3), Lie subgroups and submanifolds of SE(3). With low dimensional subgroups and submanifolds providing models for the so called primitive generators, the high dimensional subgroups and regular submanifolds provide models for the set of desired end-effector motions. Two important classes of regular submanifolds of SE(3) are studied in detail. Then, starting from a given list of primitive generators, we give a rigorous definition of the synthesis problem for a serial manipulator subchain, and develop a general procedure for solving the synthesis problem when the set of desired end-effector motions is a Lie subgroup or a regular submanifold.

Kinematic design of parallel manipulators is addressed in this paper. By observation that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects both requirements on the workspace shape and quality. Dexterity index is utilized to characterize the effectiveness of the workspace. The optimal design problem is then formulated to find a manipulator geometry that maximizes the effective regular workspace. Since the optimal design problem is a constrained nonlinear optimization problem without explicit analytical expressions, the controlled random search (CRS) technique, which was reported robust and reliable, is applied to numerically solve the problem. The commonly-used Stewart-Gough platform is employed as an example to demonstrate the design procedure.

Due to the joint clearance, parallel manipulators always exhibit some position and orientation errors at the mobile platform. This paper aims to present a novel and general approach for evaluating the maximal pose deviation of the mobile platform under the influence of joint clearance. First, it shows and proves that overconstrained parallel manipulators can not work without clearance. Then, an efficient method is proposed to evaluate the maximal pose errors for general spatial parallel manipulators with joint clearance. A numerical example shows the application and efficiency of the proposed approach.

Various parallel kinematic manipulator (PKM) type design papers enumerate eligible links as the combination of revolute and prismatic joints and synthesize using local screw theory, but analysis and comparison on real capacity of different types has not been developed yet. This paper applies differential Lie group tools to developing a spectrum of so called regular link spatial translation (T(3)) PKM, which maximized workspace from a topological point of view.

Large-scale motion of the grasped object is one of the tasks, which is involved in practical dexterous manipulation of multifingered robotic hand. When the large-scale motion can not be accomplished only by rolling and sliding of the finger, finger gaiting, or regrasping, is used. In this paper, we propose a joint space representation of grasps, which represents a stable grasp by a set of joints values with several grasping constraints. Using primitives describing the regrasping process with the joint space representation, we build a kinematic model of finger gaiting as a hybrid automaton, by using which all grasping constraints are involved. Then, a simple but representative simulation is setup, whose results verify the validity and efficiency of the model. Finally, we state several interesting future works, which can greatly be extended based on the hybrid automaton we proposed in this paper.

In the contouring control, the trajectory and the tolerance information are specified in the task space. Based on this observation we propose to design the controller in the task space directly. First, by defining the projection map on the cotangent space of the mechanical system the equation of motion is derived in the task space. Then a novel contouring controller is got based on the geometric control theory. The controller is transferred into the joint space for implementation. The simulation results show the performance of the controller.

This paper deals with the problem of optimal geometry design of parallel manipulators. In order to reduce the main drawbacks of parallel manipulators, relatively small workspace and more singularities, two requirements, workspace and condition number, are considered. The design problem is thus formulated to find a parallel mechanism such that its Cartesian workspace contains a prescribed workspaces with good condition numbers in it. By observing that those requirements can be locally cast into Linear Matrix Inequalities (LMIs), we formulate the design problem locally as a convex optimization problem subject to LMIs with a max-det function as its objective function. Hence, at each node of discretized space of design parameters, there is an LMI-based convex optimization problem. A two-level algorithm can be applied to solve for a set of optimal design parameters: (1) Discretize the space of design parameters into a set of discrete nodes; (2) At each node the Newton algorithm is applied to solve the max-det optimization problem. By comparing all the locally optimal costs, we can obtain a corresponding set of globally optimal design parameters correspondingly. Simulation results verify the effectiveness of the proposed approach.

Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multi-fingered robotic hands and in fixture planning for manufacturing automation. We formulate the grasp-planning problem as optimization problems with respect to several grasp quality functions. For real-time computation, a simplified min-analytic-center problem is proposed. Simulation and experimental results illustrate the validity of the proposed approach for optimal grasp planning.

Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning problem as optimization problems with respect to three grasp quality functions. The physical significance and properties of each quality function are explained, and computation of the corresponding gradient flows is provided. One noticeable property of some of these quality functions is that the optimal solutions are also force-closure grasps if they do exist for the given object. Furthermore, when specialized to two-fingered or three-fingered grasps on a spherical object, the optimal solutions become the familiar antipodal grasp, or the symmetric grasp, respectively. Thus, by following the gradient flows with arbitrary initial conditions, the optimal grasp synthesis problem is solved for objects with smooth geometries manipulated by hands with any number of fingers. Also, note that our solutions do not involve linearization of the friction cones. We discuss two simplified versions of these problems when real-time solutions are needed, e.g. coordinated manipulation of a robotic hand with contact points servoing. We give simulation and experimental results illustrating validity of the proposed approach for optimal grasp planning. Note to Practitioners: This paper presents three new quality functions for comparing and planning grasps and fixtures. These measures improve on the traditional measure of force closure. We propose a method for computing the optimal solutions of these functions, and a method for reducing their computation time through reasonable simplification/approximation. Preliminary experiments with a three-fingered robotic hand demonstrate that the proposed functions can be used to optimize the grasp quality during manipulation/manufacturing, and keep the optimal grasp configuration once it is reached. However, we only obtain the local optimal solutions for the functions without simplification except for some special cases. We also assume that the object/workpiece is ideally rigid in all three functions. In future research, we will improve these limitations through a compliance model.

This paper addresses an optimal planning problem for workpiece localization with coordinate measurements. The fundamental issue is to find the best probing locations and a suitable sampling size, such that the uncertainty of the localization error is within a predefined limited bound. First, we introduce two sequential optimization algorithms to incrementally increase the localization accuracy, defined by the determinant of the information matrix of the measurements. Then, a reliability analysis method is incorporated for finding a sample size that is sufficient to reduce the uncertainty of the localization error to a limited bound. By combining these two analysis tools, we present a near-optimal probing strategy for finding the best probing locations and a suitable sampling size. With this strategy, given the desired translation and orientation error bounds and desired confidence limit, we can experimentally determine the least number of points needed to measure. Simulation and experimental results show the efficiency of the proposed probing strategy.

Real-time grasping force optimization problem can be naturally formulated as a convex optimization problem on the Riemannian manifold of positive definite matrices subject to linear constraints for which many algorithms, including gradient algorithms, Newton algorithms, and interior point algorithms, have been developed. In all these algorithms we need to specify a step size in every iteration. In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm. By investigating the structure of the affine-scaling vector fields associated with the optimization problem, we give a detailed convergence analysis of these algorithms. Experimental results show the different performance of these algorithms from convergence rates.

Real-time grasping force optimization problem can be naturally formulated as a convex optimization problem on the Riemannian manifold of positive definite matrices subject to linear constraints for which many algorithms, including gradient algorithms, Newton algorithms, and interior point algorithms, have been developed. In all these algorithms we need to specify a step size in every iteration and a valid initial point to start the recursion. In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm and one method for searching a valid initial point. Simulation and experimental results show the different performances of these algorithms from computation time and convergence rates.

This paper deals with the problem of optimal design of parallel manipulators which are singularityless, of high stiffness and manipulability and the most economic. By observing that those requirements can be cast into Linear Matrix Inequalities (LMIs), we formulate the design problem as a convex optimization problem subject to LMIs with either a linear function or a max-det function as its objective function. The variables x associated with LMIs are nonlinear functions of some key kinematic parameters /spl alpha/. If the dimension of x, t, is equal to the number of kinematic parameters, l/sub 0/, a two-level algorithm can be applied to solve for a set of optimal kinematic parameters: (1) Applying the interior point algorithm for solving of x; (2) Applying Newton method to a set of nonlinear algebraic equations for solving of /spl alpha/. If the dimension of x is greater than the number of kinematic parameters (i.e., x are not linearly independent), we consider the constrained semi-definite programming problems and the constrained max-det problems by taking account of an additional set of nonlinear constraints. We propose a simplified constrained gradient algorithm for solving of x in such cases, /spl alpha/ derives from x using Newton method. Simulation results verify the effectiveness of the proposed algorithms.

This paper presents an optimal planning problem for workpiece measurement. Two sequential optimization algorithms are introduced to find maximum determinant solutions. Then, based on a reliability analysis of workpiece localization and the sequential optimization algorithms, a computer-aided probing strategy is proposed. With this strategy, given the desired translation and orientation error bounds and desired confidence limit, we can experimentally find the least number of points needed to measure. Simulation results show the efficiency of the computer-aided probing strategy.

In this paper, we propose two algorithms for the auto-calibration of the home position or the joint angle offsets for a parallel manipulator by utilizing the extra sensor(s) information (sensor redundancy), sampling over the workspace, and optimizing a suitably chosen cost function, without resorting to any other external equipment. Meanwhile, a measure or estimate of the precision of the machine is also obtained. It is very useful and convenient if the machine needs frequent re-calibration. Simulations and experiments are also performed to show the effectiveness of the algorithms.

This paper provided a unified geometric framework for kinematic analysis and synthesis of parallel manipulators. We gave a strict definition on motion types of a mechanism based on distributions on a Lie group. We derived conditions for parallel manipulators with Lie subgroup motions using the intersection of the permissible velocity spaces, or the direct sum of the constraint force spaces of each subchain, and the integration theory on a Lie group. Several practical examples were studied in detail to verify our approach.

This paper deals with the problem of optimal design of parallel manipulators which have no singularity, have high stiffness and manipulability and are the most economic. By observing that those requirements can be cast into linear matrix inequalities (LMIs), we formulate the design problem as a convex optimization problem subject to LMIs with either a linear function or a max-det function as its objective function. The variables x associated with LMIs are nonlinear functions of some key kinematic parameters /spl alpha/. If the dimension of x is equal to the number of independent kinematic parameters, a two-level algorithm can be applied to solve for a set of optimal kinematic parameters: (1) applying the interior-point algorithm for solving of x; (2) applying the Newton method to a set of nonlinear algebraic equations for solving of /spl alpha/. If the dimension of x is greater than the number of independent kinematic parameters (i.e., x are not linearly independent), we consider the constrained semi-definite programming problems and the constrained max-det problems by taking account of an additional set of nonlinear constraints. We propose a simplified constrained gradient algorithm for solving of x in such cases, /spl alpha/ derives from x using Newton method. Simulation results verify the effectiveness of the proposed algorithms.

Planning a proper set of contact points on a given object/workpiece so as to satisfy a certain optimality criterion is a common problem in grasp synthesis for multifingered robotic hands and in fixture planning for manufacturing automation. In this paper, we formulate the grasp planning problem as optimization problems with respect to two grasp quality functions. For real-time computation, a simplified Min-analytic-center problem is proposed. Simulation and experimental results illustrate the validity of the proposed approach for optimal grasp planning.

In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm and a method for searching a valid initial point. By investigating the structure of the affine-scaling vector fields associated with the optimization problem, we give a detailed convergence analysis of these algorithms. Simulation and experimental results show the different performance of these algorithms from computation time and convergence rates.

A parallel manipulator is naturally associated with a set of constraint functions defined by its closure constraints. The differential forms arising from these constraint functions completely characterize the geometric properties of the manipulator. In this paper, using the language of differential forms, we provide a thorough geometric study on the various types of singularities of a parallel manipulator, their relations with the kinematic parameters and the configuration spaces of the manipulator, and the role redundant actuation plays in reshaping the singularities and improving the performance of the manipulator. First, we analyze configuration space singularities by constructing a Morse function on some appropriately defined spaces. By varying key parameters of the manipulator, we obtain homotopic classes of the configuration spaces. This allows us to gain insight on configuration space singularities and understand how to choose design parameters for the manipulator. Second, we define parametrization singularities which include actuator and end-effector singularities (or other equivalent definitions) as their special cases. This definition naturally contains the closure constraints in addition to the coordinates of the actuators and the end-effector and can be used to search a complete set of actuator or end-effector singularities including some singularities that may be missed by the usual kinematics methods. We give an intrinsic classification of parametrization singularities and define their topological orders. While a nondegenerate singularity poses no problems in general, a degenerate singularity can sometimes be a source of danger and should be avoided if possible.

Coordinated manipulation of objects by multifingered. robotic hands aims to resolve the redundancy in object level and hand level, increase the rigidity and robustness of grasping, and achieve a good dynamic performance in trajectory control. In the paper a contact space approach and an active joint space approach are explored. The model places the following problems associated with the coordinated manipulation with non-fixed contact into a unified framework: 1. sufficient conditions for the controllability of hand motion including both the velocity of contact coordinates and the object; 2. kinematic measure of robust grasp to generate the coordinated motion of contact coordinates; 3. searching a group of internal forces lying in the strict interior of the friction cone by a LMI method; 4. hybrid control algorithms for simultaneous control of motion of hand and the internal grasping forces; and 5. controlling the internal grasping force to ensure the total contact force lying in the friction cone. Experimental results done on HKUST hands are reported.

Presents an inertia equivalence principle that exposes the relation between the dynamics of a parallel manipulator, and that of its arbitrary reduced tree systems. This principle, along with the D'Alembert principle, leads to a precise proof of the nontrivial fact that the virtual work principle is also valid for the two different physical systems, a parallel manipulator and its reduced tree system, under a given condition. The dynamics of parallel manipulators and its properties are then given. Two control algorithms are then provided. Firstly, we implement a geometric control algorithm that is based on the Riemannian metric structure associated with the kinetic energy of the manipulator. Motivated by this, an adaptive control algorithm is then proposed in which only dynamic parameters are required to be updated. Geometric reinterpretation of this algorithm as the passive port controlled system is given. Its asymptotic stability is therefore obvious. The new content of this algorithm compared with the traditional ones is discussed. Experimental results are reported that demonstrate the effectiveness of the algorithms.

Workpiece localization has many applications in manufacturing automation. Symmetric localization plays an important role in it, since many commonly used features in engineering design are symmetric. We discuss some new found problems in symmetric localization. We find that multiple solutions exist even for localizing a cube, for which it was known that a unique solution should be found before. Then, we re-explore the symmetry subspaces for symmetric features. After that, we find that some symmetric features have different configuration spaces as known before. This is actually the cause of the problem. A symmetric localization algorithm and simulation results are given to fix the existing problems.

This article deals with the problem of real-time grasping force optimization for multifingered manipulation. Based on a review of existing approaches, the BHM and the HTL algorithms, a need for a strictly possible initial solution is found to be a common problem. Two approaches, the max-det approach and min-max approach, are proposed to resolve this problem. The first approach, although efficient in most cases, suffers from the problem of singularity. The latter can resolve the singularity problem, but is relatively slow compared with the former. The two approaches are combined in real implementations to efficiently compute a strictly initial solution, which is in turn used in the HTL algorithm (also the BHM algorithm). The whole algorithm is shown to be fast, fully automatic, and applicable to a wide class of manipulation tasks irrespective of the number of fingers and also the geometry of the manipulated objects. Experiments on the HKUST hand demonstrate the convergence and speed of the algorithm.

This paper investigates the synthesis of a spatial stiffness matrix using simple line springs. A new algorithm is developed, which enables the selection of constituent springs based on their positions and directions. The constraining space of the line springs is then investigated. It is shown that an isotropic stiffness matrix, in general, can be split into the sum of two rank-3 stiffness matrices. The three line springs of the first matrix can be selected to pass through any arbitrary points in space, while the three line springs of the second stiffness matrix lie on a quadric surface, which is usually a hyperboloid of one sheet.

Dynamic control of constrained mechanical systems, such as robotic manipulators under end-effector constraints, parallel manipulators, and multifingered robotic hands under closure constraints have been classic problems in robotics research. In this paper, we provide a unified geometric framework for modeling, analysis, and control of constrained mechanical systems. Starting with the constraint, we define two canonical subspaces, namely the subspace of constraint forces and the tangent space of the constraint manifold for holonomic constraint. Using the kinetic energy metric, we define the remaining subspaces and show explicitly the relations among these subspaces. We project the Euler-Lagrange equation of a constrained mechanical system into two orthogonal components and give geometric and physical interpretations of the projected equations. Based on the projected equations, a unified and asymptotically stable hybrid position/force-control algorithm is proposed, along with experimental results for several practical examples. In the case of nonholonomic constraints, we show that the equations can be projected to the distribution/codistribution associated with the constraints and the control law reduces to hybrid velocity/force control.

As we all know, singularity is commonly encountered in parallel mechanisms. It is shown that the behavior of singularity of parallel mechanisms could be more complicated than that of serial ones. However, it is not very clear whether singularity will bring problems to kinematics, dynamics or other characteristics and what result will be caused when parallel mechanisms fall into the neighborhood of a singularity. We focus on the study of the undesired effects of singularity in parallel mechanisms and propose a method to solve them, namely the method of redundancy. Three kinds of redundant methods are developed and their advantages are discussed. In the experiments, we concentrate on the control of redundantly actuated parallel mechanisms. We control the parallel mechanisms tracking a given trajectory by kinematic control method and dynamic control method respectively. Experimental results verified the efficiency of the proposed algorithms.

Workpiece localization has direct relations with many manufacturing automation applications. In order to gain accurate workpiece measurement by coordinate measuring machines (CMM) or on-machine measurement system, the touch trigger probe is widely adopted. In spite of the high repeatability of the touch trigger probe, there are still error sources associated with the probe. In this paper, we will focus on probe radius compensation. Several compensation methods in related papers are reviewed. In addition, a new radius compensation method is proposed in this paper. Simulation and experimental results of probe radius compensation by different methods are given. It is shown that our proposed method has the best performance both in terms of compensation accuracy and computational time. The method is also implemented in a computer aided setup (CAS) system.

Studies the dynamics of parallel manipulators. We first have a brief review and discussion on different dynamics formulations in the literature (Newton-Euler, direct Lagrangian, and Lagrange-D'Alembert formulation on the reduced system). Then we show the equivalence of these methods. Based on the concepts from differential manifolds, we prove that away from configuration singularity, there exists a projection from the joint space to parameterize the configuration space. The fact that the dynamics is well defined even at actuators singularity, end-effector singularity and other kinds of parameterization singularity is highlighted. For the method of reduced systems, there are two main drawbacks. Firstly the joints being cut for forming the tree system are presumed to have no external torque. Secondly the force and torque applied to other links of the manipulator is not considered. We propose two methods to remedy the situation. Firstly by cutting a link instead of a joint, all the joints torque can be incorporated into our equations of motion. This is useful not only for the case of actuating all the joints, but also if we consider compensating the joints friction. Secondly we propose a concept of transforming force to the generalized force space so that all the other forces and torque can be considered.

Parallel manipulators with redundant actuation present both problems and advantages. We analyze some major advantages of redundancy to demonstrate its usefulness. The dynamics of closed-chain mechanisms has been studied by many researchers. However, they often only consider the case of normal actuation. Few methods are suitable for closed-chain mechanisms with redundant actuation. In the article, the dynamic model of redundantly actuated closed-chain mechanisms is presented explicitly by applying Lagrange-D'Alembert formulations. As an illustrative example, the dynamic model of a 2-DOF planar parallel redundant manipulator is presented. A PID control algorithm in the joint space is experimentally implemented on this parallel manipulator to perform trajectory tracking. The experimental results show the validity of PID control.

Singularity is a fundamental problem in the analysis of parallel mechanisms. The distribution of singularity in the workspace will determine to a great extent the properties of parallel mechanisms. We study the distribution of actuator singularity, which can also be applied to analyze end-effector singularity. A very important observation has been made that these two kinds of singularities are caused by the parameterization of a configuration manifold by actuator coordinates or end-effector coordinates. Despite the various styles of singularities of parallel mechanisms, there are some rules which govern the behavior of stable singularities. These rules provide some useful ideas in the design of redundant parallel mechanisms so as to achieve better performance in high speed motion and improve their stiffness. Optimal kinematic and dynamic control algorithms are designed and implemented which make use of the redundancy of the parallel mechanism. Experimental results agree with our expectation.

Workpiece localization and similar problems have attracted many researcher in robotics, computer vision and image processing research fields. Workpiece localization algorithms have close relations with workpiece setup in manufacturing process. However when these algorithms apply to a computer aided setup (CAS) system, many problems, like online measurement planning and error compensation etc., should be solved first. In this paper, a CAD model based CAS system will be introduced. This system is based on an open architecture CNC machine. Some problems in implementation are also addressed, such as algorithm divergence. The system has used a new method to avoid the possible divergence of localization algorithms. New error compensation method has been applied in the localization algorithms, instead of directly compensating the measurement data. Experimental results will be given to show the effect of these new methods and the efficiency of the CAS system.

Dextrous manipulation is a fundamental problem in the study of multifingered robotic hands. Given a robotic hand and an object to be manipulated by the hand in an environment filled with obstacles, the main objectives of dextrous manipulation are to have the hand grasp the object and transfer it from a start configuration to a goal configuration without collision. To fulfill such a task in general, we will need: (a) a manipulation planner to generate a feasible path for the hand; and (b) a controller to implement the planned path. In this overview paper, we define the manipulation planning problem and present a unified control system architecture for multifingered manipulation (CoSAM/sup 2/). By incorporating the various kinematic and static relationships of a multifingered robotic hand system with proper sensory data inputs at different stages, CoSAM/sup 2/ achieves the various objectives of dextrous manipulation. Theoretical background of the control system design along with real-time experimental results are described.

A datum reference frame (DRF) is a coordinate system used to locate and orient part features. Constructing a DRF from a set of datum features is a complicated process involving: a) specifying a valid combination and the precedence of the datum features which define the DRF; b) developing datum from datum features of the part; and c) determining the position and orientation of the DRF from the datums. We develop a geometric theory for establishing DRFs. The theory is based on the observation that a datum feature such as a plane, a cylinder or a sphere has a symmetry subgroup G/sub 0/ under the action by the group SE(3) of rigid motions in R/sup 3/. Thus, the configuration space of a datum feature can be identified with the homogeneous space SE(3)/G/sub 0/, and the problem of datum development can be posed as a minimization problem in SE(J)/G/sub 0/. We give conditions under which a datum feature qualifies to be a secondary or a tertiary datum. We present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem in the homogeneous spaces of SE(3). We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach.

Investigates the stiffness and kinematics of an object grasped by multiple elastic fingers. The derivation is based on the work of Svinin (1995), but derived with the approach of minimization of energy and using Montana's (1989) equations of contact model. The result gives a closed form expression of object stiffness in terms of contact finger stiffness, contact locations and contact point curvatures.

We first propose a hybrid localization/inspection/machinability problem. Next, we formulate the hybrid problem using differential geometric theory and the minimax method. Then, we develop a methodology for treating localization, online inspection and machinability of workpieces simultaneously. Using the geometric properties of the hybrid problem, the hybrid problem is decoupled into a (symmetric) localization/inspection problem and a machinability problem. Then both problems are formulated as constrained optimization problems and are solved by a sequence of linear programming problems. Finally, we present simulation results to demonstrate the efficiency of our method for the hybrid problem.

A datum reference frame is a coordinate system used to locate and orient port features. Constructing a datum reference frame from a set of features is a complicated process involving: 1) specifying a valid combination and the precedence of the datum features which define the datum reference frame; 2) developing from datum features of the part; and 3) determining the position and orientation of the datum reference frame from the data. In this paper, we develop a geometric theory for establishing datum reference frames, and present a sequential procedure that transforms the primary, secondary and tertiary datum problems as a minimization or a constrained minimization problem. We develop simple algorithms to solve these problems, and give simulation results illustrating efficiency and simplicity of the approach.

Three important problems in the study of grasping and manipulation by multi-fingered robotic hands are: 1) given a grasp characterised by a set of contact points and the associated contact models, determine if the grasp has force closure; 2) if the grasp does not have force closure, determine if the fingers are able to apply a specified resultant wrench on the object; and 3) compute "optimal" contact forces if the answer to problem (2) is affirmative. In this paper, based on an early result by Buss-Hashimoto-Moore (1996), which transforms the nonlinear friction cone constraints into positive definiteness of certain symmetric matrices, we further cast the friction cone constraints into linear matrix inequalities (LMIs) and formulate all three of the problems stated above as a set of convex optimization problems involving LMIs. We perform simulation studies to show the simplicity and efficiency of the LMI formulation to the three problems.

Dextrous manipulation is an important issue in the study of multifingered robotic hands. Determining the contact velocities in dextrous manipulation with rolling contact is the key problem. We propose a coordinated manipulation scheme in which the contact velocities are determined by tactile sensor feedback. We address coordinated motion generation which maintains or improves the grasp quality in dextrous manipulation. We implement several experiments using the HKUST three-fingered robotic hand. The experimental results illustrate the effectiveness of the proposed scheme.

Capacitive tactile sensors are constructed and installed to the fingers of the HKUST hands for measurement of position, force and direction of principle curvature of contact point. The hardware and software for signal processing are designed such that the contact information is sent to the motion control computer in real time. Experiments in rolling and sliding contact motions are then performed for testing the functionality of the tactile sensing system in motion control. The measurement of contact velocities obtained from the sensor is also compared with that calculated from the theoretical contact equations. This paper describes the tactile sensing system and the experimental result in contact motion control.

We first present a unified geometric formulation of form tolerances using an extended least-squares (E-LSQ) approach. Then, using properties of configuration space of symmetric features an iterative algorithm is developed to solve the E-LSQ problem. Simulation results show that the algorithm not only keeps computational efficiency of the least-squares approach, but also possesses of computational accuracy of min-max algorithms. The outstanding properties of the geometric formulation include: 1) coordinate-free representation; 2) in conformance to the tolerance standard; and 3) easy implementation.

This paper defines a hybrid localization/envelopment problem, develops a formulation of the hybrid localization/envelopment problem, and presents a simple algorithm for computing its solutions. First, we show that when the finished surfaces of a workpiece are inadequate to fully constrain the rigid motions of the workpiece, then the remaining set of free motions must form a subgroup G/sub 0/ of the Euclidean group SE(3). This allows us to decompose the hybrid problem into a (symmetric) localization problem on the homogeneous space SE(3)/G/sub 0/ and an envelopment problem on G/sub 0/. The geometric properties of SE(S)/G/sub 0/ are used to convert the envelopment problem into a nonlinear programming problem with a convex objective function, which is then solved using techniques from nonlinear programming. Finally, we present simulation results to illustrate the effectiveness of our method for the hybrid problem.

Workpiece localization plays a vital role in automation of many important manufacturing processes, such as workpiece setup, refixturing and dimensional inspection. In this paper, we provide a unified treatment of three geometric algorithms for workpiece localization, and develop new techniques to make these local algorithms globally convergent. We also study and analyze, along with extensive simulation results, their performance with respect to convergence and computational efficiency. Finally, we present a method for analyzing reliability of localization solutions and give a lower bound on the number of measurement points needed for reliable recovering of Euclidean transformations.

The rapid proliferation of coordinate measuring machines (CMM) triggered the need for precise and rigorous formulations of each tolerance concept. In this paper, we employ the concept of configuration space of symmetric features to define each type of datum features and orientation tolerances. The establishment of datum features and orientation tolerances are formulated in an linear programming approach. Using properties of Lie groups and Lie algebra, a simple, unified and coordinate free algorithm for datum establishment and orientation tolerance is developed. The results of the algorithm comply to the definitions stipulated in the standard ANSI Y14.5M.

In this paper, we propose a unified control system architecture for multifingered manipulation (CoSAM/sup 2/). CoSAM/sup 2/ achieves simultaneously three objectives of multifingered manipulation: (a) Motion trajectory (velocity/force) tracking of a grasped object; (b) Improving the grasp configuration in the course of object manipulation; and (c) Optimizing grasping forces to enforce contact constraint and compensate for external object wrenches. CoSAM/sup 2/ is organized in a modular and hierarchic structure so that each module implements a specified function using inputs from its predecessors and a minimum number of sensory data signals. CoSAM/sup 2/ is also flexible in accommodating addition of new modules. Here, we give the details for the coordinated motion generation module and the grasping force generation module.

We design a fuzzy system to compensate the delays due to backlash nonlinearity. The fuzzy compensator is constructed from some common-sense rules. We consider the general case of the unknown backlash parameter and develop an adaptation algorithm to estimate the backlash parameter online. We prove that under certain conditions the fuzzy compensator with the adaptation algorithm guarantees that the backlash output converges to the desired trajectory. Simulation and hardware implementation results show that the fuzzy compensator is robust to the estimation errors in the backlash parameters. Application to an industrial CNC machine tool is described.

Accurate and efficient localization of symmetric features plays an important role in dimensional inspection of machined parts and machining of partially finished workpieces. We present a geometric theory for efficient and accurate localization of symmetric features. First, we show that the configuration space of a symmetric feature can be naturally identified with the homogeneous space SE/sub (3/)/G/sub o/ of the Euclidean group SE/sub (3/), where G/sub o/ is the symmetry group of the feature. Then, we explore the geometric structure of the homogeneous space and present a simple and unifying algorithm for symmetric localization. Finally, we give simulation results illustrating several unique features of the algorithm: 1) implementational simplicity; 2) robustness with respect to initial conditions; 3) high accuracy in computed results; and 4) computational efficiency.

We present a unified geometric theory for localization of three types of workpieces: 1) general three-dimensional (3D) workpieces where points from the finished surfaces fully constrain the rigid motions of the workpieces; 2) symmetric workpieces; 3) partially machined workpieces where points from the finished surfaces are inadequate to fully constrain the rigid motions of the workpieces. Applications of the study include workpiece setup, refixturing and dimensional inspections in a flexible manufacturing environment. First, we formulate the localization problem for a general 3D workpiece and study the mathematical properties of the underlying problem. We discuss an iterative approach for solving the general localization problem and show how different considerations in updating the Euclidean transformation lead to various geometric algorithms. Then, we extend the localization techniques to symmetric workpieces and partially machined workpieces and present a simple algorithm for each of the problems. Finally, we present simulation results showing convergence and robustness properties of the various geometric algorithms.

Workpiece localization, with novel applications such as workpiece setup, refixturing and dimensional inspections, is a problem of permanent importance in manufacturing. Using the popular least square formulation, several geometric algorithms have been developed for workpiece localization over the last few years. In this paper, we analyze and compare the performance of three localization algorithms based on the following criteria: (a) robustness with respect to variations in initial conditions; (b) accuracy of computed results; and (c) computational efficiency. We develop an approach for improving the robustness of the algorithms for workpieces with sculptured surfaces for which the region of convergence is typically small. Based on simulation results, we also discuss sensitivity of the algorithms with respect to the number of measurement points and give a lower bound on this number for recovering a Euclidean transformation with certain accuracy.

In this paper an efficient method for automatic probing and localisation of 3D workpiece arbitrarily fixed to the machine table of a five-axis milling machine is presented. First, by formulating localisation problem as minimizing a least-square question an explicit solution is obtained. Based upon this solution and sensitivity analysis, we present some guidelines and develop a CAD-based automatic probing strategy. By means of the knowledge about the approximate location of workpiece computed by 3D localisation algorithm as estimator, together with the CAD model of workpiece, we then generate online a new collision free probing trajectory to probe additional point on a neighbourhood of the previous sampling point. Utilizing the newly measurement point, we improve the Euclidean transformation which in turn is used together With the CAD model, to generate another collision free probing path to probe more points on the surfaces of workpiece. This process continuous until the workpiece is accurately located. Experimental results show that this algorithm overcomes the need of home surface identification process and is thus suitable for real-time implementation in manufacturing or inspection process.

A deadzone compensator is designed for industrial positioning systems using a fuzzy logic (FL) controller. The classification property of FL systems makes them a natural candidate for the rejection of errors induced by the deadzone, which has regions in which it behaves differently. A tuning algorithm is given for the FL parameters, so that the deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. The adaptive FL deadzone compensator is implemented on an actual industrial CNC machine tool to show its efficacy.

Presents an algebraic algorithm for workpiece localization. First, we formulate the problem as a least-square problem in the configuration space Q=SE(3)/spl times/R/sup 3n/, where SE(3) is the Euclidean group, and n is the number of measurement points to be matched by corresponding home surface points of the workpiece. Then, the authors use the geometric properties of the Euclidean group to compute for the critical points of the objective function. Doing so the authors derive an algebraic formula for the optimal Euclidean transformation in terms of the measurement points and the corresponding home surface points. The authors also give for each measurement point a system of two nonlinear equations from which the corresponding home surface point nearest to the measurement point can be solved. Finally, based on these analytic results the authors present an iterative algorithm for obtaining the complete solution of the least-square problem.

A three-fingered robotic hand manipulation system, employing three Motoman K-3S1 robots as its fingers, and a VME based multiprocessor system with the Vx-work real-time operating system as its control system, has been developed in the Robot Manipulation Laboratory of the Hong Kong University of Science and Technology for the study of dextrous manipulation. One of the major problems we encounter in this study is the determination of contact locations between fingertips and the object to be grasped/manipulated. We propose the use of measurement data supplied by a force/torque sensor mounted at the end of the fingertip for localization of contact. We first give a mathematical formulation of the problem. We incorporate gravitational effects in the model and show how to eliminate the biasing effect during real implementation. Then, we perform an error analysis of the computed results from which we can infer accuracy of the proposed approach. Finally, we give experimental results obtained using a Lord FT335x force/torque sensor mounted at the end of the fingertip. It is shown that force/torque based approach can yield results of good resolution compared with the tactile-based approach, and the former is also easier to implement with commercially available components.

The authors formulate the dynamic equations of a system consisting of a 3-degree-of-freedom Puma-like manipulator attached to a space platform (e.g. a space station or a satellite) as an NMP (nonholonomic motion planning) problem and discuss controllability of the system. They describe the application of a simple algorithm for obtaining approximate optimal solutions. They conclude with results of a simulation experiment.>

Nonholonomic motion planning (NMP) problems arise not only from the classical nonholonomic constraints, but also from symmetries and conservation laws of holonomic systems. In NMP problems an admissible configuration space path is constrained to a given nonholonomic distribution. Thus, NMP deals with the problem of (optimal) path finding subject to a nonholonomic distribution and possibly to additional holonomic constraints. The authors first study several representative NM systems and formulate the NMP problem. Variational principles are used to characterize optimal solutions to these problems. A simple algorithm solving an NMP problem is proposed, and simulation results are presented.>

A discussion is presented of the control of legged-robot body orientation in flight using the internal motion of the leg. The angular momentum constraint (nonholonomic) is used to recast the problem into a nonholonomic motion planning problem. Chow's theorem is then applied to verify that the system is controllable, and the concept of holonomy is introduced for constructing an optimal path. Finally, linearization control is used in the internal motion space to realize the planned path. An additional degree of control to dynamically balance a legged robot that runs is provided with this strategy.>

The motion of two rigid bodies under rolling constraint is considered. In particular, the following two problems are addressed: (1) given the geometry of the rigid bodies, determine the existence of an admissible path between two contact configurations; and (2) assuming that an admissible path exists, find such a path. First, the configuration space of contact is defined, and the differential equations governing the rolling constraint are derived. Then, a generalized version of Frobenius's theorem, known as Chow's theorem, for determining the existence of motion is applied. Finally, an algorithm is proposed that generates a desired path with one of the objects being flat. Potential applications of this study include adjusting grasp configurations of a multifingered robot hand without slipping, contour following without dissipation or wear by the end-effector of a manipulator, and wheeled mobile robotics.>

The authors formulate the dextrous manipulation problem for a robot hand. First, dextrous manipulation is decomposed into coordinated manipulation, rolling motion, sliding motion, and finger relocation. Then the authors develop motion constraints for each of the manipulation modes and show that for finger motions that satisfy these constraints there exists a well-defined lift to the total space that links two contact configurations. Of special note is the incorporation of nonholonomic as well as holonomic and unilateral as well as bilateral constraints in motion planning.>

Two problems in the study of multifingered robot hands are considered, namely grasp planning and the determination of coordinated control laws with point contact models. using the dual notions of grasp stability and manipulability, and a procedure previously developed for task modeling, the structure grasp quality measures are defined. These measures are then integrated to devise a grasp planning algorithm. Based on the assumption of point contact models, a computed-torque-like control algorithm is developed for the coordinated manipulation of a multifingered robot hand. This control algorithm, which takes into account both the dynamics of the object and the dynamics of the hand, is computationally effective and can be generalized to allow rolling motion of the object with respect to the fingertip.>

The problem of optimal grasping of an object by a multifingered robot hand is discussed. Using screw theory and elementary differential geometry, the concept of a grasp is axiomated and its stability characterized. Three quality measures for evaluating a grasp are then proposed. The last quality measure is task-oriented and needs the development of a procedure for modeling tasks as ellipsoids in the wrench space of the object. Numerical computations of these quality measures and the selection of an optimal grasp are addressed in detail. Several examples are given using these quality measures to show that they are consistent with measurements yielded by the authors' experiments on grasping.>

We discuss the problem of optimal grasping to an object by a multifingered robot hand. We axiomatize using screw theory and elementary differential geometry the concept of a grasp and characterize its stability. Three quality measures for evaluating a grasp are then proposed. The last quality measure is task oriented and needs the development of a procedure for modeling tasks as ellipsoids in the wrench space of the object. Numerical computations of these quality measures and the selection of an optimal grasp are addressed in detail. Several examples are given using these quality measures to show that they are consistent with human grasping experience.