In this article, we characterize the passivity of a class of haptic systems modeled as a simple sampled-data system. We guarantee passivity by ensuring that there is sufficient damping in the haptic interface. Previous work established a necessary and sufficient bound on damping, but the corresponding mathematical expressions were complicated, and the derivation was not completely rigorous. After providing a rigorous proof, we derive a more tractable expression. Using this improved expression, we establish passivity conditions for several classes of transfer functions representing virtual environments, including some special cases with time delay. The original results assumed that the operator can be modeled by a passive but otherwise arbitrary transfer function. This assumption is weakened to allow the operator model to have a shortage of passivity. This requires only a slight modification of the passivity bound.

Power hardware-in-the-loop (PHIL) simulation is a technique whereby actual power hardware is interfaced to a virtual surrounding system, simulated in real-time, through PHIL interfaces making use of power amplifiers and/or actuators. A number of seemingly disparate interface algorithms (IA) have been proposed in the literature for achieving the virtual coupling between the simulated and physical portions of the system, with each presenting different strengths and shortcomings. In this work, a framework based on an architecture for bilateral teleoperation systems is described, which is suitable for the formulation of linear PHIL IAs, encompassing the majority of the existing IAs proposed in the literature. Formulations of a number of existing PHIL IAs are given in the context of the described framework. Requirements for achieving transparency with the IAs are described, and several of the existing IAs are discussed in terms of the framework, adherence to the transparency requirements, and performance. As the architecture also lends itself to the development of flexible IA modules for real-time simulators, the implementation and application of an IA module reflecting this architecture is also described.

A local definition of fault tolerance, based on properties of the manipulator Jacobian, is used to generate the kinematics of seven degree-of-freedom (DOF) revolute joint manipulators. The measure of fault tolerance used is the smallest singular value over all possible Jacobians resulting from single locked joint failures. The canonical form for an optimal fault-tolerant Jacobian that maximizes this measure has been previously identified. It has also been known that it is not possible to generate a seven DOF revolute manipulator that corresponds to this theoretically optimal Jacobian. However, in this paper, it is shown how to generate physically realizable Jacobians that are very close to being optimal. It is further shown that there exist 7! different manipulators, from a single Jacobian, that have the same local fault tolerance properties. To evaluate the global properties of these different manipulators, a technique for computing six-dimensional fault-tolerant workspaces is presented. The size of these workspaces vary significantly among these 7! manipulators.

It is well known that anthropomorphic manipulators, such as the PA-10, are intolerant to a single locked joint failure of the elbow. This is because the elbow is the only joint that can change the distance between the spherical shoulder joint and the spherical wrist. In this work, it is shown how such arms can be made significantly more fault tolerant by a minor modification to the kinematic structure of the arm. We quantify the degree of fault tolerance to locked joint failures as the minimum of the smallest singular value of the resulting seven Jacobians over all possible single failures. The DH parameters for the modified arm are designed so that the corresponding fault tolerant properties are close to those of a robot with an optimally failure tolerant Jacobian. The fault tolerance of the designed robot is evaluated for two different classes of applications, i.e., point-to-point motions and specified end-effector trajectories.

The wave variable method allows for stable bilateral teleoperation in the presence of time delay. However, the appearance of transient oscillations, known as wave reflections, affect teleoperation performance when using the wave variable method. The frequency characteristics of these wave reflections have been previously considered to be primarily related to the time delay across the communication channel. In this paper we show that the frequency characteristics of wave reflections are also affected by changes to the mass of the teleoperated system. We propose a wave-variable-based controller that diminishes the effects of wave reflections as the slave dynamics changes during teleoperation. Simulation results using our proposed method is compared to the traditional wave variable method.

Kinematically redundant manipulators are inherently more robust to locked joint failures than non-redundant manipulators. However, if poorly designed, performance degradation may still occur in the presence of a single locked joint. This paper presents a technique for designing a desired operating workspace for a kinematically redundant manipulator that can be guaranteed after the occurrence of an arbitrary single locked joint failure. The existence of such a workspace, called a failure-tolerant workspace, will be guaranteed by imposing a suitable set of artificial joint limits prior to a failure. Conditions are presented that characterize end-effector locations within the failure-tolerant region. Based on these conditions, an algorithm for computing the failure-tolerant workspace is presented. The algorithm is based upon identifying the boundaries of the failure-tolerant workspace. Examples are presented to illustrate the application of the proposed algorithm to various manipulator design problems.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of local optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers the global analysis of seven-joint manipulators that have been designed to be locally optimal in terms of fault tolerance when used for six-dimensional tasks. An algorithm for calculating a six-dimensional volume that is composed of a three-dimensional positioning component and a three-dimensional orientation component is presented. Two example manipulators are then analyzed and compared, illustrating a wide degree of variability between their global fault tolerant properties. It is further shown that there are 7! = 5040 different such manipulator designs due to the number of permutations of the Jacobian matrix.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. In this work, the desired property is fault tolerance, defined as the post-failure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. A mathematical analysis based on the Gram matrix that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. It is shown that rearranging the columns of the Jacobian or multiplying one or more of the columns of the Jacobian by ±1 will not affect local fault tolerance; however, this will typically result in a very different manipulator. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are analyzed. This analysis shows that there is a large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian. It is especially surprising that major differences in global behavior occurs for manipulators that are identical in the working area.

This work presents a method for identifying all the kinematic designs of spatial positioning manipulators that are optimally fault tolerant in a local sense. We use a common definition of fault tolerance, i.e., the post-failure Jacobian possesses the largest possible minimum singular value over all possible single locked-joint failures. The large family of physical manipulators that can achieve this optimally failure tolerant configuration is then parameterized and categorized. We develop a general computational technique to evaluate the resulting manipulators in terms of their global kinematic properties, with an emphasis on failure tolerance. Several manipulators with a range of desirable kinematic properties are presented and analyzed, with a specific example of optimizing over a given class of manipulators that possess a specified kinematic constraint.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. It has been recently shown that multiple different physical robot kinematic designs can be obtained from (essentially) a single Jacobian that has desirable fault tolerant properties. Fault tolerance in this case is defined as the post-failure Jacobian possessing the largest possible minimum singular value over all possible locked-joint failures. In this work, a mathematical analysis that describes the number of possible planar robot designs for optimally fault-tolerant Jacobians is presented. Two examples, one that is optimal to a single joint failure and the second that is optimal to two joint failures, are discussed. The paper concludes by illustrating some of the large variability in the global kinematic properties of these designs, despite being generated from the same Jacobian.

Terrain classification is key to using terrain dependent control modes to improve performance of autonomous ground vehicles (AGVs). One of the most viable forms of terrain classification, reaction-based terrain classification, is subject to the problem of speed and load dependency, which requires collecting large data sets for algorithm training. The research presented here presents a method of interpolating point clouds called Singular Value Decomposition Interpolation or SVDI, which uses singular value decomposition, matrix logarithms and Catmull-Rom splines. The estimated point clouds can then substitute for empirical training data, thereby reducing the need to collect large data sets for algorithm training. Here, SVDI is applied to the problem of speed dependency using a mobile robot. Although it is seen that interpolated point clouds are not as effective as real data, interpolated point clouds are seen to be more effective than known point clouds that do not correspond to the desired vehicle speed. Therefore it is concluded that SVDI can effectively reduce the speed and load dependence of reaction-based terrain classification.

It is common practice to design a robot's kinematics from the desired properties that are locally specified by a manipulator Jacobian. For the case of optimality with respect to fault tolerance, one common definition is that the post-failure Jacobian possesses the largest possible minimum singular value over all possible locked-joint failures. This work considers a Jacobian that has been designed to be optimally fault tolerant for a simple spatial positioning manipulator. It is shown that despite the fact that the Jacobian is “unique”, up to column permutations and multiplications by ±1, there are a large family of physical manipulators that correspond to the optimal Jacobian. Two example manipulators are presented and analyzed. It is shown that there is a large degree of variability in the global kinematic properties of these designs, despite being generated from the same Jacobian.

Assuming that a 1D curve can be represented as a graph embedded in a 2D-space, the metrics of the eigenfunctions of the weighted graph-Laplacian and diffusion operator of that graph are then a representation of the shape of that curve with invariance to rotation, scale, and translation. The diffusion operator is said to preserve the local proximity between data points by constructing a representation for the underlying manifold by an approximation of the Laplace-Beltrami operator acting on the graph of this curve. This work examines 2D shape clustering problems using a spectral metric of the Laplace-Betrami eigenfunctions for shape analysis of closed curves. Results demonstrate that the spectral metrics allow for good class separation over multiple targets with noise.

Many appearance-based classification problems such as principal component analysis, linear discriminant analysis, and locally preserving projections involve computing the principal components (eigenspace) of a large set of images. Although the online expense associated with appearance-based techniques is small, the offline computational burden becomes prohibitive for practical applications. This paper presents a method to reduce the expense of computing the eigenspace decomposition of a set of images when variations in both illumination and pose are present. In particular, it is shown that the set of images of an object under a wide range of illumination conditions and a fixed pose can be significantly reduced by projecting these data onto a few low-frequency spherical harmonics, producing a set of "harmonic images." It is then shown that the dimensionality of the set of harmonic images at different poses can be further reduced by utilizing the fast Fourier transform. An eigenspace decomposition is then applied in the spectral domain at a much lower dimension, thereby significantly reducing the computational expense. An analysis is also provided, showing that the principal eigenimages computed assuming a single illumination source are capable of recovering a significant amount of information from images of objects when multiple illumination sources exist.

Parallel manipulators are widely used in industrial applications due to their rigid structures and ability to perform automated tasks at high speeds. However, because the links on a parallel manipulator are mechanically coupled, solving its kinematics and dynamics equations can be more difficult than for its serial counterpart. Nevertheless, the inverse kinematics and inverse dynamics models are a critical component of a manipulator's controller. Specifically, a more computationally simple formulation of the inverse kinematics and dynamics is necessary to achieve efficient and fast manipulator control. In this paper, both the inverse kinematics and dynamics equations for the Omega-3, a three degree-of-freedom (3-DOF) parallel manipulator, are developed. For the inverse kinematics problem, the concept of loop closure equations is used to simplify the analysis. The virtual work principle is used to create a numerically simple inverse dynamics model. Using the inverse kinematics and dynamics model, a trajectory tracking controller is implemented on the manipulator and the resulting experiments reveal good tracking behavior.

Eigendecomposition has been used to classify three-dimensional objects from two-dimensional images in a variety of computer vision and robotics applications. The biggest on-line computational expense associated with using eigendecomposition is the determination of the closest point on an image manifold embedded in a high-dimensional space. The dimensionality and complexity of the space is a result of the p principal eigenimages that are selected. Unfortunately, for some real-time applications, this search may be prohibitively expensive. This work presents a method to reduce the on-line expense associated with using eigendecomposition for pose estimation. The approach is based on selecting a linear combination of the principal eigenimages to design an eigenspace manifold having a desirable geometric structure that reduces the cost associated with classification.

Determining the pose of a three-dimensional object under unknown lighting conditions is a challenging problem. Eigenspace methods represent one computationally efficient method for doing illumination invariant pose estimation, and have been applied in a variety of application domains. Unfortunately, determining the appropriate eigenspace dimension, as well as the eigenspace itself, is computationally prohibitive for real-world applications. This paper presents a method to reduce this expense by using results from spectral theory. In particular, this paper shows that a set of images of an object under a wide range of illumination conditions and a fixed pose can be significantly reduced by projecting this data on to a few low-frequency spherical harmonics, producing a set of ¿harmonic images¿. It is then shown that the dimensionality of the set of harmonic images can be further reduced by utilizing the fast Fourier transform. An eigendecomposition is then applied in the spectral domain thus relieving the computational burden. Experimental results are presented to compare the proposed algorithm to the true eigendecomposition, as well as assess the computational savings.

Equiangular tight frames have applications in communications, signal processing, and coding theory. Previous work demonstrates that few real equiangular tight frames exist for most pairs (n,d), where the frame ¿n,dis a d × n matrix with d ¿ n. This work proposes a genetic algorithm as a solution to the frame design problem. Specifically, the problem of designing real equiangular tight frames by minimizing the subspace minor angle sum-squared error. Numerical experiments show that the proposed method is successful for pairs (n,d) with d less than nine.

A haptics investigation is conducted when human subjects have to deal with a bilateral teleoperation system with two levels of time delay (400 and 1,000 ms) and four types of scaling matrices that provide a passivity form of stabilization. The wave variable method was implemented to produce a controllable human-machine response. What is of interest is the resulting performance that occurs from such systems which remain passive but impacts the overall human tracking performance that can be achieved. The question addressed is how these imposed stability restrictions (via architecture constraints) may degrade human tracking performance?

An important problem in computer vision is to determine the orientation of a rigid body in an image. This can be accomplished by matching points or line segments that naturally appear on the object. Several elegant and computationally fast algorithms based on the singular value decomposition and quaternions have been introduced to solve this problem. In this article, the authors first examine the important special case of identifying the attitude of 2D objects and introduce a particularly elegant solution based on the mathematical structure of the complex plane. Motivated by this simple solution to the 2D case, a new derivation of the 3D case based on the polar decomposition is presented. This derivation is in many ways more natural than previous derivations, particularly when the model and data contain no noise.

Eigendecomposition represents one computationally efficient approach for dealing with object detection and pose estimation, as well as other vision-based problems, and has been applied to sets of correlated images for this purpose. The major drawback in using eigendecomposition is the off line computational expense incurred by computing the desired subspace. This off line expense increases drastically as the number of correlated images becomes large (which is the case when doing fully general 3-D pose estimation). Previous work has shown that for data correlated on S(1), Fourier analysis can help reduce the computational burden of this off line expense. This paper presents a method for extending this technique to data correlated on S(2) as well as SO3 by sampling the sphere appropriately. An algorithm is then developed for reducing the off line computational burden associated with computing the eigenspace by exploiting the spectral information of this spherical data set using spherical harmonics and Wigner-D functions. Experimental results are presented to compare the proposed algorithm to the true eigendecomposition, as well as assess the computational savings.

Unmanned ground vehicles (UGV's) commonly used in military applications must possess the capability to traverse various terrains that may largely affect the performance and controllability of the vehicle. A UGV that can autonomously perceive its terrain using navigational sensors can make necessary changes to its control strategy. The research presented uses the output of the induced vehicle's vibration measured by navigational sensors to classify the underlying terrain at multiple speeds. The classification algorithm incorporates Principal Component Analysis (PCA) for feature extraction and dimension reduction. The PCA transformation coefficients are then used to develop a manifold curve that uses these known coefficients to interpolate unknown coefficients of the terrains as the robot's speed changes. Experimental data is collected using two distinctly different unmanned ground vehicle platforms. Results demonstrate the performance of the method for classifying multi-differentiated terrains broadly classified as grass, asphalt, mud, and gravel.

The pose detection of three-dimensional (3-D) objects from two-dimensional (2-D) images is an important issue in computer vision and robotics applications. Specific examples include automated assembly, automated part inspection, robotic welding, and human robot interaction, as well as a host of others. Eigendecomposition is a common technique for dealing with this issue and has been applied to sets of correlated images for this purpose. Unfortunately, for the pose detection of 3-D objects, a very large number of correlated images must be captured from many different orientations. As a result, the eigendecomposition of this large set of images is very computationally expensive. In this work, we present a method for capturing images of objects from many locations by sampling S2appropriately. Using this spherical sampling pattern, the computational burden of computing the eigendecomposition can be reduced by using the spherical harmonic transform to "condense" information due to the correlation in S2. We propose a computationally efficient algorithm for approximating the eigendecomposition based on the spherical harmonic transform analysis. Experimental results are presented to compare and contrast the algorithm against the true eigendecomposition, as well as quantify the computational savings.

In this paper, the authors examine the problem of designing nominal manipulator Jacobians that are optimally fault tolerant to one or more joint failures. Optimality is defined here in terms of the worst-case relative manipulability index. While this approach is applicable to both serial and parallel mechanisms, it is especially applicable to parallel mechanisms with a limited workspace. It is shown that a previously derived inequality for the worst-case relative manipulability index is generally not achieved for fully spatial manipulators and that the concept of optimal fault tolerance to multiple failures is more subtle than previously indicated. Lastly, the authors identify the class of 8-DOF Gough--Stewart platforms that are optimally fault tolerant for up to two joint failures. Examples of optimally fault-tolerant 7- and 8-DOF mechanisms are presented.

In addition to possessing a number of other important properties, kinematically redundant manipulators are inherently more tolerant to locked-joint failures than non-redundant manipulators. However, a joint failure can still render a kinematically redundant manipulator useless if the manipulator is poorly designed or controlled. This paper presents a method for identifying a region of the workspace of a redundant manipulator for which task completion is guaranteed in the event of a locked-joint failure. The existence of such a region, called a failure-tolerant workspace, will be guaranteed by imposing a suitable set of artificial joint limits prior to a failure. Conditions are presented that characterize end-effector locations in this region. Based on these conditions, a method is presented that identifies the boundaries of the failure-tolerant workspace. Optimized failure-tolerant workspaces for a three degree-of-freedom planar robot are presented.

We establish robustness stability results for a specific type of artificial neural networks for associative memories under parameter perturbations and determine conditions that ensure the existence of global asymptotically stable equilibria of the perturbed neural system that are near the asymptotically stable equilibria of the original unperturbed neural network. The proposed stability analysis tool is the sliding mode control and it facilitates the analysis by considering only the nominal plant under the nonlinear nominal control, which annihilates the matched uncertainties.

In addition to possessing a number of other important properties, kinematically redundant manipulators are inherently more tolerant to locked-joint failures than non- redundant manipulators. However, a joint failure can still render a kinematically redundant manipulator useless if the manipulator is poorly designed or controlled. This paper focuses on the implementation issues involved in identifying a region of the workspace for which task completion is guaranteed in the event of a locked-joint failure for a general class of planar 3R manipulators. The existence of such a region, called a failure-tolerant workspace, will be guaranteed by imposing a suitable set of artificial joint limits prior to a failure. The authors have developed a graphical user interface (GUI) that computes all workspace boundaries of interest for the planar 3R manipulators. This GUI allows the user to explore different robot geometries, and adjust the artificial joint limits, in an attempt to gain further understanding of a manipulator's failure-tolerant workspace.

In this article, the authors examine the problem of designing nominal manipulator Jacobians that are optimally fault tolerant to one or more joint failures. In this work, optimality is defined in terms of the worst case relative manipulability index. While this approach is applicable to both serial and parallel mechanisms, it is especially applicable to parallel mechanisms with a limited workspace. It is shown that a previously derived inequality for the worst case relative manipulability index is generally not achieved for fully spatial manipulators and that the concept of optimal fault tolerance to multiple failures is more subtle than previously indicated. Lastly, the authors identify the class of eight degree-of-freedom Gough-Stewart platforms that are optimally fault tolerant for up to two locked joint failures. Examples of optimally fault tolerant seven and eight degree-of-freedom mechanisms are presented.

Time delay is a serious problem for bilateral teleoperation systems. Even a small time delay in a bilateral teleoperation system would generally degrade the system's performance and cause instability. An important approach that guarantees stability for any fixed time delay is the wave variable method. In this paper we present some recent material dealing with teleoperation systems using wave variables. In particular, we describe a wave variable scheme based on a family of scaling matrices for multiple degree-of-freedom bilateral teleoperation system. We include a derivation of a larger family of scaling matrices that guaranteed the system remains stable for a fixed time delay. A multiple degree-of-freedom bilateral teleoperation system using the new wave variable method is simulated using a SIMULINK model. In addition, the new derivation was implemented in hardware using an Immersion joystick and a C++ program

We establish robustness stability results for uncertain two-time scale neural networks under parameter perturbations and determine conditions that ensure the existence of asymptotically stable equilibria of the perturbed neural system. It is assumed that the system uncertainties are limited by the upper bounds of their norms. We derive a Lyapunov function for the coupled system and an upper bound for the fast time scale associated with the neural activity state.

Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition can become prohibitively expensive when dealing with very high-resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known a priori how this will affect the quality of the resulting eigendecomposition. The work presented here provides an analysis of how different resolution reduction techniques affect the eigendecomposition. A computationally efficient algorithm for calculating the eigendecomposition based on this analysis is proposed. Examples show that this algorithm performs well on arbitrary video sequences.

This work considers kinematic failure tolerance when obstacles are present in the environment. It addresses the issue of finding a collision-free path such that a redundant robot can successfully move from a start to a goal position and/or orientation in the workspace despite any single locked-joint failure at any time. An algorithm is presented that searches for a simply-connected, obstacle-free surface with no internal local minimum or maximum in the configuration space that guarantees the existence of a solution. The method discussed is based on the following assumptions: a robot is redundant relative to its task, only a single locked-joint failure occurs at any given time, the robot is capable of detecting a joint failure and immediately locks the failed joint, and the environment is static and known. The technique is illustrated on a seven degree-of-freedom commercially available redundant robot. Although developed and illustrated for a single degree of redundancy, it is possible to extend the algorithm to higher degrees of redundancy

Singular value decomposition (SVD) is a common technique that is performed on video sequences in a number of computer vision and robotics applications. The left singular vectors represent the eigenimages, while the right singular vectors represent the temporal properties of the video sequence. It is obvious that spatial reduction techniques affect the left singular vectors; however, the extent of their effect on the right singular vectors is not clear. Understanding how the right singular vectors are affected is important because many SVD algorithms rely on computing them as an intermediate step to computing the eigenimages. The work presented here quantifies the effects of different spatial resolution reduction techniques on the right singular vectors that are computed from those video sequences. Examples show that using random sampling for spatial resolution reduction rather than a low-pass filtering technique results in less perturbation of the temporal properties.

This work considers kinematic failure tolerance when obstacles are present hi the environment. An example is given using a fully spatial redundant robot, the seven degree-of-freedom Mitsubishi PA-10. This article addresses the issue of finding a collision-free path such that a redundant robot can successfully move from a start to a goal position and/or orientation in the workspace despite any single locked-joint failure at any time. An algorithm is presented that searches for a continuous obstacle-free monotonic surface in the configuration space that guarantees the existence of a solution. The method discussed is based on the following assumptions: a robot is redundant relative to its task, only a single locked-joint failure occurs at any given time, the robot is capable of detecting a joint failure and immediately locks the failed joint, and the environment is static and known.

Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition becomes prohibitively expensive when dealing with very high resolution images. Reducing the resolution of the images reduces the computational expense, it is not known how this affects the quality of the resulting eigendecomposition. The work presented here gives the theoretical background for quantifying the effects of varying the resolution of images on the eigendecomposition that is computed from those images. A computationally efficient algorithm for this eigendecomposition is proposed using derived analytical expressions. Examples show that this algorithm performs very well on arbitrary video sequences.

Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition can become prohibitively expensive when dealing with very high resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known a priori how this will affect the quality of the resulting eigendecomposition. The work presented here provides an analysis of how different resolution reduction techniques affect the eigendecomposition. A computationally efficient algorithm for calculating the eigendecomposition based on this analysis is proposed. Examples show that this algorithm performs very well on arbitrary video sequences.

This work considers the failure tolerant operation of a kinematically redundant manipulator in an environment containing obstacles. In particular, the article addresses the problem of planning a collision-free path for a manipulator operating in a static environment such that the manipulator can reach its desired goal despite a single locked-joint failure and the presence of obstacles in the environment. A method is presented that searches for a continuous obstacle-free space between the starting configuration and the desired final end-effector position, which is characterized in the joint space by the goal self-motion manifold. This method guarantees completion of critical tasks in the event of a single locked-joint failure in the presence of obstacles.

Achieving adequate force control is an important problem in the application of robotics technology to manufacturing tasks. One approach to this problem is the use of passive compliance. A number of methods have been proposed for designing a passive compliance mechanism with a prescribed spatial stiffness or compliance matrix using a parallel or serial connection of elastic devices. If the spatial stiffness or compliance matrix is isotropic, the constituent elastic devices are simple in the sense that they are strictly translational or rotational. Non-isotropic stiffness and compliance matrices require the use of elastic screw devices that couple translation and rotation. These screw devices are of a more complicated nature than the simple elastic devices that are sufficient for the isotropic case. In this article the authors demonstrate how these screw devices can be eliminated by using a hybrid connection of parallel and serial configurations consisting of only simple elastic devices. This method can be used to achieve any prescribed non-isotropic stiffness or compliance matrix.

Eigendecomposition is a common technique that is performed on sets of correlated images in a number of computer vision and robotics applications. Unfortunately, the computation of an eigendecomposition can become prohibitively expensive when dealing with very high resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known how this affects the quality of the resulting eigendecomposition. The work presented here proposes a framework for quantifying the effects of varying the resolution of images on the eigendecomposition that is computed from those images. Preliminary results show that an eigendecomposition from low-resolution images may be nearly as effective in some applications as those from high-resolution images.

A key result in the study of spatial stiffness matrices is Loncaric's normal form. When a spatial stiffness matrix is described in an appropriate coordinate frame, it will have a particularly simple structure. In this form, the 3/spl times/3 off-diagonal blocks of the stiffness matrix are diagonal. It has been shown that generically, a spatial stiffness matrix can be written in a normal form. For example, it is fairly well known that this is true for any positive definite spatial stiffness matrix. In this article, it is shown that any symmetric positive semi-definite matrix can be written in a normal form. Also, the conditions under which the spatial stiffness matrix can be diagonalized are identified. These results are used to design a compact parallel compliance mechanism with a prescribed positive semi-definite spatial stiffness matrix.

Eigendecomposition-based techniques are popular for a number of computer vision problems, e.g., object and pose detection, because they are purely appearance-based and they require few on-line computations. Unfortunately, they also typically require an unobstructed view of the object whose pose is being detected. The presence of occlusion precludes the use of the normalizations that are typically applied and significantly alters the appearance of the object under detection. This work presents an algorithm that is based on applying eigendecomposition to a quadtree representation of the image dataset used to describe the appearance of an object. This allows decisions concerning the pose of an object to be based on only those portions of the image in which the algorithm has determined that the object is not occluded. The accuracy and computational efficiency of the proposed approach is evaluated on sixteen different objects with up to 50% of the object being occluded.

There has been some recent interest in the problem of designing compliance mechanisms with a given spatial stiffness matrix. A key result that has proven useful in the design of such mechanisms is Loncaric's normal form. When a spatial stiffness matrix is described in an appropriate coordinate frame, it will have a particularly simple structure. In this form the 3/spl times/3 off-diagonal blocks of the stiffness matrix are diagonal. It has been shown that generically, a spatial stiffness matrix can be written in normal form. For example, it is fairly well known that this is possible for any positive definite spatial stiffness matrix. In this article, it is shown that any symmetric positive semi-definite matrix can be written in normal form. As an application this result is used to design a compact parallel compliance mechanism with a prescribed positive semi-definite spatial stiffness matrix.

This article presents a method for determining a minimal realization of an arbitrary spatial stiffness matrix K through the use of a mechanism constructed of a parallel connection of springs. Two types of springs are used: simple and complex. The term simple spring refers to a purely translational or purely rotational passive spring while a complex spring couples translational and rotational components. Any symmetric positive definite spatial stiffness matrix can be realized with a parallel connection of such springs. However, to reduce the compliance mechanism's complexity, it is desirable to minimize the number of complex springs. This article presents a method for determining minimal realizations for any symmetric positive definite or semi-definite spatial stiffness matrix. These realizations are minimal in the sense that they minimize both the number of complex springs and the total number of springs.

Presents a method for determining a minimal realization of an arbitrary spatial stiffness matrix K through the use of a mechanism constructed of a parallel connection of springs. The springs are of two types: simple and screw. The term simple spring refers to a purely translational or purely rotational passive spring, while a screw spring couples translational and rotational components. Any spatial stiffness matrix can be realized with a parallel connection of such springs. However, as the names suggest, simple springs are much easier to implement than screw springs. Thus, to reduce the compliance mechanism's complexity, it is desirable to minimize the number of screw springs. The article presents a method for determining minimal realizations for any symmetric positive definite or semidefinite spatial stiffness matrix. These realizations are minimal in the sense that they minimize both the number of screw springs and the total number of springs.

This article presents a method for determining a minimal realization of an arbitrarily specified stiffness dominated spatial impedance through the use of a mechanism constructed of passive springs. This mechanism consists of simple springs connected in parallel, where the term simple spring refers to a purely translational or purely rotational passive spring. Not every stiffness matrix K can be realized with a parallel connection of simple springs. The characterizing condition is that the zipper right 3/spl times/3 submatrix of K has zero trace. Using this condition, the author shows how one can always synthesize any realizable spatial stiffness matrix with r parallel simple springs where r is the rank of K. These results are also applicable to realizing a spatial damping matrix.

This article presents a method for determining a minimal realization of an arbitrarily specified stiffness dominated spatial impedance through the use of a mechanism constructed of passive springs. This mechanism consists of simple springs connected in parallel where the term simple spring refers to a purely translational or purely rotational passive spring. Not every stiffness matrix K can be realized with a parallel connection of simple springs. The characterizing condition is that the upper right 3/spl times/3 submatrix of K has zero trace. Using this condition, the author shows how one can always synthesize any realizable spatial stiffness matrix with r parallel simple springs, where r is the rank of K. These results are also applicable to realizing a spatial damping matrix.

When a manipulator suffers a joint failure, its performance can be significantly affected. If the failed joint is locked, the resulting manipulator Jacobian is given by the original Jacobian, except that the column associated with the failed joint is removed. The rank of the resulting Jacobian then determines if the manipulator still has the ability to perform arbitrary end-effector motions. Unfortunately, even at an operating configuration that has a relatively high manipulability index, a joint failure may still result in a singular Jacobian. This work examines the problem of determining the reduced manipulability of a manipulator after one or more joint failures. Configurations that result in a minimal reduction of the manipulability index for any set of joint failures are determined.

This paper examines the kinematics of robotic wrists by using the singular value decomposition (SVD) of the wrist Jacobian. Since the manipulator Jacobian of a wrist is relatively simple, it is possible to calculate the SVD in closed form via a simple matrix factorization. Once this has been accomplished, a variety of issues can be examined including kinematic singularities and the evaluation of the manipulability and dexterity measures. These results are then applied to robots with spherical wrists and a motion simulator.>

A kinematically redundant manipulator is a robotic system that has more than the minimum number of degrees of freedom that are required for a specified task. Due to this additional freedom, control strategies may yield solutions which are not repeatable in the sense that the manipulator may not return to its initial joint configuration for closed end effector paths. The authors present two methods for choosing repeatable control strategies which minimize their distance from a non-repeatable inverse with desirable properties. The first method minimizes the integral norm of the difference of the desired inverse and a repeatable inverse. While this is the more appropriate criterion, it results in a difficult optimization. The second method, which minimizes the distance of the null vectors associated with the desired and the repeatable inverses, is somewhat easier to implement. As an illustrative example the pseudoinverse is approximated in a region of the joint space using both techniques.>

Kinematically redundant manipulators, by definition, possess an infinite number of generalized inverse control strategies for solving the Jacobian equation. These control strategies are not, in general, repeatable in the sense that closed trajectories for the end-reflector do not result in closed trajectories in the joint space. The Lie bracket condition (LBC) can be used to check for the possibility of integral surfaces, also called stable surfaces, which define regions of repeatable behavior. However, the LBC is only a necessary condition. A necessary and sufficient condition for the existence of stable surfaces is used to illustrate that such surfaces are much rarer than previously thought. A technique for designing a repeatable control that is nearest, in an integral norm sense, to a desired optimal control is presented. The desired optimal control is allowed to take the form of any generalized inverse. An example is presented that illustrates the capability of designing repeatable controls that approximate the behavior of desired optimal inverses in selected regions of the workspace.>