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.

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.

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.

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 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.

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.

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.

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.