A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration

In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration (Osher et al., Multiscale Model. Simul. 4(2):460–489, 2005) based methods, such as linearized Bregman (Osher et al., Commun. Math. Sci. 8(1):93–111, 2010; Cai et al., SIAM J. Imag. Sci. 2(1):226–252, 2009, CAM Report 09-28, UCLA, March 2009; Yin, CAAM Report, Rice University, 2009) and split Bregman (Goldstein and Osher, SIAM J. Imag. Sci., 2, 2009). The convergence of the general algorithm framework is proved under mild assumptions. The applications to ℓ ¹ basis pursuit, TV−L ² minimization and matrix completion are demonstrated. Finally, the numerical examples show the algorithms proposed are easy to implement, efficient, stable and flexible enough to cover a wide variety of applications.     

Control-orientated dynamic modeling of forging manipulators with multi-closed kinematic chains

The dynamic model, particularly with reference to controller design, is an important issue in mechanical control and design. However, this model is often difficult to achieve in complex multi-closed-loop mechanisms, such as parallel mechanisms or forging manipulators. A new approach on the dynamic modeling of a multi closed-chain mechanism in a forging manipulator, which applies screw theory and the reduced system model, is proposed in this paper. The proposed method not only allows a straightforward calculation of actuator forces but also obtains the dynamic equation of the multi-closed-loop mechanism easily. The structure of dynamic model obtained is similar to that of standard Lagrangian formulations, which can extend vast control strategies developed for serial robots to complex multi-closed-loop mechanisms. A complex multi-closed-loop mechanism on a forging manipulator is decomposed into several serial mechanisms or simpler subsystems. The Lagrangian equations associated with each subsystem are directly derived from the local generalized coordinates of the sub-mechanisms. Jacobian matrices are used to interpret the differential equations of the sub-mechanisms into the generalized coordinate or the actuated pairs according to the D’Alembert principle. Hessian matrices are also applied to form a standard Lagrangian formulation. The screw theory is introduced to overcome the difficulties of solving transformed Jacobian matrices, thereby simplifying the calculation of the matrices. Computation difficulties of transformation matrices may decrease considerably by choosing suitable generalized coordinates instead of direct actuator variables. The full dynamics of the complex multi-closed-loop mechanism in a forging manipulator is presented. Simulations and experiments illustrate the reliability of the proposed method and the correctness of the dynamic model of the forging manipulator.     

New Architecture of a Hybrid Two-Fingered Micro–Nano Manipulator Hand: Optimization and Design

This paper presents the synthesis and design optimization of a compact and yet economical hybrid two-fingered micro–nano manipulator hand. The proposed manipulator hand consists of two series modules, i.e., an upper and lower modules. Each of them consists of a parallel kinematics chain with a glass pipette (1 mm diameter and 3–10 cm length) tapered to a very sharp end as an end-effector. It is driven by three piezo-electric actuated prismatic joints in each of the three legs of the parallel kinematics chain. Each leg of the kinematics chain has the prismatic–revolute–spherical joint structure. As the length of the glass pipette end-effector is decreased, the resolution and accuracy of the micro–nano manipulator hand is increased. For long lengths of the glass pipette end-effector, this manipulator works as a micro manipulator and for short lengths it works as a nano manipulator. A novel closed-form solution for the problem of inverse kinematics is obtained. Based on this solution, a simulation program has been developed to optimally choose the design parameters of each module so that the manipulator will have a maximum workspace volume. A computer-aided design model based on optimal parameters is built and investigated to check its workspace volume. Experimental work has been carried out for the purpose of calibration. Also, the system hardware setup of the hybrid two-fingered micro–nano manipulator hand and its practical Jacobian inverse matrices are presented.     

Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement

In the present research, application of the Natural Orthogonal Complement (NOC) for the dynamic analysis of a spherical parallel manipulator, referred to as SST, is presented. Both inverse and direct dynamics are considered. The NOC and the SST fully parallel robot are explained. To drive the NOC for the SST manipulator, constraints between joint variables are written using the transformation matrices obtained from three different branches of the robot. The Newton–Euler formulation is used to model the dynamics of each individual body, including moving platform and legs of the manipulator. D’Alembert’s principle is applied and Newton–Euler dynamical equations free from non-working generalized constraint forces are obtained. Finally two examples, one for direct and one for inverse dynamics are presented. The correctness and accuracy of the obtained solution are verified by comparing with the solution of the virtual work method as well as commercial multi-body dynamics software.     

Predictive simulation of human walking transitions using an optimization formulation

A general optimization formulation for transition walking prediction using 3D skeletal model is presented. The formulation is based on a previously presented one-step walking formulation (Xiang et al., Int J Numer Methods Eng 79:667–695, 2009b). Two basic transitions are studied: walk-to-stand and slow-to-fast walk. The slow-to-fast transition is used to connect slow walk to fast walk by using a step-to-step transition formulation. In addition, the speed effects on the walk-to-stand motion are investigated. The joint torques and ground reaction forces (GRF) are recovered and analyzed from the simulation. For slow-to-fast walk transition, the predicted ground reaction forces in step transition is even larger than that of the fast walk. The model shows good correlation with the experimental data for the lower extremities except for the standing ankle profile. The optimal solution of transition simulation is obtained in a few minutes by using predictive dynamics method.     

Dynamics and Coupling Actuation of Elastic Underactuated Manipulators

This paper investigates the constraint and coupling characteristics of underactuated manipulators by proposing an elastic model of the manipulator and examining the second order constraint equation. A dynamic model and a coupling constraint equation are developed from a Jacobian matrix and the Newton‐Euler formulation. The inertia matrix and the Christoffel tensor are analyzed and decomposed into the part concerning actuated joints and the part concerning passive joints. This decomposition is further extended to the dynamic coupling equation and generates an actuation coupling matrix and a dynamic coupling tensor. Two new dynamic coupling indices are hence identified. One is related to an actuation input and the other is related to centrifugal and Coriolis forces. The former reveals the dynamic coupling between the input and the acceleration of passive joints and gives the actuation effect on the passive joints. The latter reveals the dynamic coupling between the centrifugal and Coriolis forces and the acceleration of passive joints and provides the centrifugal and Coriolis effect on the acceleration of passive joints. The study reveals the coupling characteristics of an underactuated manipulator. This is then demonstrated in a three‐link manipulator and extended to a serial manipulator with passive prismatic joint. © 2003 Wiley Periodicals, Inc.     

Dynamic Feedback Control of XYnR̄ Planar Robots with n Rotational Passive Joints

We consider the problem of trajectory planning and control for an XYnR? Planar robot with the first two joints (rotational or prismatic) actuated and n rotational passive joints, moving both in the presence and the absence of gravity. Under the assumption that each passive link is attached at the center of percussion of the previous passive link, dynamics of the system can be expressed through the behavior of n special points of the plane. These points are called link‐related acceleration points (LRAP) since their instantaneous acceleration is oriented as the axis of the related passive links. Moreover, LRAP dynamics present a backward recursive form which can be exploited to recursively design a dynamic feedback that completely linearizes the system equations. We use this approach to solve trajectory planning and tracking problems and report simulation results obtained for an RR2R? robot having the first two rotational joints actuated. © 2003 Wiley Periodicals, Inc.     

A comparative study of existing metrics for 3D-mesh segmentation evaluation

In this paper, we present an extensive experimental comparison of existing similarity metrics addressing the quality assessment problem of mesh segmentation. We introduce a new metric, named the 3D Normalized Probabilistic Rand Index (3D-NPRI), which outperforms the others in terms of properties and discriminative power. This comparative study includes a subjective experiment with human observers and is based on a corpus of manually segmented models. This corpus is an improved version of our previous one (Benhabiles et al. in IEEE International Conference on Shape Modeling and Application (SMI), 2009). It is composed of a set of 3D-mesh models grouped in different classes associated with several manual ground-truth segmentations. Finally the 3D-NPRI is applied to evaluate six recent segmentation algorithms using our corpus and the Chen et al.’s (ACM Trans. Graph. (SIGGRAPH), 28(3), 2009) corpus.     

A note on double splittings of different monotone matrices

Comparison theorems between the spectral radii of different matrices are a useful tool for judging the efficiency of preconditioners. For single splittings of different monotone matrices, Elsner et al. (Linear Algebra Appl. 363:65–80, 2003) gave out comparison theorems for spectral radii. For double splittings, some convergence and comparison theorems of a monotone matrix are presented by Shen et al. (Comput. Math. Appl. 51:1751–1760, 2006). In this note we give the comparison theorem for the spectral radii of matrices arising from double splittings of different monotone matrices.     

A general force/torque relationship and kinematic representation for flexible link manipulators

A technique to determine the relationship between the generalized joint torque and the generalized force exerted by the end-effector of a flexible link manipulator on the environment is presented. First, a systematic technique which accounts for the links' bending and torsion is used to determine the kinematic equations of the manipulator. A procedure to determine a “pseudo” Jacobian matrix which accounts for the links' flexibility is then developed. In the determination of the pseudo Jacobian matrix, partial derivatives are not used, thus reducing inaccuracies resulting from approximating the bending and torsion of the links. Using the principle of virtual work, a force and torque relationship between the joints and end-effector is obtained. To demonstrate the validity of the technique presented, computer simulations of the resulting force/torque relationship are compared to results obtained experimentally.     

A note on the alternating group network

The class of alternating group networks was introduced in the late 1990’s as an alternative to the alternating group graphs as interconnection networks. Recently, additional properties for the alternating group networks have been published. In particular, Zhou et al., J. Supercomput (2009), doi:, was published very recently in this journal. We show that this so-called new interconnection topology is in fact isomorphic to the (n,n−2)-star, a member of the well-known (n,k)-stars, 1≤k≤n−1, a class of popular networks proposed earlier for which a large amount of work have already been done. Specifically, the problem in Zhou et al., J. Supercomput (2009), doi:, was addressed in Lin and Duh, Inf. Sci. 178(3), 788–801, 2008, when k = n−2.     

The effects of scent and game play experience on memory of a virtual environment

Scent has been well documented as having significant effects on emotion (Alaoui-Ismaili in Physiol Behav 62(4):713–720, 1997; Herz et al. in Motiv Emot 28(4):363–383, 2004), learning (Smith et al. in Percept Mot Skills 74(2):339–343, 1992; Morgan in Percept Mot Skills 83(3)(2):1227–1234, 1996), memory (Herz in Am J Psychol 110(4):489–505, 1997) and task performance (Barker et al. in Percept Mot Skills 97(3)(1):1007–1010, 2003). This paper describes an experiment in which environmentally appropriate scent was presented as an additional sensory modality consistent with other aspects of a virtual environment called DarkCon. Subjects’ game play habits were recorded as an additional factor for analysis. Subjects were randomly assigned to receive scent during the VE, and/or afterward during a task of recall of the environment. It was hypothesized that scent presentation during the VE would significantly improve recall, and that subjects who were presented with scent during the recall task, in addition to experiencing the scented VE, would perform the best on the recall task. Skin-conductance was a significant predictor of recall, over and above experimental groups. Finally, it was hypothesized that subjects’ game play habits would affect both their behavior in and recall of the environment. Results are encouraging to the use of scent in virtual environments, and directions for future research are discussed. The project described herein has been sponsored by the US Army Research, Development, and Engineering Command (RDECOM). Statements and opinions expressed do not necessarily reflect the position or the policy of the US Government; no official endorsement should be inferred.     

Using Biologically Inspired Features for Face Processing

In this paper, we show that a new set of visual features, derived from a feed-forward model of the primate visual object recognition pathway proposed by Riesenhuber and Poggio (R&P Model) (Nature Neurosci. 2(11):1019–1025, 1999) is capable of matching the performance of some of the best current representations for face identification and facial expression recognition. Previous work has shown that the Riesenhuber and Poggio Model features can achieve a high level of performance on object recognition tasks (Serre, T., et al. in IEEE Comput. Vis. Pattern Recognit. 2:994–1000, 2005). Here we modify the R&P model in order to create a new set of features useful for face identification and expression recognition. Results from tests on the FERET, ORL and AR datasets show that these features are capable of matching and sometimes outperforming other top visual features such as local binary patterns (Ahonen, T., et al. in 8th European Conference on Computer Vision, pp. 469–481, 2004) and histogram of gradient features (Dalal, N., Triggs, B. in International Conference on Computer Vision & Pattern Recognition, pp. 886–893, 2005). Having a model based on shared lower level features, and face and object recognition specific higher level features, is consistent with findings from electrophysiology and functional magnetic resonance imaging experiments. Thus, our model begins to address the complete recognition problem in a biologically plausible way.     

Dynamics Analysis of Some Limited-Degree-of-Freedom Parallel Manipulators with n UPS Active Legs and a Passive Constraining Leg

This paper presents a methodology for the unified analysis of the dynamics of some parallel manipulators (PMs) with n UPS-type active legs and a passive constraining leg. First, some formulae are derived for solving linear/angular velocity of active and constraining legs at their mass center, linear/angular accelerations of active and constraining legs at their mass center, and Jacobian matrices of active and constraining legs. Second, based on the principle of virtual work and Jacobian matrices of active and constraining legs, the inertia wrench and gravity of active/constraining legs and the friction of the joints in a PM are mapped into a part of the dynamic workload. Third, the general formulae are derived for solving the dynamic workload and the dynamic active forces/constrained wrench. Finally, the procedure is illustrated by means of a PM with 4 UPS active legs and one passive constraining leg.     

Dynamic modeling and base inertial parameters determination of a 2-DOF spherical parallel mechanism

This paper deals with the dynamic modeling and base inertial parameter determination of a general 5R 2-degree-of-freedom spherical parallel manipulator. By using a new geometric approach, inverse and forward kinematic problem are transformed to the problem of determining the intersection of two cones with common vertex. Compared to other proposed methods, this approach yields more compact and closed-form solutions. The instantaneous kinematic and acceleration problem is solved via employing the screw theory. The dynamic model is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. In order to verify the proposed methods and equations, a case study is performed, in which an orthogonal 2-DOF spherical parallel manipulator, named TezGoz, is considered. Performed simulations and comparisons with a SimMechanics model show the correctness of the derived equations. Furthermore, a reduced dynamic model is obtained by determining the base inertial parameters. To do so, first the dynamic model is rewritten in a linear matrix form with respect to the inertial parameters of the mechanism, then parameters are grouped to obtain a set of independent base parameters, reducing the number of inertial parameters from 40 to 19. As a result, while maintaining the accuracy, the computational time is reduced to 63% of that of the original dynamic model. Finally, to calibrate the dynamic model, an experimental dynamic identification is performed.     

Dynamic formulation and performance evaluation of the redundant parallel manipulator

The dynamic formulation and performance evaluation of the redundant parallel manipulator are presented in this paper. By means of the principle of virtual work and the concept of link Jacobian matrices, the inverse dynamic model of the redundant parallel manipulator is set up. It consists of six linear consistent equations with eight unknown quantities. Then, the optimum solution of the actuating torques is achieved by employing the Moore-Penrose inverse matrix. It is with minimum norm and least quadratic sum among the possible actuating torque vectors. A series of new dynamic performance indices with obvious physical meanings have been proposed in the paper. By decoupling the inverse dynamics in the exhaustive way, a novel dynamic performance index combining the acceleration, velocity and gravity terms of the dynamic equations has been presented to evaluate the dynamic characteristic of the redundant parallel manipulator. With the index, it is possible to control the performance in the different direction. The index has been applied to the dynamic characteristic evaluation of the redundant parallel manipulator in the simulation. It is general and can be used for the dynamic performance evaluation of other types of parallel manipulators.     

欠驱动冗余度空间机器人优化控制

欠驱动控制是空间技术中容错技术的重要方面.本文研究了被动关节中有制动器的欠驱动冗余度空间机器人系统的运动优化控制问题.从系统动力学方程出发,分析了欠驱动冗余度空间机器人的优化能力和控制方法;给出了主、被动关节间的耦合度指标;提出了欠驱动冗余度空间机器人系统的“虚拟模型引导控制”方法,在这种方法中采用与欠驱动机器人机构等价的全驱动机器人作为模型来规划机器人的运动,使欠驱动系统在关节空间中逼近给出的规划轨迹,实现了机器人末端运动的连续轨迹运动优化控制;通过末关节为被动关节的平面三连杆机器人进行了仿真,仿真的结果证明了提出算法的有效性.     

A Kane’s based algorithm for closed-form dynamic analysis of a new design of a 3RSS-S spherical parallel manipulator

This paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a new design of a fully spherical robot that is called a 3(RSS)-S parallel manipulator with real co-axial actuated shafts. The proposed robot can completely rotate about a vertical axis and can be used in celestial orientation and rehabilitation applications. After describing the robot and its inverse position, velocity and acceleration analysis is performed. Next, based on Kane’s method, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated.

     

The Complexity of Counting Eulerian Tours in?4-regular Graphs

We investigate the complexity of counting Eulerian tours (#ET) and its variations from two perspectives—the complexity of exact counting and the complexity w.r.t. approximation-preserving reductions (AP-reductions, Dyer et al., Algorithmica 38(3):471–500, 2004). We prove that #ET is #P-complete even for planar 4-regular graphs.     

Kinematic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the kinematic and Jacobian analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of the next generation of giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at the macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. Furthermore, the Jacobian matrices of the manipulator at the macro and micro level are derived, and a thorough singularity and sensitivity analysis of the system is presented. The kinematic and Jacobian analysis of the macro–micro structure is extremely important to optimally design the geometry and characteristics of the LAR structure. The optimal location of the base and moving platform attachment points in both macro and micro manipulators, singularity avoidance of the system in nominal and extreme maneuvers, and geometries that result in high dexterity measures in the design are among the few characteristics that can be further investigated from the results reported in this paper. Furthermore, the availability of the extra degrees of freedom in a macro–micro structure can result in higher dexterity provided that this redundancy is properly utilized. In this paper, this redundancy is used to generate an optimal trajectory for the macro–micro manipulator, in which the Jacobian matrices derived in this analysis are used in a quadratic programming approach to minimize performance indices like minimal micro manipulator motion or singularity avoidance criterion.