Modular Architecture for Humanoid Walking Pattern Prototyping and Experiments

In this paper we describe the use of design patterns as a basis for creating humanoid walking pattern generator software having a modular architecture. This architecture enabled the rapid porting of several novel walking algorithms on a full-size humanoid robot, HRP-2. The body of work currently available allows extracting a general software architecture usable with inter-exchange between simulations and real experiments. The proposed architecture with the associated design patterns is described together with several applications: a pattern generator for a HRP-2 with passive toe joints, a pattern for dynamically stepping over large obstacles and a new quadratic problem (QP) formulation for the generation of the reference zero-momentum point. Thanks to the versatility and the modularity of the proposed framework, the QP method has been implemented and experienced within 4 days only.     

A fast impulsive contact suite for rigid body simulation

A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of "stationary" bodies. This suite can generate realistic-looking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an "hourglass". Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be "plugged into" any simulation algorithm to provide fast and realistic-looking animations of rigid bodies.     

HRP-2W: A humanoid platform for research on support behavior in daily life environments

We introduce a concept of a real-world-oriented humanoid robot that can support humans’ activities in daily life. In such environments, robots have to watch humans, understand their behavior, and support their daily life tasks. In particular, these robots must be capable of such real-world behavior as handling tableware and delivering daily commodities by hand. We developed a humanoid robot, HRP-2W, which has an upper body of HRP-2 [K. Kaneko, F. Kanehiro, S. Kajita, H. Hirukawa, T. Kawasaki, M. Hirata, K. Akachi, T. Isozumi, Humanoid Robot HRP-2, in: Proceedings of the 2004 IEEE International Conference on Robotics & Automation, 2004, pp. 1083–1090] and a wheel module instead of legs, as a research platform to fulfill this aim. We also developed basic software configuration in order to integrate our platform with other research groups. Through experiments, we demonstrated the feasibility of the humanoid robot platform and the potential of the software architecture.     

Quadratic programming algorithms for large-scale model predictive control

Quadratic programming (QP) methods are an important element in the application of model predictive control (MPC). As larger and more challenging MPC applications are considered, more attention needs to be focused on the construction and tailoring of efficient QP algorithms. In this study, we tailor and apply a new QP method, called QPSchur, to large MPC applications, such as cross directional control problems in paper machines. Written in C++, QPSchur is an object oriented implementation of a novel dual space, Schur complement algorithm. We compare this approach to three widely applied QP algorithms and show that QPSchur is significantly more efficient (up to two orders of magnitude) than the other algorithms. In addition, detailed simulations are considered that demonstrate the importance of the flexible, object oriented construction of QPSchur, along with additional features for constraint handling, warm starts and partial solution.     

面向冗余度机械臂QP问题求解的E47和94LVI数值算法

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束,且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求。考虑同时受制于上述三种约束的二次规划问题的求解,给出并研究两种数值算法(E47和94LVI算法)。这类带约束的二次规划问题被等价转换为分段线性投影方程。应用E47和94LVI算法求解上述分段线性投影方程,从而得到二次规划问题的最优数值解。同时,通过大量的数值实验,研究两种算法面向冗余度机械臂的QP问题求解性能,并给出E47、94LVI算法与经典有效集算法的对比实验结果。最终证实了E47和94LVI两种算法在求解二次规划问题上的高效性和优越性。     

Distributed power adjustment based on control theory for cognitive radio networks

In this paper, we propose two power adjustment methods for cognitive radio networks. In the first algorithm, the transmitter derives the transmission power with PID control in order to satisfy the QoS constraints in secondary networks. The derived transmission power is compared with a constraint condition in order to avoid the interference with primary networks, and then the actual transmission power is decided. Because the constraint condition affects the performance of our proposed method significantly, we propose an effective update algorithm. On the other hand, the second algorithm is based on model predictive control (MPC). In this method, the decision of transmission power is formulated as quadratic programming (QP) problem and the transmission power is derived directly with the constraint condition. We evaluate the performances of our proposed methods with simulation and compare the proposed methods with the distributed power control (DPC) method. In numerical examples, we show that our proposed methods are more effective than the existing method in some situations. We also prove analytically that the interference with primary networks can be avoided with probability one by using our proposed method if each transmitter has the information about every channel gain.     

Global Convergence of Decomposition Learning Methods for Support Vector Machines

Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables     

A particular Gaussian mixture model for clustering and its application to image retrieval

We introduce a new method for data clustering based on a particular Gaussian mixture model (GMM). Each cluster of data, modeled as a GMM into an input space, is interpreted as a hyperplane in a high dimensional mapping space where the underlying coefficients are found by solving a quadratic programming (QP) problem. The main contributions of this work are (1) an original probabilistic framework for GMM estimation based on QP which only requires finding the mixture parameters, (2) this QP is interpreted as the minimization of the pairwise correlations between cluster hyperplanes in a high dimensional space and (3) it is solved easily using a new decomposition algorithm involving trivial linear programming sub-problems. The validity of the method is demonstrated for clustering 2D toy examples as well as image databases.     

Workload of window cleaners using ladders differing in rung separation

The objective of the present study was to compare energetic workload, perceived exertion, perceived discomfort, safety, and mechanical load at lower limb joints among window cleaners during usage of extension ladders with 30 and 35 cm rung separation. Eleven healthy male professional window cleaners of short and tall stature participated in this study. No significant differences between 30 and 35 cm rung separation were observed for the energetic workload. Results concerning the perceived exertion, discomfort, and safety indicate that 35 cm rung separation is preferred. Based on the mechanical load at the hip, knee, and ankle during ascending and descending the ladder, 30 cm rung separation is preferable to 35 cm rung separation. It is advised to climb ladders with the knees inside the side rails of the ladder, but this seems only possible with 35 cm rung separation. Findings of the presents study suggest that overall, a 35 cm rung separation is marginally favourable while using extension ladders.     

Proportioning with second-order information for model predictive control

We propose an algorithm for the effective solution of quadratic programming (QP) problems arising from model predictive control (MPC). MPC is a modern multivariable control method which gives the solution for a QP problem at each sample instant. Our algorithm combines the active-set strategy with the proportioning test to decide when to leave the actual active set. For the minimization in the face, we use a direct solver implemented by the Cholesky factors updates. The performance of the algorithm is illustrated by numerical experiments, and the results are compared with the state-of-the-art solvers on benchmarks from MPC.     

A method for structural optimization which combines secondorder approximations and dual techniques

A structural optimization problem is usually solved iteratively as a sequence of approximate design problems. Traditionally, a variety of approximation concepts are used, but lately second-order approximation strategies have received most interest since high quality approximations can be obtained in this way. Furthermore, difficulties in choosing tuning parameters such as step-size restrictions may be avoided in these approaches. Methods that utilize second-order approximations can be divided into two groups; in the first, a Quadratic Programming (QP) subproblem including all available second-order information is stated, after which it is solved with a standard QP method, whereas the second approach uses only an approximate QP subproblem whose underlying structure can be efficiently exploited. In the latter case, only the diagonal terms of the second-order information are used, which makes it possible to adopt dual methods that require separability. An advantage of the first group of methods is that all available second-order information is used when stating the approximate problem, but a disadvantage is that a rather difficult QP subproblem must be solved in each iteration. The second group of methods benefits from the possibility of using efficient dual methods, but lacks in not using all available information. In this paper, we propose an efficient approach to solve the QP problems, based on the creation of a sequence of fully separable subproblems, each of which is efficiently solvable by dual methods. This procedure makes it possible to combine the advantages of each of the two former approaches. The numerical results show that the proposed solution procedure is a valid approach to solve the QP subproblems arising in second-order approximation schemes.Presented at NATO ASI Optimization of Large Structural Systems, Berchtesgaden, Germany, Sept. 23 – Oct. 4, 1991     

When does QP yield the exact solution to constrained NMPC?

It is well known that the optimal control sequence for a linear system with a quadratic cost and linear inequality constraints over a finite optimisation horizon can be computed by means of a quadratic programme (QP). The aim of this article is to investigate when the optimal control sequence for a non-linear single-input single-output system also can be computed via QP. Our main contribution is to show that the optimal control sequence for non-linear systems, with a quadratic cost and linear inequality constraints can be computed in exact form via QP provided the optimisation horizon is no larger than a critical quantity that we name the ‘input–output linear horizon’. The results do not require any linearisation technique and are applicable to general non-linear systems, provided their input–output linear horizon is larger than their relative degree.     

Planning and executing navigation among movable obstacles

This paper explores autonomous locomotion, reaching, grasping and manipulation for the domain of navigation among movable obstacles (NAMO). The robot perceives and constructs a model of an environment filled with various fixed and movable obstacles, and automatically plans a navigation strategy to reach a desired goal location. The planned strategy consists of a sequence of walking and compliant manipulation operations. It is executed by the robot with online feedback. We give an overview of our NAMO system, as well as provide details of the autonomous planning, online grasping and compliant hand positioning during dynamically stable walking. Finally, we present results of a successful implementation running on the humanoid robot HRP-2.     

基于粒子群优化的有约束模型预测控制器

研究了模型预测控制(MPC)中解决带约束的优化问题时所用到的优化算法,针对传统的二次规划(QP)方法的不足,引入了一种带有混沌初始化的粒子群优化算法(CPSO),将其应用到模型预测控制中,用十解决同时带有输入约束和状态约束的控制问题.最后,引入了一个实际的带有约束的线性离散系统的优化控制问题,分别用二次规划和粒子群优化两种算法去解决,通过仿真结果的比较,说明了基于粒子群优化(PSO)的模型预测控制算法的优越性.     

Dynamic design,numerical solution and effective verification of acceleration-level obstacle-avoidance scheme for robot manipulators

For avoiding obstacles and joint physical constraints of robot manipulators, this paper proposes and investigates a novel obstacle avoidance scheme (termed the acceleration-level obstacle-avoidance scheme). The scheme is based on a new obstacle-avoidance criterion that is designed by using the gradient neural network approach for the first time. In addition, joint physical constraints such as joint-angle limits, joint-velocity limits and joint-acceleration limits are incorporated into such a scheme, which is further reformulated as a quadratic programming (QP). Two important ‘bridge’ theorems are established so that such a QP can be converted equivalently to a linear variational inequality and then equivalently to a piecewise-linear projection equation (PLPE). A numerical algorithm based on a PLPE is thus developed and applied for an online solution of the resultant QP. Four path-tracking tasks based on the PA10 robot in the presence of point and window-shaped obstacles demonstrate and verify the effectiveness and accuracy of the acceleration-level obstacle-avoidance scheme. Besides, the comparisons between the non-obstacle-avoidance and obstacle-avoidance results further validate the superiority of the proposed scheme.     

Quadratic programming method in numerical simulation of metal forming process

In this paper, a quadratic programming (QP) model based on a parametric variational principle is proposed for elastic–plastic (EP) finite element analysis of metal forming processes. The contact problem with friction between blank and tools is treated in the same way as in plastic analysis. The penalty factors, which are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of metal forming, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. The algorithms for contact analysis and plastic analysis are established in one frame and consistent with each other. Compared with the conventional EP FEM, the newly developed method requires no tedious iterative procedures, and has no convergence problems. To apply this method easily to simulation of metal forming, detailed forms of some key matrices or vectors for 2D FEM and 3D FEM are presented, and a parametric loading algorithm for the QP model is developed, which is suitable for QP problem with free variables, and can decrease memory cost by avoiding the introduction of additional slack variables and improve the solution efficiency to some extent. Finally the proposed QP model is validated by two examples, analysis of V-notched tension test and analysis of the drawing of a square box––one of the benchmarks proposed at NUMISHEET93. It can be seen that the accuracy of solution of the new EP FEM based on QP is better than that of the conventional EP FEM based on iteration. To make the new EP FEM more applicable to metal forming industries, It is necessary to develop a more efficient QP algorithm that is suitable for large-scale problems.     

Extending the mathematics in qualitative process theory

Reasoning about physical systems requires the integration of a range of knowledge and reasoning techniques. P. Hayes has named the enterprise of identifying and formalizing the common-sense knowledge people use for this task “naive physics.” Qualitative Process theory by K. Forbus proposes a structure and some of the content of naive theories about dynamics, (i.e., the way things change in a physical situation). Any physical theory, however, rests on an underlying mathematics. QP theory assumes a qualitative mathematics which captures only simple topological relationships between values of continuous parameters. While the results are impressive, this mathematics is unable to support the full range of deduction needed for a complete naive physics reasoner. A more complete naive mathematics must be capable of representing measure information about parameter values as well as shape and strength characterizations of the partial derivatives relating these values. This article proposes a naive mathematics meeting these requirements, and shows that it considerably expands the scope and power of deductions which QP theory can perform.     

Generalized Core Vector Machines

Kernel methods, such as the support vector machine (SVM), are often formulated as quadratic programming (QP) problems. However, given$m$training patterns, a naive implementation of the QP solver takes$O(m^3)$training time and at least$O(m^2)$space. Hence, scaling up these QPs is a major stumbling block in applying kernel methods on very large data sets, and a replacement of the naive method for finding the QP solutions is highly desirable. Recently, by using approximation algorithms for the minimum enclosing ball (MEB) problem, we proposed the core vector machine (CVM) algorithm that is much faster and can handle much larger data sets than existing SVM implementations. However, the CVM can only be used with certain kernel functions and kernel methods. For example, the very popular support vector regression (SVR) cannot be used with the CVM. In this paper, we introduce the center-constrained MEB problem and subsequently extend the CVM algorithm. The generalized CVM algorithm can now be used with any linear/nonlinear kernel and can also be applied to kernel methods such as SVR and the ranking SVM. Moreover, like the original CVM, its asymptotic time complexity is again linear in$m$and its space complexity is independent of$m$. Experiments show that the generalized CVM has comparable performance with state-of-the-art SVM and SVR implementations, but is faster and produces fewer support vectors on very large data sets.     

协作式整体和局部的分类机

提出了一种协作式整体局部分类算法,即C2M (Collaborative classification machine with local and global information),该算法利用两类样本各自的协方差作为整体方向信息, 获得两个带整体和局部信息的分类面,并通过组合分类器的平均规则将两个分类面组合, 得到最终的最优判决平面.该算法可用两次QP (Quadratic programming)求解,时间复杂度为O(2N3), 大大小于M4 (Maxi-min margin machine)的O(N4), 线性核时的分类精度高于只利用了局部信息的支持向量机 (Support vector machine, SVM).理论上证明了在交遇区较多时, C2M 可以比M4 更有效地利用全局信息,并提出了判断整体信息对分类是否有贡献的4个判别指标. 模拟数据和标准数据集上与M4 和SVM的对比实验证明了该算法的有效性.