Singularity Analysis of Lower Mobility Parallel Manipulators Using Grassmann–Cayley Algebra

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower mobility parallel manipulators and parallel manipulators, of which some legs have no spherical joint, are such manipulators. The geometric conditions associated with the dependency of six PlUumlcker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra (GCA). Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.     

Force Sensing Using Kalman Filtering Techniques for Robot Compliant Motion Control

Robot motion can be classified into free and contact motion. In practical tasks, however, the motion may transit from free motion to contact motion and vice versa. In such tasks, a position controller is designed in free motion. A compensator is then added in the force feedback loop to help the system reach the desired target impedance when the end-effector is in contact with the environment. To obtain accurate contact force, a Kalman filter is used to extract contact force from the wrist force sensor signal which contains inertial force of the end-effector also.     

Suboptimal Control of Rigid Body Motion with a Quadratic Cost

In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.     

Lie Algebra and System Identification Techniques for 3D Rigid Motion Estimation and Monocular Tracking

This paper addresses the parameters’ estimation of 2D and 3D transformations. For the estimation we present a method based on system identification theory, we named it the “A-method”. The transformations are considered as elements of the Lie group GL(n) or one of its subgroups. We represent the transformations in terms of their Lie Algebra elements. The Lie algebra approach assures to follow the shortest path or geodesic in the involved Lie group. To prove the potencial of our method, two experiments are presented. The first one is a monocular estimation of 3D rigid motion of an object in the visual space. With this aim, the six parameters of the rigid motion are estimated based on measurements of the six parameters of the affine transformation in the image. Secondly, we present the estimation of the affine or projective transformations involved in monocular region tracking. Jaime Ortegón-Aguilar received his degree in computer sciences at the Universidad Autonoma de Yucatan in Merida, Mexico in 2000. He earned his M.Sc. degree at the Cinvestav in Guadalajara, Mexico in 2002. He received his PhD degree from Cinvestav in 2006. His research interests include image processing, computer vision, robotics and applications of geometric algebra. Eduardo Jose Bayro-Corrochano gained his Ph.D. in Cognitive Computer Science in 1993 from the University of Wales at Cardiff. From 1995 to 1999 he has been Researcher and Lecturer at the Institute for Computer Science, Christian Albrechts University, Kiel, Germany, working on applications of geometric Clifford algebra to cognitive systems. At present is a full professor at CINVESTAV Unidad Guadalajara, México, Department of Electrical Engineering and Computer Science. His current research interest focuses on geometric methods for artificial perception and action systems. It includes geometric neural networks, visually guided robotics, humanoids, color image processing, Lie bivector algebras for early vision and robot maneuvering. He developed the quaternion wavelet transform for quaternion multi-resolution analysis using the phase concept. He is associate editor of Robotics and Journal of Advanced Robotic Systems and member of the editorial board of Journal of Pattern Recognition, Journal of Mathematical Imaging and Vision, Iberoamerican Journal of Computer and Systems and Journal of Theoretical and Numerical Approximation. He is editor and author of the following books: Geometric Computing for Perception Action Systems, E. Bayro-Corrochano, Springer Verlag, 2001; Geometric Algebra with Applications in Science and Engineering, E. Bayro-Corrochano and G. Sobczyk (Eds.), Birkhauser 2001; Handbook of Geometric Computing for Pattern Recognition, Computer Vision, Neurocomputing and Robotics, E. Bayro-Corrochano, Springer Verlag, 2005. He has published over 120 refereed journal, book chapters and conference papers. He is fellow of the IAPR society.     

Mobile Manipulator Motion Planning for Multiple Tasks Using Global Optimization Approach

A mobile manipulator can perform various tasks efficiently by utilizing mobility and manipulation functions. The coupling of these two functions creates a particular kinematic redundancy introduced by mobility, which is different from that introduced by extra joints. This redundancy is quite desirable for dexterous motion in cluttered environments, but it also significantly complicates the motion planning and control problem. In this paper we propose a new motion planning method for mobile manipulators to execute a multiple task which consists of a sequence of tasks. The task considered in this paper is that the end-effector tracks a prespecified trajectory in a fixed world frame. In a multiple task, the final configuration of each task becomes the initial configuration of the next subsequent task. Such a configuration is known as a commutation configuration, which significantly affects the performance of the multiple task.We formulate the motion planning problem as a global optimization problem and simultaneously obtain the motion trajectory set and commutation configurations. In the formulation, we take account of the case that the platform has a non-holonomic constraint as well as the one that the platform has a holonomic constraint. Simulation results are demonstrated to verify the effectiveness of the proposed method.     

Using In-frame Shear Constraints for Monocular Motion Segmentation of Rigid Bodies

It is a well known result in the vision literature that the motion of independently moving objects viewed by an affine camera lie on affine subspaces of dimension four or less. As a result a large number of the recently proposed motion segmentation algorithms model the problem as one of clustering the trajectory data to its corresponding affine subspace. While these algorithms are elegant in formulation and achieve near perfect results on benchmark datasets, they fail to address certain very key real-world challenges, including perspective effects and motion degeneracies. Within a robotics and autonomous vehicle setting, the relative configuration of the robot and moving object will frequently be degenerate leading to a failure of subspace clustering algorithms. On the other hand, while gestalt-inspired motion similarity algorithms have been used for motion segmentation, in the moving camera case, they tend to over-segment or under-segment the scene based on their parameter values. In this paper we present a principled approach that incorporates the strengths of both approaches into a cohesive motion segmentation algorithm capable of dealing with the degenerate cases, where camera motion follows that of the moving object. We first generate a set of prospective motion models for the various moving and stationary objects in the video sequence by a RANSAC-like procedure. Then, we incorporate affine and long-term gestalt-inspired motion similarity constraints, into a multi-label Markov Random Field (MRF). Its inference leads to an over-segmentation, where each label belongs to a particular moving object or the background. This is followed by a model selection step where we merge clusters based on a novel motion coherence constraint, we call in-frame shear, that tracks the in-frame change in orientation and distance between the clusters, leading to the final segmentation. This oversegmentation is deliberate and necessary, allowing us to assess the relative motion between the motion models which we believe to be essential in dealing with degenerate motion scenarios.We present results on the Hopkins-155 benchmark motion segmentation dataset [27], as well as several on-road scenes where camera and object motion are near identical. We show that our algorithm is competitive with the state-of-the-art algorithms on [27] and exceeds them substantially on the more realistic on-road sequences.     

利用几何代数进行线段模型匹配和运动估计

首先探讨了Clifford代数（几何代数）在计算机视觉中的应用,并得到了2D与3D旋转的统一表达公式,进而探讨了该公式在直线模型匹配和运动估计中的应用;在改进2D多角弧匹配算法的基础上,提出了一个同时进行线段模型的匹配和运动估计的算法。该算法通过最小化模型线段与被检测线段间的距离（距离函数定义为对应点间欧氏距离的积分）而求得的最佳运动估计中的旋转,可由一个矩阵的奇异值分解来表示,从而为首次同时解决这两个问题,进行了初步尝,且该算法不受维数限制。最后的模拟实验结果表明,该算法效果良好。     

基于多机器人的运动控制平台在刚体对接系统中的应用

针对刚体对接系统,引入虚拟分段概念,分段位姿测量技术．在统一的世界坐标框架内,建立了平台的运动学模型,导出了多机器人的协调运动方案．该方案在基于多机器人的运动平台控制中具有广泛的适用性．     

测量运动物体姿态的三自由度定位算法的研究

研究了一种采用加速度计、磁阻传感器和单片机的三自由度定位装置及其算法，给出了A/D转换器的位数与系统分辨率的关系，研究了环境磁场对测量结果的影响，提出了环境磁场补偿算法并讨论了补偿算法的误差。该装置可用于运动物体航向、俯爷和倾斜三个方向的姿态角的测量。     

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

Recently, many techniques using computational fluid dynamics have been proposed for the simulation of natural phenomena such as smoke and fire. Traditionally, a single grid is used for computing the motion of fluids. When an object interacts with a fluid, the resolution of the grid must be sufficiently high because the shape of the object is represented by a shape sampled at the grid points. This increases the number of grid points that are required, and hence the computational cost is increased. To address this problem, we propose a method using multiple grids that overlap with each other. In addition to a large single grid (a global grid) that covers the whole of the simulation space, separate grids (local grids) are generated that surround each object. The resolution of a local grid is higher than that of the global grid. The local grids move according to the motion of the objects. Therefore, the process of resampling the shape of the object is unnecessary when the object moves. To accelerate the computation, appropriate resolutions are adaptively‐determined for the local grids according to their distance from the viewpoint. Furthermore, since we use regular (orthogonal) lattices for the grids, the method is suitable for GPU implementation. This realizes the real‐time simulation of interactions between objects and smoke.     

基于遗传算法的直线光流刚体运动重建

建立一种新的基于直线光流场从单目图像序列恢复刚体运动和结构的模型,推导出直线光流场与刚体的运动参数之间的关系,用2个二阶线性微分方程表达这种关系,并提出一种求解刚体运动参数的遗传算法,只需要获得图像平面的2条直线光流即可求解刚体的旋转参数,并用合成图像测试了该算法的有效性。     

Analysis on Effective Rehabilitation of Human Arms Using Compliant Strap

International Journal of Control, Automation and Systems - This paper analyses on effective compliant rehabilitation of human arms. For this purpose, we pay attention to flexible straps that are...     

Tactics‐Based Behavioural Planning for Goal‐Driven Rigid Body Control

Controlling rigid body dynamic simulations can pose a difficult challenge when constraints exist on the bodies' goal states and the sequence of intermediate states in the resulting animation. Manually adjusting individual rigid body control actions (forces and torques) can become a very labour‐intensive and non‐trivial task, especially if the domain includes a large number of bodies or if it requires complicated chains of inter‐body collisions to achieve the desired goal state. Furthermore, there are some interactive applications that rely on rigid body models where no control guidance by a human animator can be offered at runtime, such as video games. In this work, we present techniques to automatically generate intelligent control actions for rigid body simulations. We introduce sampling‐based motion planning methods that allow us to model goal‐driven behaviour through the use of non‐deterministic Tactics that consist of intelligent, sampling‐based control‐blocks, called Skills. We introduce and compare two variations of a Tactics‐driven planning algorithm, namely behavioural Kinodynamic Rapidly Exploring Random Trees (BK‐RRT) and Behavioural Kinodynamic Balanced Growth Trees (BK‐BGT). We show how our planner can be applied to automatically compute the control sequences for challenging physics‐based domains and that is scalable to solve control problems involving several hundred interacting bodies, each carrying unique goal constraints.     

On the Consistency of Instantaneous Rigid Motion Estimation

Instantaneous camera motion estimation is an important research topic in computer vision. Although in theory more than five points uniquely determine the solution in an ideal situation, in practice one can usually obtain better estimates by using more image velocity measurements because of the noise present in the velocity measurements. However, the usefulness of using a large number of observations has never been analyzed in detail. In this paper, we formulate this problem in the statistical estimation framework. We show that under certain noise models, consistency of motion estimation can be established: that is, arbitrarily accurate estimates of motion parameters are possible with more and more observations. This claim does not simply follow from the general consistency result for maximum likelihood estimates. Some experiments will be provided to verify our theory. Our analysis and experiments also indicate that many previously proposed algorithms are inconsistent under even very simple noise models.     

Generalized Serret-Andoyer Transformation and Applications for the Controlled Rigid Body

The Serret-Andoyer transformation is a classical method for reducing the free rigid body dynamics, expressed in Eulerian coordinates, to a 2-dimensional Hamiltonian flow. First, we show that this transformation is the computation, in 3-1-3 Eulerian coordinates, of the symplectic (Marsden-Weinstein) reduction associated with the lifted left-action of SO(3) on T*SO(3)—a generalization and extension of Noether's theorem for Hamiltonian systems with symmetry. In fact, we go on to generalize the Serret-Andoyer transformation to the case of Hamiltonian systems on T*SO(3) with left-invariant, hyperregular Hamiltonian functions. Interpretations of the Serret-Andoyer variables, both as Eulerian coordinates and as canonical coordinates of the co-adjoint orbit, are given. Next, we apply the result obtained to the controlled rigid body with momentum wheels. For the class of Hamiltonian controls that preserve the symmetry on T*SO(3), the closed-loop motion of the main body can again be reduced to canonical form. This simplifies the stability proof for relative equilibria , which then amounts to verifying the classical Lagrange-Dirichlet criterion. Additionally, issues regarding numerical integration of closed-loop dynamics are also discussed. Part of this work has been presented in LumBloch:97a. This revised version was published online in July 2006 with corrections to the Cover Date.     

空间多刚体系统姿态的协同控制

将一种针对多个一般非线性系统的基于输出反馈的协同控制方法应用在采用四元数法描述的空间多个刚体姿态的协同控制系统中去，给出了空间多刚体系统姿态协同控制问题有解的充分条件，并设计了多刚体系统姿态的协同控制律．算例仿真结果表明，此法设计的协同控制器能够稳定控制描述各个刚体系统的姿态四元数，使其渐近稳定．     

人体运动的函数数据分析与合成

在许多虚拟现实的应用中,虚拟人作为人在计算机中的表示,是提高其交互能力和沉浸感的重要因素之一.然而,对于虚拟人建模而言,合成逼真、可控的虚拟人运动仍然是具有挑战性的课题.为此,提出了一种基于函数数据分析的人体运动合成方法.通过对一组样本运动进行函数主成分分析,构建出一个由特征运动构成的低维函数子空间.该低维子空间不仅能够有效地刻画样本序列内在的变化规律,而且也为有目的的运动合成提供了方法.在该空间中,通过控制各特征运动的系数即可合成出逼真、平滑的运动序列.该合成过程没有耗时的计算,因此能够满足各种实时应用     

Turn-Intent Analysis Using Body Pose for Intelligent Driver Assistance

Human-centric, pervasive computing environments, with integrated sensing, processing, networking, and displays, provide an appropriate framework for developing effective driver-assistance systems. Also essential when developing such systems are systematic efforts to understand and characterize driver behavior. In an attempt to make such a predictive turn-assistance safety system a reality, we equipped an experimental vehicle with cameras and sensors to capture the vehicle dynamics, view of the road ahead, and driver's body pose. We investigated how and to what extent we could use body-pose information to detect and predict driver activities. We analyzed the detection performance of a two-class pattern classifier using receiver-operator-characteristic curves, which describe the classifier's ability to suppress missed detections and false alarms. The curves provide a ratio indicating the system's attainable proactivity (ability to foresee a user's needs) versus its transparency (ability to avoid user annoyance). Our goal is to eventually develop vision-based body-pose-recovery and behavior-recognition algorithms for driver-assistance systems     

Motion extrapolation of auditory–visual targets

Many tasks involve the precise estimation of speed and position of moving objects, for instance to catch or avoid objects that cohabit in our environment. Many of these objects are characterised by signal representations in more than one modality, such as hearing and vision. The aim of this study was to investigate the extent to which the simultaneous presentation of auditory and visual signals enhances the estimation of motion speed and instantaneous position. Observers are asked to estimate the instant when a moving object arrives at a target spatial position by pressing a response button. This task requires observers to estimate the speed of the moving object and to calibrate the timing of their manual response such that it coincides with the true arrival time of the moving object. When both visual and auditory motion signals are available, the variability in estimating the arrival time of the moving object is significantly reduced compared to the variability in the unimodal conditions. This reduction in variability is consistent with optimal integration of the auditory and visual speed signals. The average bias in the estimated arrival times depends on the motion speed: for medium speeds (17 deg/s) observers’ subjective arrival times are earlier than the true arrival times; for high speeds (47 deg/s) observers exhibit a (much smaller) bias in the other direction. This speed-dependency suggests that the bias is due to an error in estimating the motion speeds rather than an error in calibrating the timing of the motor response. Finally, in this temporal localization task, the bias and variability show similar patterns for motion defined by vision, audition or both.