On the grasping stability and optimality under external perturbations

There are two types of grasping analysis in robotics research: find the grasping force distributions among the grasping fingers when given the contact points and find a good set of the contact points when given the shape of the object. Each kind of problem is associated with optimality and stability analysis. In this article, we investigate the grasping stability and optimality issues under the influence of external perturbations. A rotation‐displacement geometry model is used in computing the changes of grasping forces under external perturbations. Using these results, we present the concept of perturbation closure, which plays the central role in our analysis. A method for finding the local minimal perturbation resisting forces required for non‐slip contacts is developed based on this concept. A grasp so determined is guaranteed to be stable if the external perturbations do not exceed the threshold. Based on this property, we develop a quantitative measurement that can be used to evaluate the performance of different grasping configurations. One can use this measurement to determine the best grasping configuration from a set of perturbation resisting grasps. This actually gives a method which enables the optimal grasping configuration to be found. Both two‐dimensional and three‐dimensional cases are discussed in detail for determining the perturbation closure, the local minimal perturbation resisting force, and the perturbation resisting grasp. Examples are given at the end of the article to illustrate our idea. ©1999 John Wiley & Sons, Inc.     

Towards grasping in unstructured environments: grasper compliance and configuration optimization

This paper examines the role of grasper compliance and kinematic configuration in environments where object size and location may not be well known. A grasper consisting of a pair of two-link planar fingers with compliant revolute joints was simulated as it passively deflected during contact with a target object. The kinematic configuration and joint stiffness values of the grasper were varied in order to maximize successful grasp range and minimize contact forces for a wide range of target object size. Joint rest angles around 25–45 degrees produced near-optimal results if the stiffness of the base joint was much smaller than the intermediate joint, as confirmed experimentally.     

Finding effective “force targets” for two-dimensional,multifinger frictional grips

In this paper we apply techniques from computational geometry to solve several problems in grasp planning and control in robotics. We consider the problem of calculating “force targets ” for a collection ofn fingers which grasp a two-dimensional object at known positions, at which the normals to the surface are also assumed to be known at least approximately. If the points at which the fingers touch the body do not allow apositive grip to be exerted (i.e., a grip in which the fingers hold the body in equilibrium by exerting friction-free forces in the directions of the corresponding inward-directed normals), it is appropriate to find the smallest coefficient of friction for which it is possible to assign a set of forces to be exerted by the fingers (so-calledfinger-force targets) which hold the object at equilibrium and such that each individual force lies within the corresponding cone of friction. We present an algorithm for this problem which runs in time0(n log² n log logn). We also present another algorithm for preprocessing the given data so as to allow fast computation of the desired coefficient of friction for the case in which one needs to balance any given “query” external force and torque. Finally, we discuss simpler variants of our techniques which are likely to be more efficient when the problem is solved for a small number of fingers.     

Multi-fingered grasp synthesis based on the object dynamic properties

The grasping and manipulation of objects, especially when they are heavy with respect to the hand power capability, requires the synthesis of grasp configurations that explicitly take into account the dynamic properties of the object. Specifically, suitable grasp configurations reducing gravitational and inertial effects during object manipulation, and minimizing and equally distributing the grasping forces among all the available fingers, must be computed. A new method for fast synthesis of multi-fingered grasp configurations is proposed in this paper. In particular, to reduce the computational complexity, all the regions of the object surface favoring the synthesis of minimal inertia grasps are evaluated first. Then, a reduced number of discrete grasping regions are selected on the basis of the fingertip size, model uncertainty, and surface curvature. Finally, an exhaustive search of the optimal grasp configurations with respect to the grasp quality is performed. Several case studies and comparisons with other methods are proposed to demonstrate the effectiveness of the proposed approach.     

机器人多指操作的递阶控制1)

This paper presents a hierarchical control system for robot multifingered coordinate manipulation. Given a manipulation,the task planner generates a sequence of object's motion velocities at first,and then generates for coordinate motion the desired velocities of finger's motion and desired orientation change of the grasped object according to the desired velocities of object's motion.At the same time,the force planner generates the grasp forces on the fingers in order to resist the external forces on the object,according to the grasp posture.Finally,the system generates a result compliance velocity from both the desired finger's velocities and desired grasp forces,and transfers it into joint velocites through the finger's inverse Jacobian.Then the controller of joint motion implements the control of both forces and velocities for the fingers.The approach has been applied to the development of control system HKUST dexterous hand successfully.Experiment results show that it is not only possible to trail and control the object's track,but also possible to realize force control and the hybrid control of both forces and velocities through this method.     

Iterative learning of grasp adaptation through human corrections

In the context of object interaction and manipulation, one characteristic of a robust grasp is its ability to comply with external perturbations applied to the grasped object while still maintaining the grasp. In this work, we introduce an approach for grasp adaptation which learns a statistical model to adapt hand posture solely based on the perceived contact between the object and fingers. Using a multi-step learning procedure, the model dataset is built by first demonstrating an initial hand posture, which is then physically corrected by a human teacher pressing on the fingertips, exploiting compliance in the robot hand. The learner then replays the resulting sequence of hand postures, to generate a dataset of posture-contact pairs that are not influenced by the touch of the teacher. A key feature of this work is that the learned model may be further refined by repeating the correction-replay steps. Alternatively, the model may be reused in the development of new models, characterized by the contact signatures of a different object. Our approach is empirically validated on the iCub robot. We demonstrate grasp adaptation in response to changes in contact, and show successful model reuse and improved adaptation with additional rounds of model refinement.     

Experimental validation of an optimization formulation of the human grasping quality sense

An experimental procedure that evaluates the quality of a grasp is developed. In this procedure human subjects grasp a rigid object that is subjected to an external load. Three formulations that capture the sense of grasping quality through the energy level stored in the gripper, maximum value of the applied finger forces, and through the distribution of the grasping forces are considered. The applied finger forces are measured and the quality values of the grasp based on these three different formulations are computed. These grasping quality values are compared with numerical human assessments, that are obtained via a psychophysical magnitude estimation method. We derive an augmented weighted functional that combines these three formulations, and show that it exhibits a high correlation with human quality assessment. Our results demonstrate that the most dominant mechanism that characterizes the quality of a rigid body grasp is the uniformity level of the contact forces. © 1997 John Wiley & Sons, Inc.     

A real-time strategy for dexterous manipulation: Fingertips motion planning,force sensing and grasp stability

This paper presents a global strategy for object manipulation with the fingertips with an anthropomorphic dexterous hand: the LMS Hand of the ROBIOSS team from PPRIME Institute in Poitiers (France). Fine manipulation with the fingertips requires to compute on one hand, finger motions able to produce the desired object motion and on the other hand, it is necessary to ensure object stability with a real time scheme for the fingertip force computation. In the literature, lot of works propose to solve the stability problem, but most of these works are grasp oriented; it means that the use of the proposed methods are not easy to implement for online computation while the grasped object is moving inside the hand. Also simple real time schemes and experimental results with full-actuated mechanical hands using three fingers were not proposed or are extremely rare. Thus we wish to propose in a same strategy, a robust and simple way to solve the fingertip path planning and the fingertip force computation. First, finger path planning is based on a geometric approach, and on a contact modelling between the grasped object and the finger. And as force sensing is required for force control, a new original approach based on neural networks and on the use of tendon-driven joints is also used to evaluate the normal force acting on the finger distal phalanx. And an efficient algorithm that computes fingertip forces involved is presented in the case of three dimensional object grasps. Based on previous works, those forces are computed by using a robust optimization scheme.In order to validate this strategy, different grasps and different manipulation tasks are presented and detailed with a simulation software, SMAR, developed by the PPRIME Institute. And finally experimental results with the real hand illustrate the efficiency of the whole approach.     

Computation of Independent Contact Regions for Grasping 3-D Objects

Precision grasp synthesis has received a lot of attention in past few last years. However, real mechanical hands can hardly assure that the fingers will precisely touch the object at the computed contact points. The concept of independent contact regions (ICRs) was introduced to provide robustness to finger positioning errors during an object grasping: A finger contact anywhere inside each of these regions assures a force-closure grasp, despite the exact contact position. This paper presents an efficient algorithm to compute ICRs with any number of frictionless or frictional contacts on the surface of any 3-D object. The proposed approach generates the independent regions by growing them around the contact points of a given starting grasp. A two-phase approach is provided to find a locally optimal force-closure grasp that serves as the starting grasp, considering as grasp quality measure the largest perturbation wrench that the grasp can resist, independently of the perturbation direction. The proposed method can also be applied to compute ICRs when several contacts are fixed beforehand. The approach has been implemented, and application examples are included to illustrate its performance.      

机器人多指操作的递阶控制

为机器人多指协调操作建立一递阶控制系统.给定一操作任务,任务规划器首先生 成一系列物体的运动速度;然后,协调运动规划器根据期望的物体运动速度生成期望的手指 运动速度和期望的抓取姿态变化;同时,抓取力规划器为平衡作用在物体上的外力,根据当前 的抓取姿态,生成各手指所需的抓取力;最后,系统将手指的期望运动速度与为实现期望抓取 力而生成的顺应速度合并,并通过手指的逆雅可比转化为手指关节运动速度后,由手指的关 节级运动控制器实现手指的运动和抓取力的控制.该控制方法已成功应用于香港科技大学 (HKUST)灵巧手控制系统的开发.实验证明该方法不仅能完成物体轨迹的跟踪控制任务, 而且能完成物体对环境的力控制和力与速度的混合控制.     

A Polyhedral Bound on the Indeterminate Contact Forces in Planar Quasi-Rigid Fixturing and Grasping Arrangements

This paper considers multiple-contact arrangements where several bodies grasp, fixture, or support an object via frictional point contacts. Within a strictly rigid-body modeling paradigm, when an external wrench (i.e., force and torque) acts on the object, the reaction forces at the contacts are typically indeterminate and span an unbounded linear space. This paper analyzes the contact reaction forces within a generalized quasi-rigid-body framework that keeps the desirable geometric properties of rigid-body modeling, while also including more realistic physical effects. We describe two basic principles that govern the contact mechanics of quasi-rigid bodies. The main result is that for any given external wrench acting on a quasi-rigid object, the statically feasible contact reaction forces lie in a bounded polyhedral set that depends on the external wrench, the grasp's geometry, and the preload forces. Moreover, the bound does not depend upon any detailed knowledge of the contact mechanics parameters. When some knowledge of the parameters is available, the bound can be sharpened. The polyhedral bound is useful for “robust” grasp and fixture synthesis. Given a set of external wrenches that may act upon an object, the grasp's geometry and preload forces can be chosen such that all of these external wrenches would be automatically supported by the contacts.     

Computation for Maximum Stable Grasping in Dynamic Force Distribution

One of the fundamental problems in grasping and manipulation of an object by a multi-fingered robotic hand is the computation of contact forces to equilibrate the dynamic external wrench on the grasped object. This paper proposes a two-phase algorithm to calculate the contact forces in order to achieve maximum grasp stability, assuming there is no any slippage in the process of grasping. In the off-line phase, a nonsingular simplex set is obtained by the zone triangulation of the contact primitive wrench set in the wrench space, and the neighbors of the resultant simplexes are recorded by a neighbor-searching procedure. In the on-line phase, a specific simplex in which the required resultant wrench is located can find out rapidly since all neighbors of each simplex have been recorded before. The optimal contact forces can be obtained by the combination of the primitive forces corresponding to the vertices of this simplex. A numerical example shows the proposed algorithm takes a thousandth of the computation time exhausted by the sequential quadratic programming (SQP) or the straightforward bisection method with only a slight lost of optimality, and obtains better solution compared to the decomposition and positive combination (DPC) algorithm at the similar computation speed.     

Seven fingers allow force-torque closure grasps on any convex polyhedron

We prove that a robot hand whose fingers make frictionless contact with a convex polyhedral object will be able to find a grasp where the hand can exert any desired force-torque on the object provided the hand has seven fingers. We present an algorithm for grasping any convex polyhedron and we prove rigorously that it works for any convex polyhedron. The algorithm requiresO(n ^3/2logn) steps (in the worst case) wheren is the number of vertices.     

Dynamic force/torque balance of 2D polygonal objects by a pair of rolling contacts and sensory‐motor coordination

It is well known that three frictionless fingers suffice to immobilize any 2D object with triangular shape but four fingers are necessary for a parallelepiped. However, it has been recently shown that only two fingers are enough to realize secure grasp of a rigid object with parallel flat surfaces in a dynamic sense if finger ends have a hemispherical shape with appropriate radius and thereby rollings are induced between finger ends and object surfaces. This paper focuses on the two problems: (1) dynamic force/torque balance of 2D polygonal objects under the effect of gravity force by means of a pair of rolling contacts and (2) concurrent realization of dynamically secure grasp and orientation control of 2D polygonal objects by using a pair of multi‐fingered hands with hemispherical ends and sensory feedback signals without knowing object kinematics and mass center. It is shown that the force/torque balance can be attained by controlling both the contact positions and inducing adequate forces in both normal and tangential directions at each of contact points indirectly through finger joints without knowing object mass center and other kinematic parameters. © 2003 Wiley Periodicals, Inc.     

考虑物体弹性的多指抓持力的优化

本文基于多指抓持中的动力学程，在考虑了接触旋量和关节力矩的限制条件基础上，采用弹性接触力学推导了手－物体接触时法向压应力和切向剪应力的计算公式，提出了安全抓持弹性物体对接触力的限制条件，把动力学方程的静不定问题归结为具有线性的二次规划问题，使用共轭梯度投影法解决了这种二次求解问题。     

Fast Computation of Optimal Contact Forces

We consider the problem of computing the smallest contact forces, with point-contact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP) or a second-order cone problem (SOCP), and thus, can be solved using several standard algorithms for these problem classes. In this paper, we describe a custom interior-point algorithm for solving the FOP that exploits the specific structure of the problem, and is much faster than these standard methods. Our method has a complexity that is linear in the number of contact forces, whereas methods based on generic SDP or SOCP algorithms have complexity that is cubic in the number of forces. Our method is also much faster for smaller problems. We derive a compact dual problem for the FOP, which allows us to rapidly compute lower bounds on the minimum contact force and certify the infeasibility of a FOP. We use this dual problem to terminate our optimization method with a guaranteed accuracy. Finally, we consider the problem of solving a family of FOPs that are related. This occurs, for example, in determining whether force closure occurs, in analyzing the worst case contact force required over a set of external forces and torques, and in the problem of choosing contact points on an object so as to minimize the required contact force. Using dual bounds, and a warm-start version of our FOP method, we show how such families of FOPs can be solved very efficiently.     

High Precision Constrained Grasping with Cooperative Adaptive Handcontrol

A method for high precision constrained object manoeuvering for non-redundant rigid multifinger hands is proposed. A passivity-based adaptive cooperative control scheme carries out compensation of all uncertain inertial and dynamic friction forces to guarantee asymptotic tracking of all contact forces and joint position-orientation trajectories over orthogonal force- and position-based impedance error manifolds. Optimal internal and external force trajectories are obtained to minimize the contact forces onto the constrained object while exerting a given desired contact force onto the environment. The simulation study of two robot fingers manipulating a constrained object for combined fast and slow velocity regimes shows that when the dynamic friction compensation is turned on tracking errors decrease tenfold.     

虚拟手抓持力觉生成算法真实性的评价

目的 虽然许多学者研发了多种虚拟手交互触力觉生成算法,但是如何评价虚拟手交互触力觉生成算法的真实性是一个富有挑战性的新问题,值得深入研究.方法 构建手指抓持力测量平台,设计3种抓持姿态下指尖静力抓持球体实验内容,测得各指尖作用力的实测值;通过虚拟手静力抓持力觉生成算法,求得这3种抓持姿态下各手指作用力的理论值;对实测值进行统计和分析,并与理论值进行对比和讨论;结果 日常抓持经验和实测值是完全相符的,实测值和理论值很接近且偏差均在可接受范围之内.单个手指作用力或多个手指合力的实测值与理论值的偏差均在1%6%.结论 本文实现了一种基于物理的实验方法,评价和分析了虚拟手静力抓持力觉生成算法的真实性,证实此算法可以逼真地生成虚拟手抓持力,可应用于具有力反馈的自然的虚拟手交互.     

Compliant grasping with passive forces

Because friction is central to robotic grasp, developing an accurate and tractable model of contact compliance, particularly in the tangential direction, and predicting the passive force closure are crucial to robotic grasping and contact analysis. This paper analyzes the existence of the uncontrollable grasping forces (i.e., passive contact forces) in enveloping grasp or fixturing, and formulates a physical model of compliant enveloping grasp. First, we develop a locally elastic contact model to describe the nonlinear coupling between the contact force with friction and elastic deformation at the individual contact. Further, a set of “compatibility” equations is given so that the elastic deformations among all contacts in the grasping system result in a consistent set of displacements of the object. Then, combining the force equilibrium, the locally elastic contact model, and the “compatibility” conditions, we formulate the natural compliant model of the enveloping grasp system where the passive compliance in joints of fingers is considered, and investigate the stability of the compliant grasp system. The crux of judging passive force closure is to predict the passive contact forces in the grasping system, which is formulated into a nonlinear least square in this paper. Using the globally convergent Levenberg‐Marquardt method, we predict contact forces and estimate the passive force closure in the enveloping grasps. Finally, a numerical example is given to verify the proposed compliant enveloping grasp model and the prediction method of passive force closure. © 2005 Wiley Periodicals, Inc.     

Finding locally optimum force-closure grasps

This paper presents an iterative procedure to find locally optimum force-closure grasps on 3D objects, with or without friction and with any number of fingers. The object surface is discretized in a cloud of points, so the approach is applicable to objects with any arbitrary shape. The approach finds an initial force-closure grasp that is then iteratively improved through an oriented search procedure. The grasp quality is measured considering the largest perturbation wrench that the grasp can resist with independence of the direction of perturbation. The efficiency of the algorithm is illustrated through numerical examples.