Due to their stability and robustness properties, Stable Dynamical Systems (SDS) have received considerable attention as a means of representing motions in learning from demonstration tasks. Designing vector fields that fit complex trajectories while ensuring stability still remains a key challenge; although recent deep learning-based methods have shown substantial progress in this direction, their tendency to overfit to demonstration trajectories often leads to undesirable behaviors, particularly as tasks deviate from demonstrations. At a fundamental level, the only reliable way to address this lack of generalization is to provide supervision in out-of-demonstration regions. Focusing on two types of general behaviors, mimicking and contracting, we propose a Behavior-Controllable Stable Dynamics Model (BCSDM), a one-parameter family of SDS that allows users to adjust the system's overall behavior depending on user intent. We show how to extend BCSDM to accommodate demonstrations of multiple tasks, and also propose a Deep Operator Vector Field (DeepOVec) for memory-efficient encoding of multiple dynamical systems. Extensive experiments on tasks that involve mimicking or contracting behaviors demonstrate the advantages of BCSDMs over existing state-of-the-art SDS learning methods.

The performance of learning-based object detection algorithms, which attempt to both classify and locate objects within images, is determined largely by the quality of the annotated dataset used for training. Two types of labelling noises are prevalent: objects that are incorrectly classified (categorization noise) and inaccurate bounding boxes (localization noise); both noises typically occur together in large-scale datasets. In this paper we propose a distillation-based method to train object detectors that takes into account both categorization and localization noise. The key insight underpinning our method is that the early-learning phenomenon - in which models trained on noisy data with mixed clean and false labels tend to first fit to the clean data, and memorize the false labels later -- manifests earlier for localization noise than for categorization noise. We propose a method that uses models from the early-learning phase (before overfitting to noisy data occurs) as a teacher network. A plug-in module implementation compatible with general object detection architectures is developed, and its performance is validated against the state-of-the-art using PASCAL VOC, MS COCO and VinDr-CXR medical detection datasets.

When using an autoencoder to learn the low-dimensional manifold of high-dimensional data, it is crucial to find the latent representations that preserve the geometry of the data manifold. However, most existing studies assume a Euclidean nature for the high-dimensional data space, which is arbitrary and often does not precisely reflect the underlying semantic or domain-specific attributes of the data. In this paper, we propose a novel autoencoder regularization framework based on the premise that the geometry of the data manifold can often be better captured with a well-designed similarity graph associated with data points. Given such a graph, we utilize a Riemannian geometric distortion measure as a regularizer to preserve the geometry derived from the graph Laplacian and make it suitable for larger-scale autoencoder training. Through extensive experiments, we show that our method outperforms existing state-of-the-art geometry-preserving and graph-based autoencoders with respect to learning accurate latent structures that preserve the graph geometry, and is particularly effective in learning dynamics in the latent space. Code is available at https://github.com/JungbinLim/GGAE-public.

We present a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when the number of generation time steps is small. Similar to how IRL trains a policy based on the reward function learned from expert demonstrations, we train (or fine-tune) a diffusion model using the log probability density estimated from training data. Since we employ an energy-based model (EBM) to represent the log density, our approach boils down to the joint training of a diffusion model and an EBM. Our IRL formulation, named Diffusion by Maximum Entropy IRL (DxMI), is a minimax problem that reaches equilibrium when both models converge to the data distribution. The entropy maximization plays a key role in DxMI, facilitating the exploration of the diffusion model and ensuring the convergence of the EBM. We also propose Diffusion by Dynamic Programming (DxDP), a novel reinforcement learning algorithm for diffusion models, as a subroutine in DxMI. DxDP makes the diffusion model update in DxMI efficient by transforming the original problem into an optimal control formulation where value functions replace back-propagation in time. Our empirical studies show that diffusion models fine-tuned using DxMI can generate high-quality samples in as few as 4 and 10 steps. Additionally, DxMI enables the training of an EBM without MCMC, stabilizing EBM training dynamics and enhancing anomaly detection performance.

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias in standard kernel density estimates for density ratios, leading to improved estimates of prediction posteriors and information-theoretic measures. In the process, we shed light on some fundamental aspects of density estimation, particularly from the perspective of algorithms that employ KDEs as their main building blocks.

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point along a low-dimensional manifold that approximates the training dataset. Then, EBM is trained to maximize the probability of recovering the original data. The training involves the generation of negative samples via MCMC, as in conventional EBM training, but from a different distribution concentrated near the manifold. The resulting near-manifold negative samples are highly informative, reflecting relevant modes of variation in data. An energy function of MPDR effectively learns accurate boundaries of the training data distribution and excels at detecting out-of-distribution samples. Experimental results show that MPDR exhibits strong performance across various anomaly detection tasks involving diverse data types, such as images, vectors, and acoustic signals.

Grasping previously unseen objects for the first time, in which only partially occluded views of the object are available, remains a difficult challenge. Despite their recent successes, deep learning-based end-to-end methods remain impractical when training data and resources are limited and multiple grippers are used. Two-step methods that first identify the object shape and structure using deformable shape templates, then plan and execute the grasp, are free from those limitations, but also have difficulty with partially occluded objects. In this paper, we propose a two-step method that merges a richer set of shape primitives, the deformable superquadrics, with a deep learning network,DSQNet, that is trained to identify complete object shapes from partial point cloud data. Grasps are then generated that take into account the kinematic and structural properties of the gripper while exploiting the closed-form equations available for deformable superquadrics. A seven-dof robotic arm equipped with a parallel jaw gripper is used to conduct experiments involving a collection of household objects, achieving average grasp success rates of 93% (compared to 86% for existing methods), with object recognition times that are ten times faster. Code is available athttps://github.com/seungyeon-k/DSQNet-publicNote to Practitioners—This paper provides a comprehensive two-step method for grasping previously unseen objects, in which only partially occluded views of the object may be available. End-to-end deep learning-based methods typically require large amounts of training data, in the form of images of the objects taken from different angles and with different levels of occlusion, and grasping experiments that record the success and failure of each attempt; if a new gripper is used, more often than not the training data must be recollected and a new set of experiments performed. Two-step methods that first identify the object structure and shape using deformable shape templates, then plan the grasp based on knowledge of the object shape, are currently a more practical solution, but also have difficulty when only occluded views of the object are available. Our newly proposed two-step method takes advantage of a more flexible set of shape primitives, and also uses a supervised deep learning network to identify the object from occluded views. Our experimental results indicate improved grasp success rates against the state-of-the-art, with recognition rates that are up to ten times faster. Our method shows high recognition and grasping performance so is well applicable on most of the general household objects, but it cannot be directly applied to more diverse public 3D datasets since it requires some human-annotated segmentation labels. In future research, we will develop our deep learning network to automatically learn segmentation without human-annotated labels, allowing it to recognize more complex and diverse object shapes.

Recounts the career and contributions of Peter Luh.

Many problems in machine learning involve data sets in which each data point is a point cloud in $\mathbb{R}^D$. A growing number of applications require a means of measuring not only distances between point clouds, but also angles, volumes, derivatives, and other more advanced concepts. To formulate and quantify these concepts in a coordinate-invariant way, we develop a Riemannian geometric framework for point cloud data. By interpreting each point in a point cloud as a sample drawn from some given underlying probability density, the space of point cloud data can be given the structure of a statistical manifold – each point on this manifold represents a point cloud – with the Fisher information metric acting as a natural Riemannian metric. Two autoencoder applications of our framework are presented: (i) smoothly deforming one 3D object into another via interpolation between the two corresponding point clouds; (ii) learning an optimal set of latent space coordinates for point cloud data that best preserves angles and distances, and thus produces a more discriminative representation space. Experiments with large-scale standard benchmark point cloud data show greatly improved classification accuracy vis-á-vis existing methods. Code is available at https://github.com/seungyeon-k/SMF-public.

It has been observed that the generalization performance of neural networks correlates with the sharpness of their loss landscape. Dinh et al. (2017) have observed that existing formulations of sharpness measures fail to be invariant with respect to scaling and reparametrization. While some scale-invariant measures have recently been proposed, reparametrization-invariant measures are still lacking. Moreover, they often do not provide any theoretical insights into generalization performance nor lead to practical use to improve the performance. Based on an information geometric analysis of the neural network parameter space, in this paper we propose a reparametrization-invariant sharpness measure that captures the change in loss with respect to changes in the probability distribution modeled by neural networks, rather than with respect to changes in the parameter values. We reveal some theoretical connections of our measure to generalization performance. In particular, experiments confirm that using our measure as a regularizer in neural network training significantly improves performance.

Likelihood is a standard estimate for outlier detection. The specific role of the normalization constraint is to ensure that the out-of-distribution (OOD) regime has a small likelihood when samples are learned using maximum likelihood. Because autoencoders do not possess such a process of normalization, they often fail to recognize outliers even when they are obviously OOD. We propose the Normalized Autoencoder (NAE), a normalized probabilistic model constructed from an autoencoder. The probability density of NAE is defined using the reconstruction error of an autoencoder, which is differently defined in the conventional energy-based model. In our model, normalization is enforced by suppressing the reconstruction of negative samples, significantly improving the outlier detection performance. Our experimental results confirm the efficacy of NAE, both in detecting outliers and in generating in-distribution samples.

Vanilla autoencoders often produce manifolds that overfit to noisy training data, or have the wrong local connectivity and geometry. Autoencoder regularization techniques, e.g., the denoising autoencoder, have had some success in reducing overfitting, whereas recent graph-based methods that exploit local connectivity information provided by neighborhood graphs have had some success in mitigating local connectivity errors. Neither of these two approaches satisfactorily reduce both overfitting and connectivity errors; moreover, graph-based methods typically involve considerable preprocessing and tuning. To simultaneously address the two issues of overfitting and local connectivity, we propose a new graph-based autoencoder, the Neighborhood Reconstructing Autoencoder (NRAE). Unlike existing graph-based methods that attempt to encode the training data to some prescribed latent space distribution -- one consequence being that only the encoder is the object of the regularization -- NRAE merges local connectivity information contained in the neighborhood graphs with local quadratic approximations of the decoder function to formulate a new neighborhood reconstruction loss. Compared to existing graph-based methods, our new loss function is simple and easy to implement, and the resulting algorithm is scalable and computationally efficient; the only required preprocessing step is the construction of the neighborhood graph. Extensive experiments with standard datasets demonstrate that, compared to existing methods, NRAE improves both overfitting and local connectivity in the learned manifold, in some cases by significant margins. Code for NRAE is available at https://github.com/Gabe-YHLee/NRAE-public.

Abstract We present the iterative medial axis transform (IMAT), an iterative descent method that constructs a medial axis transform (MAT) for a sparse, noisy, oriented point cloud sampled from an object's boundary. We first establish the equivalence between the traditional definition of the MAT of an object, i.e., the set of centres and corresponding radii of all balls maximally inscribed inside the object, with an alternative characterization matching the boundary enclosing the union of the balls with the object boundary. Based on this boundary equivalence characterization, a new MAT algorithm is proposed, in which an error function that reflects the difference between the two boundaries is minimized while restricting the number of balls to within some a priori specified upper limit. An iterative descent method with guaranteed local convergence is developed for the minimization that is also amenable to parallelization. Both quantitative and qualitative analyses of diverse 2D and 3D objects demonstrate the noise robustness, shape fidelity, and representation efficiency of the resulting MAT.

For smart manufacturing, an automated robotic assembly system built upon an autoprogramming environment is necessary to reduce setup time and cost for robots that are engaged in frequent task reassignment. This article presents an approach to the autoprogramming of robotic assembly tasks with minimal human assistance. The approach integrates “robotic learning of assembly tasks from observation” and “robotic embodiment of learned assembly tasks in the form of skills.” In the former, robots observe human assembly operations to learn a sequence of assembly tasks, which is formalized into a human assembly script. The latter transforms the human assembly script into a robot assembly script in which a sequence of robot-executable assembly tasks are defined based on action planning supported by workspace modeling and simulated retargeting. The assembly tasks, in the form of the robot assembly script, are then implemented via pretrained robot skills. These skills aim to enable robots to execute difficult tasks that involve inherent uncertainties and variations. We validate the proposed approach by building a prototype of the automated robotic assembly system for a power breaker and an electronic set-top box. The results verify that the proposed automated robotic assembly system is not only feasible but also viable, as it is associated with a dramatic reduction in the human effort required for automating robotic assembly.

A robot's dynamic model depends on both the kinematic and mass-inertial parameters of a robot. Robot model identification therefore typically begins with kinematic identification; the mass-inertial parameters are then identified with the identified kinematic parameters used in the dynamic model. In this article we show that poorly identified kinematic parameters can lead to an uncorrectable bias in the dynamic model, leading to errors in the mass-inertial parameters that are many times that of kinematic parameter errors. We instead argue that a unified kinodynamic identification leads to more accurate identification of both the kinematic and mass-inertial parameters. A linearly weighted kinodynamic objective function is proposed, in which the weight can be interpreted from a maximum likelihood perspective as the relative accuracy of the kinematic sensors vis-à-vis the dynamic sensors. Recursive algorithms for computing exact analytic gradients of the kinodynamic objective function are newly derived, leading to robust and fast-converging identification algorithms. Extensive numerical and hardware experiments demonstrate the advantages of our unified kinodynamic identification procedure.

Recent work has shed light on the often unreliable performance of constrained least-squares estimation methods for robot mass-inertial parameter identification, particularly for high degree-of-freedom systems subject to noisy and incomplete measurements. Instead, differential geometric identification methods have proven to be significantly more accurate and robust. These methods account for the fact that the mass-inertial parameters reside in a curved Riemannian space, and allow perturbations in the mass-inertial properties to be measured in a coordinate-invariant manner. Yet, a continued drawback of existing geometric methods is that the corresponding optimization problems are inherently nonconvex, have numerous local minima, and are computationally highly intensive to solve. In this paper, we propose a convex formulation under the same coordinate-invariant Riemannian geometric framework that directly addresses these and other deficiencies of the geometric approach. Our convex formulation leads to a globally optimal solution, reduced computations, faster and more reliable convergence, and easy inclusion of additional convex constraints. The main idea behind our approach is an entropic divergence measure that allows for the convex regularization of the inertial parameter identification problem. Extensive experiments with the 3-DoF MIT Cheetah leg, the 7-DoF AMBIDEX tendon-driven arm, and a 16-link articulated human model show markedly improved robustness and generalizability vis-à-vis existing vector space methods while ensuring fast, guaranteed convergence to the global solution.

Existing adaptive robot control laws typically require an engineering choice of a constant adaptation gain matrix, which often involves repeated and time-consuming trial and error. Moreover, physical consistency of the estimated inertial parameters or the uniform positive definiteness of the estimated robot mass matrix cannot in general be guaranteed without nonsmooth corrections, e.g., projection to the boundary of the feasible parameter set. In this paper we present a natural adaptive control law that mitigates many of these difficulties, by exploiting the coordinate-invariant differential geometric structure of the space of physically consistent inertial parameters. Our approach provides a more generalizable and physically consistent adaptation law for the robot parameters without significant additional computations compared to existing methods. Simulation results showing markedly improved tracking error convergence over existing adaptive control laws are provided as validation.

Nearest-neighbor estimators for the Kullback-Leiber (KL) divergence that are asymptotically unbiased have recently been proposed and demonstrated in a number of applications. However, with a small number of samples, nonparametric methods typically suffer from large estimation bias due to the nonlocality of information derived from nearest-neighbor statistics. In this letter, we show that this estimation bias can be mitigated by modifying the metric function, and we propose a novel method for learning a locally optimal Mahalanobis distance function from parametric generative models of the underlying density distributions. Using both simulations and experiments on a variety of data sets, we demonstrate that this interplay between approximate generative models and nonparametric techniques can significantly improve the accuracy of nearest-neighbor-based estimation of the KL divergence.

Classical discriminant analysis attempts to discover a low-dimensional subspace where class label information is maximally preserved under projection. Canonical methods for estimating the subspace optimize an information-theoretic criterion that measures the separation between the class-conditional distributions. Unfortunately, direct optimization of the information-theoretic criteria is generally non-convex and intractable in high-dimensional spaces. In this work, we propose a novel, tractable algorithm for discriminant analysis that considers the class-conditional densities as interacting fluids in the high-dimensional embedding space. We use the Bhattacharyya criterion as a potential function that generates forces between the interacting fluids, and derive a computationally tractable method for finding the low-dimensional subspace that optimally constrains the resulting fluid flow. We show that this model properly reduces to the optimal solution for homoscedastic data as well as for heteroscedastic Gaussian distributions with equal means. We also extend this model to discover optimal filters for discriminating Gaussian processes and provide experimental results and comparisons on a number of datasets.

One of the challenges in applying convolutional neural networks to automated optical inspection is the lack of sufficient training data. In this paper we show that transfer learning can be successfully applied using image data from an entirely different domain. Focusing on optical inspection of texture images, we transfer weights from a source network trained with arbitrary unrelated images from the ImageNet dataset. Inspection experiments using our method show that one epoch of fine-tuning is sufficient to achieve 99.95% classification accuracy, while conventional transfer learning without fine-tuning achieves only 78.76%. An in-depth analysis of the effects of fine-tuning reveals that after fine-tuning, most of the unnecessary features encoded in the weights of the source network are deactivated, while meaningful features of the target data are amplified to capture new variations in the target domain.

This paper shows how metric learning can be used with Nadaraya-Watson (NW) kernel regression. Compared with standard approaches, such as bandwidth selection, we show how metric learning can significantly reduce the mean square error (MSE) in kernel regression, particularly for high-dimensional data. We propose a method for efficiently learning a good metric function based upon analyzing the performance of the NW estimator for Gaussian-distributed data. A key feature of our approach is that the NW estimator with a learned metric uses information from both the global and local structure of the training data. Theoretical and empirical results confirm that the learned metric can considerably reduce the bias and MSE for kernel regression even when the data are not confined to Gaussian.

Robotic instruments based on concentric tube technology are well suited to minimally invasive surgery since they are slender, can navigate inside small cavities and can reach around sensitive tissues by taking on shapes of varying curvature. Elastic instabilities can arise, however, when rotating one precurved tube inside another. In contrast to prior work that considered only tubes of piecewise constant precurvature, we allow precurvature to vary along the tube's arc length. Stability conditions for a planar tube pair are derived and used to formulate an optimal design problem. An analytic formulation of the optimal precurvature function is derived that achieves a desired tip orientation range while maximizing stability and respecting bending strain limits. This formulation also includes straight transmission segments at the proximal ends of the tubes. The result, confirmed by both numerical and physical experiment, enables designs with enhanced stability in comparison to designs of constant precurvature.

Although existing mechanics-based models of concentric tube robots have been experimentally demonstrated to approximate the actual kinematics, determining accurate estimates of model parameters remains difficult due to the complex relationship between the parameters and available measurements. Further, because the mechanics-based models neglect some phenomena like friction, nonlinear elasticity, and cross section deformation, it is also not clear if model error is due to model simplification or to parameter estimation errors. The parameters of the superelastic materials used in these robots can be slowly time-varying, necessitating periodic re-estimation. This paper proposes a method for estimating the mechanics-based model parameters using an extended Kalman filter as a step toward on-line parameter estimation. Our methodology is validated through both simulation and experiments.

Asymptotically unbiased nearest-neighbor estimators for K-L divergence have recently been proposed and demonstrated in a number of applications. With small sample sizes, however, these nonparametric methods typically suffer from high estimation bias due to the non-local statistics of empirical nearest-neighbor information. In this paper, we show that this non-local bias can be mitigated by changing the distance metric, and we propose a method for learning an optimal Mahalanobis-type metric based on global information provided by approximate parametric models of the underlying densities. In both simulations and experiments, we demonstrate that this interplay between parametric models and nonparametric estimation methods significantly improves the accuracy of the nearest-neighbor K-L divergence estimator.

Recent advances in robot technologies coupled with the growing economic competitiveness of robots in the workplace vis-a-vis human workers has spurred a renewed interest in robotic manufacturing. Major national research and development initiatives in robotics and manufacturing are underway in many countries, and several manufacturers have released commercial prototypes of dual-arm and other advanced robot systems intended for manufacturing applications. In this talk we survey this latest landscape, and try to identify the core technologies that are needed in order for robots to proliferate into new manufacturing settings beyond traditional applications like welding and structured assembly.

Summary form only given. We propose some basic elements of a robot motor control system that have direct counterparts in human motor control, based on the premise that optimality is the fundamental principle underlying both human and robot motor control. We first review some of the basic principles and hypotheses from human motor control, particularly those mechanisms for coping with the degrees of freedom problem, and the role of noise, feedback, and attention in motor control and learning. The state-of-the-art in robot motion optimization and optimal control is then examined, focusing on robust algorithms for generating optimal trajectories, and the use of dimension reduction techniques from machine learning. We then propose a new class of problems that are a direct consequence of some of the optimality paradigms from human motor control - these include kinematic feedback control laws for generating natural motions based on the minimum variance principle, and an LQR tracking control laws that minimize attention - and examine how their solutions can be used as primitives in a robot motor control system.

Robot control requires the rapid computation of robot shape, which for continuum robots typically involves solving complex mechanics-based models. Furthermore, shape computation based on kinematic input variables can be inaccurate due to parameter errors and model simplification. An alternate approach is to compute the shape in real-time from a set of sensors positioned along the length of the robot that provide measurements of local curvature, e.g., optical fiber Bragg gratings. This paper proposes a general framework for selecting the number and placement of such sensors with respect to arclength so as to compute the forward kinematic solution accurately and quickly. The approach is based on defining numerically-efficient shape reconstruction models parameterized by sensor number and location. Optimization techniques are used to find the sensor locations that minimize shape and tip error between a reconstruction model and a mechanics-based model. As a specific example, several reconstruction models are proposed and compared for concentric tube robots. These results indicate that the choice of reconstruction model as well as sensor placement can have a substantial effect on robot shape estimation.

Minimally invasive surgery can involve navigating inside small cavities or reaching around sensitive tissues. Robotic instruments based on concentric tube technology are well suited to these tasks since they are slender and can be designed to take on shapes of high and varying curvature along their length. One limitation of these robots, however, is that elastic instabilities can arise when rotating one pre-curved tube inside another. While prior work has considered tubes of piecewise-constant pre-curvature, this paper proposes varying tube pre-curvature as a function of arc length as a means to enhance stability. Stability conditions for a planar tube pair are derived and used to define an optimal design problem. This framework enables solving for pre-curvature functions that achieve a desired tip orientation range while maximizing stability and respecting bending strain limits. Analytical and numerical examples of the approach are provided.

Existing approaches to template-based visual tracking, in which the objective is to continuously estimate the spatial transformation parameters of an object template over video frames, have primarily been based on deterministic optimization, which as is well-known can result in convergence to local optima. To overcome this limitation of the deterministic optimization approach, in this paper we present a novel particle filtering approach to template-based visual tracking. We formulate the problem as a particle filtering problem on matrix Lie groups, specifically the three-dimensional Special Linear group SL(3) and the two-dimensional affine group Aff(2). Computational performance and robustness are enhanced through a number of features: (i) Gaussian importance functions on the groups are iteratively constructed via local linearization; (ii) the inverse formulation of the Jacobian calculation is used; (iii) template resizing is performed; and (iv) parent-child particles are developed and used. Extensive experimental results using challenging video sequences demonstrate the enhanced performance and robustness of our particle filtering-based approach to template-based visual tracking. We also show that our approach outperforms several state-of-the-art template-based visual tracking methods via experiments using the publicly available benchmark data set.

This paper examines the extent to which nonlinear dimension reduction techniques from machine learning can be exploited to determine dynamically optimal motions for high degree of freedom systems. Using the Gaussian Process Latent Variable Model (GPLVM) to learn the low-dimensional embedding, and a density function that provides a nonlinear mapping from the low-dimensional latent space to the full-dimensional pose space, we determine optimal motions by optimizing in the latent space, and mapping the optimal latent space trajectory to the pose space. The notion of variance tubes are developed to ensure that kinematic and other constraints are appropriately satisfied without sacrificing naturalness or richness of the motions. Case studies involving a 62-dof humanoid performing two sports motions—a golf swing and throwing a baseball—demonstrate that our method can be a highly effective and computationally efficient method for generating dynamically optimal motions.

We propose an online compensation scheme for rollover prevention of mobile manipulators based on the invariance control framework, and that makes use of recursively computed analytic gradients of the zero-moment point (ZMP) function. Our controller relaxes many of the assumptions made in existing approaches, and enhances robustness as well as effectiveness through the use of exact gradient information. Several case studies demonstrate the improved performance of our controller over existing rollover prevention schemes.

This paper sheds light on some fundamental connections of the diffusion decision making model of neuroscience and cognitive psychology with k-nearest neighbor classification. We show that conventional k-nearest neighbor classification can be viewed as a special problem of the diffusion decision model in the asymptotic situation. Applying the optimal strategy associated with the diffusion decision model, an adaptive rule is developed for determining appropriate values of k in k-nearest neighbor classification. Making use of the sequential probability ratio test (SPRT) and Bayesian analysis, we propose five different criteria for adaptively acquiring nearest neighbors. Experiments with both synthetic and real datasets demonstrate the effectivness of our classification criteria.

Motion planning for robots subject to holonomic constraints typically involves planning on constraint manifolds. In this paper we present the Tangent Space Rapidly Exploring Random Tree (TS-RRT) algorithm for planning on constraint manifolds. The key idea is to construct random trees not on the constraint manifold itself, but rather on tangent space approximations to the constraint manifold. Curvature-based methods are developed for constructing bounded tangent space approximations, as well as procedures for random node generation and bidirectional tree extension. Extensive numerical experiments suggest that the TS-RRT algorithm, despite its increased preprocessing and bookkeeping, outperforms existing constrained planning algorithms for a wide range of benchmark planning problems.

We propose a geometric method for visual tracking, in which the 2-D affine motion of a given object template is estimated in a video sequence by means of coordinate-invariant particle filtering on the 2-D affine group Aff(2). Tracking performance is further enhanced through a geometrically defined optimal importance function, obtained explicitly via Taylor expansion of a principal component analysis based measurement function on Aff(2). The efficiency of our approach to tracking is demonstrated via comparative experiments.

We propose a framework for online generation of efficient gaits on uneven terrain. A set of dynamically optimal leg swing motion primitives for irregular terrains is first constructed offline-this is done by generating minimum torque motions for various starting and ending ground configurations, extracting dominant principal components, and forming basis functions. Gaits are then generated online via linear interpolation of the principal component basis functions, using a distance metric on SO(3) to select the components. The algorithm is verified via dynamic simulations involving the STriDER, a three legged passive-walking robot. Our results show that gaits using only knee-actuated leg swings are able to traverse uneven terrain of bounded variation.

This paper investigates the extent to which biarticular actuation mechanisms-antagonistic actuation schemes with spring stiffness that extend over two joints, similar in function to biarticular muscles found in legged animals-improve the performance of jumping and other fast explosive robot movements. Robust gradient-based optimization algorithms that take into account the dynamic properties and various contact and actuator constraints of biarticular systems are developed. We then quantitatively evaluate the gains in jumping vis-a-vis conventional joint actuation schemes. We also examine the effects of biarticular link stiffness and link mass distributions on the jumping performance of the biarticular mechanism.

Recent studies have shown that the perception of natural movements-in the sense of being "humanlike"-depends on both joint and task space characteristics of the movement. This paper proposes a movement generation framework that merges two established techniques from gesture recognition and motion generation-hidden Markov models (HMMs) and principal components-into an efficient and reliable means of generating natural movements, which uniformly considers joint and task space characteristics. Given human motion data that are classified into several movement categories, for each category, the principal components extracted from the joint trajectories are used as basis elements. An HMM is, in turn, designed and trained for each movement class using the human task space motion data. Natural movements are generated as the optimal linear combination of principal components, which yields the highest probability for the trained HMM. Experimental case studies with a prototype humanoid robot demonstrate the various advantages of our proposed framework.

We address general filtering problems on the Euclidean group SE(3). We first generalize, to stochastic nonlinear systems evolving on SE(3)9 the particle filter of Liu and West (2001) for simultaneously estimating the state and covariance. The filter is constructed in a coordinate-invariant way, and explicitly takes into account the geometry of SE(3) and P(n)9 the space of symmetric positive definite matrices. An experimental case study involving vision-based robot end-effector pose estimation is also presented.

A widely used approach to image registration involves finding the general linear transformation that maximizes the mutual information between two images, with the transformation being rigid-body [i.e., belonging to SE(3)] or volume-preserving [i.e., belonging to SL(3)]. In this paper, we present coordinate-invariant, geometric versions of the Nelder-Mead optimization algorithm on the groups SL(3), SE(3), and their various subgroups, that are applicable to a wide class of image registration problems. Because the algorithms respect the geometric structure of the underlying groups, they are numerically more stable, and exhibit better convergence properties than existing local coordinate-based algorithms. Experimental results demonstrate the improved convergence properties of our geometric algorithms.

We show that a large class of active balancing problems for legged robots can be framed as a second-order cone programming (SOCP) problem, a convex optimization problem for which efficient and numerically robust algorithms exist. We describe this general SOCP balancing framework, show that several existing optimization-based balancing strategies reduce to special cases of this more general formulation, and investigate the computational performance of our SOCP algorithms through simulation studies involving a humanoid model.

This paper proposes a hidden Markov model (HMM) based approach to generate human-like movements for humanoid robots. Given human motion capture data for a class of movements, principal components are extracted for each class, and used as basis elements that in turn represent more general movements within each class. A HMM is also designed and trained for each movement class using the movement data. Humanoid movement is then generated by selecting the linear combination of basis elements that yields the highest probability for the trained HMM, subject to user-specified movement boundary conditions. The feasibility of our proposed method is demonstrated via case studies of various arm motions

We propose a framework for robot movement coordination and learning that combines elements of movement storage, dynamic models, and optimization, with the ultimate objective of efficiently generating natural, human-like motions. One of the novel features of our approach is that each movement primitive is represented and stored as a set of joint trajectory basis functions; these basis functions are extracted via a principal component analysis of human motion capture data. By representing arbitrary movements as a linear combination of these basis functions, and by taking advantage of recently developed geometric optimization algorithms for multibody systems, dynamics-based optimization can be more efficiently performed. Case studies with a diverse set of arm movements demonstrate the feasibility of our approach.

This paper describes Newton and quasi-Newton optimization algorithms for dynamics-based robot movement generation. The robots that we consider are modeled as rigid multibody systems containing multiple closed loops, active and passive joints, and redundant actuators and sensors. While one can, in principle, always derive in analytic form the equations of motion for such systems, the ensuing complexity, both numeric and symbolic, of the equations makes classical optimization-based movement-generation schemes impractical for all but the simplest of systems. In particular, numerically approximating the gradient and Hessian often leads to ill-conditioning and poor convergence behavior. We show in this paper that, by extending (to the general class of systems described above) a Lie theoretic formulation of the equations of motion originally developed for serial chains, it is possible to recursively evaluate the dynamic equations, the analytic gradient, and even the Hessian for a number of physically plausible objective functions. We show through several case studies that, with exact gradient and Hessian information, descent-based optimization methods can be forged into an effective and reliable tool for generating physically natural robot movements.

We present a noise sensitivity analysis of the differential optimal structure from motion problem. Given optical flow measurements for a set of feature points, we formulate a least squares cost function based on a more reasonable additive isotropic model of measurement noise, normalized by depth, that also leads to statistically consistent estimates of the shape and motion parameters. A cyclic coordinate descent algorithm is developed, and its performance examined through experiments.

With few exceptions, most previous approaches to the structure from motion problem have been based on a decoupling between shape and motion recovery, usually via discrete or differential versions of the epipolar constraint. This paper offers a differential geometric framework for the simultaneous shape and motion recovery problem. We first pose the simultaneous shape and motion recovery problem as one of fitting a parameterized differentiable manifold to a finite set of points in a larger ambient manifold endowed with a distance metric; this framework includes epipolar constraint-based approaches as a special case. Based on this framework, we then examine a class of least-squares and total least squares fitting criteria, and the physical implications of these criteria with respect to both noise models and choice of distance metric on the relevant manifolds. We show that these criteria lead to linear objective functions on SO(3) that admit analytic solutions. We also derive a set of cyclic coordinate descent (CCD) optimization algorithms and show that simple analytic formulas can be obtained for each iteration. Simulation results on accuracy and noise sensitivity of these algorithms are also presented.

We present the cyclic coordinate descent (CCD) algorithm for optimizing quadratic objective functions on SE(3), and apply it to a class of robot sensor calibration problems. Exploiting the fact that SE(3) is the semidirect product of SO(3) and /spl Rfr//sup 3/, we show that by cyclically optimizing between these two spaces, global convergence can be assured under a mild set of assumptions. The CCD algorithm is also invariant with respect to choice of fixed reference frame (i.e., left invariant, as required by the principle of objectivity). Examples from camera calibration confirm the simplicity, efficiency, and robustness of the CCD algorithm on SE(3), and its wide applicability to problems of practical interest in robotics.

This paper presents the Eclipse II, a new six-degrees-of-freedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse II is capable of x, y, and z axes translations, and a, b, and c axes rotations. In particular, it has the advantage of enabling continuous 360/spl deg/ spinning of the platform. We first describe the computational procedures for the forward and inverse kinematics of the Eclipse II. Next, the complete singularity analysis is presented for the two cases of end-effector singularity and actuator singularity. Finally, two additional actuators are added to the original mechanism to eliminate both types of singularity within the workspace.

This paper presents the Eclipse-II, a new six degree-of-freedom parallel mechanism, which can be used as a basis for general motion simulators. The Eclipse-II is capable of s, p and z-axis translations and n, b and c-axis rotations. In particular, it has the advantage of enabling continuous 360-degree spinning of the platform. The computational procedures for forward and inverse kinematics of the Eclipse-II are described. The complete singularity analysis is presented for the two cases of end-effector singularity and actuator singularity. Two additional actuators are added to the original mechanism to eliminate both types of singularity within the workspace.

This paper describes the design, construction, and performance analysis of the Eclipse, a redundantly actuated six-degree-of-freedom parallel mechanism intended for rapid machining. The Eclipse is a compact mechanism capable of performing five-face machining in a single setup while retaining the advantages of high stiffness and high accuracy characteristic of parallel mechanisms. We compare numerical and algebraic algorithms for the forward and inverse kinematics of a class of the Eclipse and formalize the notion of machine tool workspace. We also develop a simple method for the first-order elasto-kinematic analysis of parallel mechanisms that is amenable to design iterations. A complete characterization of the singularities of the Eclipse is given, and redundant actuation is proposed as a solution. The Eclipse case study demonstrates how diverse analytical tools originally developed in a robotics context can be synthesized into a practical design methodology for parallel mechanisms.

In this paper we describe a technique to generate realistic human movement, specifically platform dives, by solving an optimal control problem requiring little a priori information. Solving the optimal control problem reliably requires computing exact analytic gradients of the objective function, which is made possible by a hybrid recursive algorithm that calculates the dynamics of the system. This algorithm is formulated with Lie algebra techniques and matrix exponentials, resulting in equations that are easily differentiable. This quality is essential when solving ill-conditioned systems such as the diver. Also, the importance of initial conditions in light of the constant angular momentum constraint is discussed.

We present a methodology for the first-order stiffness and vibration analysis of general robotic systems including parallel mechanisms, based on geometric methods for kinematics and elasticity analysis. We exploit the uniformity and structure typically extant in parallel mechanisms to develop an accurate and computationally tractable method of stiffness and vibration analysis that is amenable 60 design iterations and optimization. By way of our analysis we formalize the notion of a mechanism's structural compliance matrix and derive an associated set of dynamic equations that model elastic effects without resorting to assumed modes or finite element models. Our methodology is illustrated with a case study involving the Eclipse, a novel six degree-of-freedom parallel mechanism designed for rapid machining.

We perform an in-depth analysis on the energy efficiency of a mobile robot employing a spherical type continuously variable transmission (S-CVT). The S-CVT permits the motor to operate in its most power-efficient regime of high-speed and low-torque, and allows for smooth operation of the mobile robot in all phases of forward, neutral, and reverse motion without the use of any brakes or clutches. Changes in steering direction are achieved by a novel pivoting device that enables the robot to rotate about its center. The current study takes into account features of the DC motors, the S-CVT, and the mobile robot dynamics to perform a comprehensive study on the overall system performance. We develop optimal control laws for both the reduction gear unit and S-CVT equipped mobile robots, and compare their energy efficiency through numerical studies. We then present numerical results that demonstrate the power savings possible front the use of the S-CVT mechanism over standard reduction gear units.

We develop a high-level, unified framework for the calibration of kinematic chains containing closed loops, passive joints, and an arbitrary number of actuators. Our approach rests on viewing the configuration space of the kinematic chain as an embedded sub-manifold of an ambient manifold, and formulating error measures based on the natural metric in this ambient manifold. Both joint encoder readings and end-effector position and orientation measurements can be uniformly included into this framework. Kinematic calibration is now formulated in a coordinate-invariant way (i.e., independent of the local representation of the forward and inverse kinematics, and of the loop closure constraints) as an optimal multidimensional surface-fitting problem to a given set of data points. We present algorithms that directly solve this nonlinear constrained optimization problem, in contrast to the existing coordinate-dependent approaches that are based on a linearization of the kinematic equations. Experimental and simulation results are presented for the Eclipse, a novel 6 DOF overactuated parallel mechanism designed for rapid machining applications.

The paper presents a class of Newton-type algorithms for the optimization of robot motions that take into account the dynamics. Using techniques from the theory of Lie groups and Lie algebras, the equations of motion of a rigid multibody system can be formulated in such a way that both the first and second derivatives of the dynamic equations with respect to arbitrary joint variables can be computed analytically. The result is that one can formulate the exact gradient and Hessian of an objective function involving the dynamics, and develop efficient second-order Newton-type optimization algorithms for generating optimal robot motions. The methodology is illustrated with a nontrivial example.

Introduces the design and analysis of a type of wheeled mobile robot that uses a spherical continuously variable transmission (S-CVT) element. The S-CVT is composed of a sphere, input and output discs, and variators, and power transmission is based on the friction force between the discs and the sphere. Use of the S-CVT allows for smooth operation of the mobile robot over all phases of forward, neutral, and reverse motion without the use of any brakes or clutches. The S-CVT also permits the motors to operate in their most power-efficient regimes. Motion in the plane, including pure rotation about its center is achieved by a novel pivoting device that eliminates the need for an actuated steering wheel, or an additional motor for differentiating the wheel velocities. We describe the conceptual principle behind our CVT-based mobile robot, and present a complete design and analysis of its capabilities based on a prototype currently under construction.

We present, using methods from the theory of Lie groups and Lie algebras, a coordinate-invariant formulation of the dynamics of open kinematic chains. We first re-formulate the recursive dynamics algorithm originally given by Park et al. (1995) for open chains in terms of standard linear operators on the Lie algebra of the special Euclidean group. Using straight forward algebraic manipulations, we then recast the resulting algorithm into a set of closed-form dynamic equations. We then reformulate Featherstone's (1987) articulated body inertia algorithm using this same geometric framework, and re-derive Rodriguez et al.'s (1991, 1992) square factorization of the mass matrix and its inverse. An efficient O(n) recursive algorithm for forward dynamics is also extracted from the inverse factorization. The resulting equations lead to a succinct high-level description of robot dynamics in both joint and operational space coordinates that minimizes symbolic complexity without sacrificing computational efficiency, and provides the basis for a dynamics formulation that does not require link reference frames in the description of the forward kinematics.

We present a differential geometric analysis of manipulability for holonomic multiple robot systems containing active and passive joints. Our analysis treats both redundant and nonredundant systems, including the case of redundant actuation, in a uniform manner. Dynamic characteristics of the robot system and manipulated object can also be naturally included by an appropriate choice of Riemannian metric. Our geometric framework also suggests a classification of kinematic singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for kinematic singularities that is independent of the choice of local coordinates used to describe the robot kinematics.

We provide a coordinate-free description of the dynamics for general open and closed chain mechanisms. The mechanism is assumed to consist of rigid links, and subject only to holonomic constraints. For an m degree of freedom mechanism consisting of k links, we define an appropriate mapping f from the m-dimensional configuration space M to N=SE(3)x...x SE(3) (k copies). By endowing N with the Riemannian metric defined by the link kinetic energies, the generalized inertia matrix can then be regarded as the pullback metric with respect to f, and the Coriolis terms given by the Christoffel symbols (of the first kind) with respect to the pullback metric. The coordinate-free description elucidates the basic differences in the various coordinate-based dynamics formulations that have been proposed in the literature, and provides a high-level view of robot dynamics that provides insight on how best to choose coordinates for computations.

In this article we develop a geometric formulation of operational space dynamics and control based on standard results from the theory of Lie groups and Lie algebras. Beginning with the coordinate invariant formulation of robot dynamics presented in Park et al. (1995), we extend these results to develop the equations of motion in operational space coordinates. The resulting equations can be expressed in a recursive fashion for applications requiring computationally efficient algorithms, or can be expressed in terms of simple matrix factors in which the robot parameters appear transparently for applications involving high-level manipulation of the equations of motion. Further, our formulation of operational space dynamics and control is not bound to any specific choice of local reference frames to carry out the dynamic analysis.

We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolated a given ordered set of rotation matrices at their specified knot times. In our approach we regard SO(3) as a Lie group with a bi-invariant Riemannian metriac, and apply the coordinate-invariant methods of Riemannian geometry. The resulting rotation curve is easy to compute, invariant with respect to fixed and moving reference frames, and also approximately minimizes angular acceleration.

This article addresses the problem of designing a robotic mechanism such that it end-effector frame comes closest to reaching a set of desired goal frames. We formulate this as an optimization problem, in which the kinematic parameters are selected to minimize the total distance between the end-effector frame and each goal frame. The objective function is defined in terms of a class of distance metrics on the rigid body motions that are invariant with respect to choice of fixed reference frame. A main contribution of this article is an explicit expression for the gradient of this objective function with respect to the kinematic parameters. With this analytic gradient, efficient optimization algorithms can now be developed for the design of general spatial mechanisms. Our design methodology is illustrated with an example involving the base positioning of two cooperating robots.

We present, using standard ideas from Lie groups and Riemannian geometry, a computationally efficient recursive algorithm for the inverse dynamics of an open-chain manipulator. Our algorithm bears close resemblance to Featherstone's (1991) approach, but is derived entirely from Lie theoretic concepts and definitions. Our geometric approach permits a high-level view of robot dynamics that emphasizes the coordinate-free aspects of the equations of motion while preserving the computational efficiency of recursive algorithms.>

The equation AX=XB on the Euclidean group arises in the problem of calibrating wrist-mounted robotic sensors. In this article the authors derive, using methods of Lie theory, a closed-form exact solution that can be visualized geometrically, and a closed-form least squares solution when A and B are measured in the presence of noise.>

The optimal kinematic design of spherical and spatial mechanisms for dexterity and workspace volume is addressed. The concept of dexterity used is based on the distortion measure of harmonic mappings which is defined in a natural, coordinate-invariant way. The author analyzes the performance of robotic wrists with respect to these kinematic criteria, and determines the optimal link lengths for a simple two-link, 3R spatial open chain. In addition, he compares the kinematic dexterity of three redundant 7R open chains.>

An investigation is conducted of the computational aspects of the product of exponentials (POE) formula, and an application to resolved-rate motion control of a six-degree-of-freedom manipulator based on a table lookup scheme is presented. It is shown that the computational requirements for evaluating the Jacobian are comparable to the more standard recursive methods discussed in the work of D. Orin and W. Schrader (1984). In addition to having intuitive geometric appeal, the POE formula adds some measure of device-independence to the kinematic equations of a manipulator.>