3DPointCaps++: Learning 3D Representations with Capsule Networks

International Journal of Computer Vision - We present 3DPointCaps++ for learning robust, flexible and generalizable 3D object representations without requiring heavy annotation efforts or...     

Learning Latent Representations of 3D Human Pose with Deep Neural Networks

Most recent approaches to monocular 3D pose estimation rely on Deep Learning. They either train a Convolutional Neural Network to directly regress from an image to a 3D pose, which ignores the dependencies between human joints, or model these dependencies via a max-margin structured learning framework, which involves a high computational cost at inference time. In this paper, we introduce a Deep Learning regression architecture for structured prediction of 3D human pose from monocular images or 2D joint location heatmaps that relies on an overcomplete autoencoder to learn a high-dimensional latent pose representation and accounts for joint dependencies. We further propose an efficient Long Short-Term Memory network to enforce temporal consistency on 3D pose predictions. We demonstrate that our approach achieves state-of-the-art performance both in terms of structure preservation and prediction accuracy on standard 3D human pose estimation benchmarks.     

Robust proportional-derivative control on SO(3) with disturbance compensation for quadrotor UAV

International Journal of Control, Automation and Systems - This paper presents a control law that can counter both random disturbance and inertia matrix perturbation in quadrotor attitude...     

Programs for generating Clebsch-Gordan coefficients of SU(3) in SU(2) and SO(3) bases

Computer codes are developed to calculate Clebsch-Gordan coefficients of SU(3) in both SU(2)- and SO(3)-coupled bases. The efficiency of this code derives from the use of vector coherent state theory to evaluate the required coefficients directly without recursion relations. The approach extends to other compact semi-simple Lie groups. The codes are given in subroutine form so that users can incorporate the codes into other programs.

Program summary

Title of program: SU3CGVCSCatalogue identifier: ADTNProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTNProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: Persons requesting the program must sign the standard CPC non-profit use licenseComputers for which the program is designed and others on which it is operable: SGI Origin 2000, HP Apollo 9000, Sun, IBM SP, PentiumOperating systems under which the program has been tested: IRIX 6.5, HP UX 10.01, SunOS, AIX, LinuxProgramming language used: FORTRAN 77Memory required to execute with typical data: On the HP system, it requires about 732 KBytes.Disk space used for output: 2100+2460 bytesNo. of bits in a word: 32 bit integer and 64 bit floating point numbers.No. of processors used: 1Has the code been vectorized: NoNo. of bytes in distributed program, including test data, etc.: 26 309No. of lines in distributed program, including test data, etc.: 3969Distribution format: tar gzip fileNature of physical problem: The group SU(3) and its Lie algebra have important applications, for example, in elementary particle physics, nuclear physics, and quantum optics [1-3]. The code presented is particularly relevant for the last two fields. Clebsch-Gordan (CG) coefficients are required whenever the symmetries of many-body systems are used for the evaluation of matrix elements of tensor operators. Moreover, the construction of CG coefficients for SU(3) serves as a nontrivial prototype for larger compact semi-simple Lie algebras and even for non semi-simple Lie algebras. It is the simplest Lie algebra to have multiplicity in its outer products and a non-canonical subalgebra, i.e., SO(3).Method of solution: Vector coherent state theory is first used to construct bases for the products of two irreducible representations (irreps) [4]. The bases are SU(2)-coupled so that SU(2)-reduced CG (or isoscalar factors) can be constructed naturally. The CG coefficients in the SO(3) bases are constructed subsequently from the overlaps between the SU(2) and SO(3) bases.Restriction on the complexity of the problem: The programs are limited by computer memory and the maximum size of variable arrays. As dimension overflow conditions are possible, they are flagged and can be fixed by following the directions given as part of the error message.Typical running time: The calculation time for a single SU(3) CG coefficient is very different for SU(2) and SO(3) bases. It varies between 7.3-54.1 ns in SGI Origin 2000, 0.81-5.48 ms in HP Apollo 9000, or 0.055-0.373 ms in Intel Pentium 4 for SU(2) bases while it is between 0.027-0.255 s in Intel Pentium 4 for SO(3) bases.Unusual features of the program: Intrinsic bit functions: and, or, and shift, called iand, ior, and ishft, respectively, in FORTRAN, are used for packing and unpacking the labels for the irreps. Intrinsic logical btest is used to test the bit for the phase factor.References:[1] Y. Ne'eman, Nucl. Phys. 26 (1961) 222;  M. Gell-Man, Y. Ne'eman, The Eightfold Way, Benjamin, New York, 1964.[2] J.P. Elliott, Proc. Roy. Soc. A 245 (1958) 128, 562.[3] M. Reck, A. Zeilinger, H.J. Bernstein, P. Bertani, Phys. Rev. Lett. 73 (1994) 58;  B.C. Sanders, H. de Guise, D.J. Rowe, A. Mann, J. Phys. A 32 (1999) 7111.[4] D.J. Rowe, C. Bahri, J. Math. Phys. 41 (2000) 6544.     

基于SO(3)的多四旋翼无人机编队协同控制

针对多四旋翼无人机系统的编队飞行问题,提出了基于特殊正交群SO(3)的协同控制设计方法.在给出编队空间队形和通信拓扑描述后,建立了多四旋翼无人机系统SO(3)控制模型.由于SO(3)与传统俯仰/偏航/滚转三通道模型具有不同的结构,文中进一步研究了SO(3)中无人机之间相对误差的表示方法,设计了适用于多飞行器的SO(3)控制器实现对编队和姿态的协同控制.推力控制器用于调节无人机的位置与速度,并在此基础上构造旋转矩阵形式的姿态协同指令.文中相应设计了SO(3)姿态控制器用于实现指令跟踪,最后从理论上对协同稳定性进行了分析.提出的控制方法能够使得多四旋翼无人机形成期望的队形,并且保持姿态一致进行稳定飞行.仿真结果验证了本文方法的有效性.     

Angular velocity observer for attitude tracking on SO(3) with the separation property

This paper studies a rigid body attitude tracking control problem with attitude measurements only, when angular velocity measurements are not available. An angular velocity observer is constructed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. As it is developed directly on the special orthogonal group, which completely avoids singularities, complexities, or discontinuities caused by minimal attitude representations or quaternions. Then, the presented observer is integrated with a proportional-derivative attitude tracking controller to show a separation type property, where exponential stability is guaranteed for the combined observer and attitude control system.     

基于问题与答案联合表示学习的半监督问题分类方法

问题分类旨在对问题的类型进行自动分类,该任务是问答系统研究的一项基本任务。该文提出了一种基于问题和答案联合表示学习的问题分类方法。该方法的特色在于利用问题及其答案作为共同的上下文环境,学习词的分布式表示,从而充分利用未标注样本中问题和答案隐含的分类信息。具体而言,首先,我们引入神经网络语言模型,利用问题与答案联合学习词向量表示,增加问题词向量的信息量;其次,加入大量未标注的问题与答案样本参与词向量学习,进一步增强问题词向量表示能力;最后,将已标注的问题样本以词向量形式表示作为训练样本,采用卷积神经网络建立问题分类模型。实验结果表明,该文提出的基于半监督问题分类方法能够充分利用词向量表示和大量未标注样本来提升性能,明显优于其他基准半监督分类方法。     

Continuous appointed-time prescribed performance attitude tracking control for rigid spacecraft with actuator faults on SO(3)

In this article, the attitude tracking problem for rigid spacecraft subject to external disturbance, inertia uncertainties, and actuator faults is investigated. A novel continuous control strategy is proposed to guarantee that the attitude tracking errors converge with desired performance before an appointed time. In addition, the proposed control law can enable the closed-loop system to be unwinding-free. For the purpose, a modified appointed-time performance function (APF) is used to construct a disturbance observer-based adaptive attitude control law based on the special orthogonal group (SO(3)). With the aid of the modified APFs, desired performance metrics, including transient and steady-state performance, on the attitude tracking error can be specified in advance without the requirement for initial values of the tracking system to avoid singularity. By resorting to error transformation and backstepping technique, the control design process is simplified and a few control gains are involved in the proposed control law. Rigorous stability analysis based on the Lyapunov theory is provided to prove the appointed-time stability of the attitude tracking error as well as the boundedness of all signals in the closed-loop system despite external disturbance, inertia uncertainties, and actuator faults. Finally, numerical simulations are conducted to support the analysis.     

Continuous adaptive-gain finite-time control for rigid body attitude dynamics on SO(3)

In this paper, the attitude tracking problem for the rigid body with model uncertainties and external disturbances is investigated in a coordinate-free way. A continuous adaptive-gain second-order sliding mode controller is designed to ensure the establishment of a real second-order sliding mode in finite time, and then the predefined nonsingular fast sliding surface further implies finite-time stability of the attitude error vector and the angular velocity error vector. The key feature of the proposed controller is that it does not require the knowledge of the boundary of the disturbance gradient. A rigorous mathematical proof for the stability of the control system is derived by using the Lyapunov function technique. Finally, simulation comparisons illustrate the effectiveness and robustness of the controller.     

四旋翼无人机SO(3) 滑模变结构姿态控制器设计

为了提高四旋翼无人机SO(3) 控制的动态性能, 对滑模变结构控制在四旋翼无人机SO(3) 姿态控制中的应用进行研究. 首先, 通过对两种四旋翼SO(3) 姿态控制模型进行分析, 确定一种奇异点较少的模型为控制对象; 随后,针对可能出现的控制奇异问题, 设计一种引入调节函数的无奇异积分型滑模面, 得到了滑模稳定性引理; 最后, 利用这种滑模面进行控制器设计和Lyapunov 稳定性分析, 证明了系统全局指数渐近稳定. 仿真结果验证了所提出的设计方案的正确性.

     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

Exponential stability of an attitude tracking control system on SO(3) for large-angle rotational maneuvers

This paper studies a tracking control system for the attitude dynamics of a rigid body. By selecting an attitude error function carefully, we show that the proposed control system guarantees a desirable tracking performance uniformly for rotational maneuvers involving a large initial attitude error. A strict Lyapunov analysis is presented to show exponential stability, and a sufficient condition to avoid non-differentiable points of the attitude error function is also shown. The proposed control system is directly developed on the special orthogonal group to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. These are illustrated by numerical examples.