Clamping weighted least-norm method for the manipulator kinematic control with constraints

One of the main challenges for kinematic control of manipulators is how to effectively address various constraints, such as obstacle avoidances. Most constraints can be converted into a virtual joint-limit problem by the general weighted least-norm method reported recently. However, a chattering of weighted factors might occur in the presence of disturbances. In this paper, in order to improve the robustness to disturbances, a clamping term forcing joints away from their limits is added to the solution of inverse kinematics, termed as the clamping weighted least-norm method. It is proved that the joint-limit constraint is always guaranteed. The proposed method is applicable to both non-redundant and redundant manipulators; the accuracy of main task is sacrificed only when there is confliction between main task and joint-limit constraint. Experiments on the seven-degree-of-freedom redundant manipulator illustrate the good performance for avoiding joint limits while tracking a given trajectory.     

Learning robustly stable open-loop motions for robotic manipulation

Robotic arms have been shown to be able to perform cyclic tasks with an open-loop stable controller. However, model errors make it hard to predict in simulation what cycle the real arm will perform. This makes it difficult to accurately perform pick and place tasks using an open-loop stable controller. This paper presents an approach to make open-loop controllers follow the desired cycles more accurately. First, we check if the desired cycle is robustly open-loop stable, meaning that it is stable even when the model is not accurate. A novel robustness test using linear matrix inequalities is introduced for this purpose. Second, using repetitive control we learn the open loop controller that tracks the desired cycle. Hardware experiments show that using this method, the accuracy of the task execution is improved to a precision of 2.5 cm, which suffices for many pick and place tasks.     

Robust object manipulation for tactile-based blind grasping

Tactile-based blind grasping addresses realistic robotic grasping in which the hand only has access to proprioceptive and tactile sensors. The robotic hand has no prior knowledge of the object/grasp properties, such as object weight, inertia, and shape. There exists no manipulation controller that rigorously guarantees object manipulation in such a setting. Here, a robust control law is proposed for object manipulation in tactile-based blind grasping. The analysis ensures semi-global asymptotic and exponential stability in the presence of model uncertainties and external disturbances that are neglected in related work. Simulation and hardware results validate the effectiveness of the proposed approach.     

Design of output constraints for model-based non-square controllers using interval operability

A steady-state interval operability methodology is introduced here for multivariable non-square systems with fewer inputs than output variables to be used in the design of model-based constrained controllers (MPC, DMC). For such systems, set-point control is not possible for all the outputs and interval control is needed. The proposed iterative approach enables the selection of the needed interval constraints systematically, so that the tightest possible control is achieved without rendering the control problem infeasible. The application of this methodology to high-dimensional industrial problems characterizing processes of Air Products and Chemicals and DuPont shows that very significant reduction of the constrained region can be achieved from the steady-state point of view. Ratios of the initial to the calculated volume of the constrained regions examined range between 10⁴ and 10⁸.     

Two hybrid algorithms for solving split equilibrium problems

The paper considers split equilibrium problems (EPs) in Hilbert spaces and proposes two hybrid algorithms for finding their solution approximations. Three methods including the diagonal subgradient method, the projection method and the proximal method have been used to design the algorithms. Using the diagonal subgradient method for EPs has allowed us to reduce complex computations on bifunctions and feasible sets. The first algorithm is designed with two projections on feasible set and with the prior knowledge of operator norm while the second algorithm is simpler in computations where only one projection on feasible set needs to be implemented and the information of operator norm is not necessary to construct solution approximations. The strongly convergent theorems are established under suitable assumptions imposed on equilibrium bifunctions. The computational performance of the proposed algorithms over existing methods is also illustrated by several preliminary numerical experiments.     

Design of low‐order controllers satisfying sensitivity constraints for unstructured uncertain plants

This paper presents a simple analytically based algorithm for the design of reduced‐order controllers satisfying frequency‐dependent sensitivity specifications for SISO plants having unstructured uncertainty. The uncertainties can be additive as well as multiplicative, and can take the form of circles, polygons or sectors located around a nominal plant. Moreover, the circle radius and polygon and sector sizes may depend on the frequency. The proposed method is applicable to both continuous and discrete designs. Copyright © 2004 John Wiley & Sons, Ltd.     

Intelligent adaptive model-based control of robotic dynamic systems with a hybrid fuzzy-neural approach

We describe in this paper a new method for adaptive model-based control of robotic dynamic systems using a new hybrid fuzzy-neural approach. Intelligent control of robotic systems is a difficult problem because the dynamics of these systems is highly nonlinear. We describe an intelligent system for controlling robot manipulators to illustrate our fuzzy-neural hybrid approach for adaptive control. We use a new fuzzy inference system for reasoning with multiple differential equations for model selection based on the relevant parameters for the problem. In this case, the fractal dimension of a time series of measured values of the variables is used as a selection parameter. We use neural networks for identification and control of robotic dynamic systems. We also compare our hybrid fuzzy-neural approach with conventional fuzzy control to show the advantages of the proposed method for control.     

Numerical method for the simultaneous determination of unknown parameters in a parabolic equation

Numerical procedures for the solution of an inverse problem of simultaneously determining unknown parameters in a linear parabolic equation are considered. The approach proposed is to approximate unknown functions using Chebyshev polynomials, which are determined consecutively from the solutions of the minimization problems based on overspecified data. Finally, the results of a numerical experiment are displayed.     

A singularity-free motion control algorithm for robot manipulators—a hybrid system approach

This paper presents the design and implementation of a singularity-free tracking algorithm for robot manipulators using a hybrid system approach. A hybrid robot motion controller is designed to ensure feasible robot motion in the neighborhood of kinematic singularities. The hybrid control system has a two-layered hierarchical structure, a discrete layer and a continuous layer. The robot workspace is partitioned into subspaces based on the singular configurations of the robot. Switching between continuous controllers is involved when the robot travels across the subspaces. With the hybrid controller, the robot can work at the vicinity of singular configurations, but also can go through and stay at the singular configurations. The stability of the hybrid system is investigated using multiple Lyapunov function theory. Experimental results have demonstrated the advantages of the hybrid robot motion control method.     

Satisfaction of gain and phase margin constraints using proportional controllers

Gain and phase margins (GM and PM) are frequently used as robustness indicators for linear time invariant systems. In many cases, the design problem is reduced to determination of a loop gain to satisfy several design criteria including gain and PM specifications. Therefore finding the set of fixed order compensators that satisfy given gain and PM specifications attracted the attention of a considerable part of the scientific community recently. It is possible to show that it may not be possible to satisfy the required gain and/or PM specifications using only a proportional controller. As a result, finding the limits of the proportional controllers for a given plant (i.e. finding the maximum achievable gain and PMs, MAGM and MAPM) is also important. After providing alternative methods (to those that already exist in the literature) for determining all stabilising proportional controllers that satisfy gain and PM constraints, a new method for calculating MAGM and MAPM using proportional controllers is given in this article. A formulation to calculate maximum gain that results in MAGM is also provided.     

Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants

This paper presents a method for the design of PID-type controllers, including those augmented by a filter on the D element, satisfying a required gain margin and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the method are: (i) it can be applied to plants of any order including non-minimum phase plants, plants with delay, plants characterized by quasi-polynomials, unstable plants and plants described by measured data, (ii) the sensors associated with the PI terms and the D term can be different (i.e., they can have different transfer function models), (iii) the algorithm relies on explicit equations that can be solved efficiently, (iv) the algorithm can be used in near real-time to determine a controller for on-line modification of a plant accounting for its uncertainty and closed-loop specifications, (v) a single plot can be generated that graphically highlights tradeoffs among the gain margin, (complementary) sensitivity bound, low-frequency sensitivity and high-frequency sensor noise amplification, and (vi) the optimal controller for a practical definition of optimality can readily be identified.     

基于遗传算法的机械臂逆运动学问题解决方案

提出应用遗传算法求解机械臂的逆运动学问题,将种群定义于机械臂的关节角轨迹层面,利用连续性函数实现算法的初始化算子,交叉算子和变异算子。算法仅使用表现型数据表示方式,克服了传统遗传算法在数据的基因型和表现型之间频繁地进行编码和解码操作。通过和传统遗传算法进行对比分析,验证了所提出的方法能够避免传统遗传算法求解逆运动学问题时存在的多重切换点现象,能够获得更平滑的关节角轨迹,缩短了算法的收敛时间,生成的笛卡尔轨迹具有更高的精度。     

Survey on model-based manipulation planning of deformable objects

A systematic overview on the subject of model-based manipulation planning of deformable objects is presented. Existing modeling techniques of volumetric, planar and linear deformable objects are described, emphasizing the different types of deformation. Planning strategies are categorized according to the type of manipulation goal: path planning, folding/unfolding, topology modifications and assembly. Most current contributions fit naturally into these categories, and thus the presented algorithms constitute an adequate basis for future developments.     

在闭环极点约束条件下研究控制系统最大鲁棒稳定界

不仅研究了一类扰动控制系统鲁棒稳定界的定义、优化等问题, 而且通过研究控制系统鲁棒稳定界与Riccati矩阵方程解的关系, 提出了在闭环极点约束条件下研究鲁棒稳定界的方法, 并给出了基于LQ逆问题参数化解的极大化鲁棒稳定界的优化算法.     

Adaptive inverse control for parametric strict feedback systems with unknown failures of hysteretic actuators

An adaptive compensation control scheme is proposed by using backstepping techniques for a class of uncertain nonlinear systems preceded by m hysteretic actuators, which exhibit unknown backlash nonlinearity and possibly experience unknown failures. An estimated smooth inverse of the actuator backlash is utilized in the controller design to compensate for the effects of the backlash and actuator failures. It is shown that the designed controllers can ensure all signals of closed‐loop system bounded for any failure pattern of hysteretic actuators and tracking performance is also maintained. Simulation studies confirm the effectiveness of the proposed controller, especially the improvement of system performances. Copyright © 2013 John Wiley & Sons, Ltd.     

基于均值改进控制策略的昂贵约束并行代理优化算法

针对具有黑箱特性的昂贵约束优化问题及工程中计算资源利用率不高问题,提出了新的基于均值改进控制策略的并行代理优化算法.该算法为了减少仿真建模计算负担,选取Kriging近似模型对目标函数和约束函数进行近似估计.在Kriging模型基础上,利用均值改进与新增试验样本间的不等关系构建具有距离特性的控制函数.算法的均值改进控制...     

采用观测器的双线性系统最优跟踪控制器设计

研究一类参考输入由外系统描述的双线性系统的最优输出跟踪控制问题.利用逐次逼近的方法,首先构造一族非齐次线性两点边值问题序列将原非线性两点边值问题解耦;然后迭代求解伴随向量的序列,得到由状态向量的线性解析函数和以伴随向量的极限形式给出的非线性部分的补偿项组成的最优输出跟踪控制律.通过构造降维观测器重构外系统的状态,解决了最优输出跟踪控制律的物理可实现问题仿真结果表明了该方法的有效性.     

面向精密调整的6-HTRT并联机器人

为实现光学精密调整,研制出了由交流伺服电机驱动的6-HTRT并联机器人,它具有6个自由度,其结构特点决定了该机器人可以完成高精度定位调整。分析了机器人的位置逆解,并对不同位姿下的工作空间进行了仿真。控制系统采用基于ISA总线的闭环控制方式,测试结果显示:该并联机器人工作空间较大、分辨率高、重复定位精度高,说明机器人结构和控制系统设计的合理性。最后应用此并联机器人成功完成了光学精密装配试验。     

A hybrid method for inversion of 3D AC resistivity logging measurements

In this paper, we propose the use of a hybrid algorithm for the inversion of 3D Alternate Current (AC) resistivity logging measurements. The forward problem is solved using a goal-oriented self-adaptive hp-Finite Element Method (hp-FEM) that provides exponential convergence of the numerical error with respect to the mesh size. The inverse problem is solved using a Hierarchical Genetic Search (HGS) coupled with a Broyden–Fletcher–Goldfar–Shanno (BFGS) method. Individuals from the genetic populations represent the resistivity of the formation layers. The fitness function is estimated based on hp-FEM results. The hybrid method controls the accuracy of evaluation of particular individuals, as well as the accuracy of the genetic coding. After finding those regions where the fitness function has small values, the local search method by means of BFGS algorithm is executed. The paper is concluded with numerical results for the hybrid algorithm.