On the existence and synthesis of multifinger positive grips

We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are calledpositive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip. We also present efficient algorithms to synthesize such positive grips for bounded polyhedral/polygonal objects; the number of fingers employed in the grips synthesized by our algorithms match the above bounds. The algorithms run in time linear in the number of faces/sides. The paper may be of independent interest for its presentation of algorithms arising in the study of positive linear spaces.     

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.     

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.     

A Theoretical Approach of an Intelligent Robot Gripper to Grasp Polygon Shaped Objects

This paper presents an approach for grasp planning and grasp forces optimization of polygon shaped objects. The proposed approach is an intelligent rule-based method that figures out the minimal number of fingers and minimal values of contact forces. These fingers are required to securely grasp a rigid body in the presence of friction and under the action of some external force. This is accomplished by finding optimal contact points on the object boundary along with minimal number of fingers required for achieving the aforementioned goal. Our system handles every object case independently. It generates a rule base for each object based on adequate values of external forces. The system uses the genetic algorithm as its search mechanism, and a rule evaluation mechanism called bucket brigade for the reinforcement learning of the rules. The process mainly consists of two stages; learning then retrieval. Retrievals act on line utilizing previous knowledge and experience embedded in a rule base. If retrievals fail in some cases, learning is presumed until that case is resolved. The algorithm is very general and can be adapted for interface with any object shape. The resulting rule base varies in size according to the degree of difficulty and dimensionality of the grasping problem.     

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.     

Learning Binary Relations Using Weighted Majority Voting

In this paper we demonstrate how weighted majority voting with multiplicative weight updating can be applied to obtain robust algorithms for learning binary relations. We first present an algorithm that obtains a nearly optimal mistake bound but at the expense of using exponential computation to make each prediction. However, the time complexity of our algorithm is significantly reduced from that of previously known algorithms that have comparable mistake bounds. The second algorithm we present is a polynomial time algorithm with a non-optimal mistake bound. Again the mistake bound of our second algorithm is significantly better than previous bounds proven for polynomial time algorithms.A key contribution of our work is that we define a non-pure or noisy binary relation and then by exploiting the robustness of weighted majority voting with respect to noise, we show that both of our algorithms can learn non-pure relations. These provide the first algorithms that can learn non-pure binary relations.The first author was supported in part by NSF grant CCR-91110108 and NSF National Young Investigator Grant CCR-9357707 with matching funds provided by Xerox Corporation, Palo Alto Research Center and WUTA. The second author was supported by ONR grant NO0014-91-J-1162 and NSF grant IRI-9123692.     

Inter-digit co-ordination and object-digit interaction when holding an object with five digits

The current study investigated inter-digit co-ordination and object-digit interaction during sustained object holding tasks by using five, six-component force/torque sensors. The sum of the individual finger normal forces and the thumb normal force showed a parallel variation with a mean median correlation coefficient of 0.941. The normal force traces demonstrated the lowest coefficient of variation (about 9% as averaged across digits) as compared with other force/torque traces. The sum for the variances of the normal forces of the index, middle, ring, and little fingers was about 50% of the variance of the summed normal force of the four fingers. Of the five digits, the thumb, index, middle, ring and little fingers accounted for 50.0, 15.4, 14.6, 11.7 and 7.3% of the total normal force; and 39.4, 9.9, 19.3, 14.0 and 17.5% of the total vertical shear force (i.e. the load), respectively. The ratios of the normal force to the resultant shear force were 2.6, 4.5, 1.8, 2.2 and 1.3 for the thumb, index, middle, ring and little finger, respectively. The centre of pressure migration area of a single digit at the object-digit surface during object holding ranged from 0.30 to 1.21 mm². The current study reveals a number of detailed object-digit mechanics and multiple digits co-ordination principle. The results of this study may help to improve ergonomic designs that involve the usage of multiple digits.     

Inter-digit co-ordination and object-digit interaction when holding an object with five digits

The current study investigated inter-digit co-ordination and object-digit interaction during sustained object holding tasks by using five, six-component force/torque sensors. The sum of the individual finger normal forces and the thumb normal force showed a parallel variation with a mean median correlation coefficient of 0.941. The normal force traces demonstrated the lowest coefficient of variation (about 9% as averaged across digits) as compared with other force/torque traces. The sum for the variances of the normal forces of the index, middle, ring, and little fingers was about 50% of the variance of the summed normal force of the four fingers. Of the five digits, the thumb, index, middle, ring and little fingers accounted for 50.0, 15.4, 14.6, 11.7 and 7.3% of the total normal force; and 39.4, 9.9, 19.3, 14.0 and 17.5% of the total vertical shear force (i.e. the load), respectively. The ratios of the normal force to the resultant shear force were 2.6, 4.5, 1.8, 2.2 and 1.3 for the thumb, index, middle, ring and little finger, respectively. The centre of pressure migration area of a single digit at the object-digit surface during object holding ranged from 0.30 to 1.21 mm(2). The current study reveals a number of detailed object-digit mechanics and multiple digits co-ordination principle. The results of this study may help to improve ergonomic designs that involve the usage of multiple digits.     

Dynamics and Stability of Blind Grasping of a 3-Dimensional Object under Non-holonomic Constraints

A mathematical model expressing the motion of a pair of multi-DOF robot fingers with hemi-spherical ends, grasping a 3-D rigid object with parallel flat surfaces, is derived, together with non-holonomic constraints. By referring to the fact that humans grasp an object in the form of precision prehension, dynamically and stably by opposable forces, between the thumb and another finger (index or middle finger), a simple control signal constructed from finger-thumb opposition is proposed, and shown to realize stable grasping in a dynamic sense without using object information or external sensing (this is called "blind grasp" in this paper). The stability of grasping with force/torque balance under non-holonomic constraints is analyzed on the basis of a new concept named "stability on a manifold". Preliminary simulation results are shown to verify the validity of the theoretical results.     

自适应融合颜色和深度信息的人体轮廓跟踪

采用活动轮廓对人体目标建模,提出一 种新的水平集框架下自适应融合RGB-D图像的颜色和深度信息的人体轮廓跟踪方法. 设计了一种基于超像素的局部自适应权重计算方法,自动确定深度信息在水平集演化中的重要性. 基于深度信息的活动轮廓驱动外力包括由边缘生成的梯度向量流和由目标/背景深度模型生成的置信图,基于颜色信息的驱动外力由目标/背景颜色模型生成的置信图,这三种外力通过局部自适应权重融合,驱动活动轮廓向目标的边界演化.为了得到更加精确的目标轮廓和防止误差漂移,基于本文观察到的人体表面在深度图像中的两个特性,提出两个简单但有效的算法对水平集方法得到的结果进行精化调整. 最后,通过实验验证了本文算法的优越性.     

Grip posture and forces during holding cylindrical objects with circular grips

Individual finger position and external grip forces were investigated while subjects held cylindrical objects from above using circular precision grips. Healthy females (n = 11) and males (n = 15) lifted cylindrical objects of various weights (05, 10 and 20kg), and varied diameters (50, 7-5 and 100cm) using the 5-finger grip mode. The effects of 4-, 3- and 2-finger grip modes in the circular grip were also investigated.

Individual finger position was nearly constant for all weights and for diameters of 5-0 and 7-5 cm. The mean angular positions for the index, middle, ring and little fingers relative to the thumb were 98°, 145°, 181°, and 236°, respectively. At the 10-cm diameter, the index and middle finger positions increased, while the ring and little finger positions decreased. There were no differences in individual finger position with regard to gender, hand dimension, or hand strength.

Total grip force increased with weight, and at diameters greater or lesser than 7-5 cm. Total grip force also increased as the number of fingers used for grasping decreased. Although the contribution of the individual fingers to the total grip force changed with weight and diameter, the thumb contribution always exceeded 38% followed by the ring and little fingers, which contributed approximately 18-23% for all weights and diameters. The contribution of the index finger was always smallest (>11%). There was no gender difference for any of the grip force variables. The effects of hand dimension and hand strength on the individual finger grip forces were subtle.     

Intelligent control of multi-fingered hands

This paper is concerned with intelligent control for grasping and manipulation of an object by multi-fingered robot hands with rigid or soft hemispheric finger ends that induce rolling contacts with the object. Even in the case of 2D motion like pinching by means of a pair of multi-degrees of freedom robot fingers, there arises an interesting family of Lagrange’s equations of motion with many geometric constraints, which are under-actuated, redundant, and non-holonomic in some sense. Regardless of underactuation of dynamics, it is possible to find a class of sensory feedback signals that realize secure grasp of an object together with control of object orientation. In regard to the secure grasping, a problem of force/torque closure for 2D objects in a dynamic sense plays a crucial role. It is shown that proposed sensory feedback signals satisfying the dynamic force/torque closure can be constructed without knowing object kinematic parameters and location of the mass center. To prove the convergence of motion of the overall fingers–object system under the circumstance of redundancy of joints, new concepts called “stability on a manifold” and “asymptotic stability on a manifold” are introduced. Based on the results found for intelligent control of robotic hands, the last two sections attempt to discuss why human multi-fingered hands can become so dexterous at grasping and object manipulation.     

Parallel algorithms for arrangements

We give the first efficient parallel algorithms for solving the arrangement problem. We give a deterministic algorithm for the CREW PRAM which runs in nearly optimal bounds ofO (logn log^* n) time andn ²/logn processors. We generalize this to obtain anO (logn log^* n)-time algorithm usingn ^d /logn processors for solving the problem ind dimensions. We also give a randomized algorithm for the EREW PRAM that constructs an arrangement ofn lines on-line, in which each insertion is done in optimalO (logn) time usingn/logn processors. Our algorithms develop new parallel data structures and new methods for traversing an arrangement.This work was supported by the National Science Foundation, under Grants CCR-8657562 and CCR-8858799, NSF/DARPA under Grant CCR-8907960, and Digital Equipment Corporation. A preliminary version of this paper appeared at the Second Annual ACM Symposium on Parallel Algorithms and Architectures [3].     

Probabilistic Algorithms for Efficient Grasping and Fixturing

Given an object with n points on its boundary where fingers can be placed, we give algorithms to select a ``strong' grasp with the least number c of fingers (up to a logarithmic factor) using several measures of goodness. Along similar lines, given an integer c , we find the ``best' κ c log c finger grasp for a small constant κ . In addition, we generalize existing measures for the case of frictionless assemblies of many objects in contact. We also give an approximation scheme which guarantees a grasp quality close to the overall optimal value where fingers are not restricted to preselected points. These problems translate into a collection of convex set covering problems where we either minimize the cover size or maximize the scaling factor of an inscribed geometric object L . We present an algorithmic framework which handles these problems in a uniform way and give approximation algorithms for specific instances of L including convex polytopes and balls. The framework generalizes an algorithm for polytope covering and approximation by Clarkson [Cla] in two different ways. Let , where d is the dimension of the Euclidean space containing L . For both types of problems, when L is a polytope, we get the same expected time bounds (with a minor improvement), and for a ball, the expected running time is for fixed d , and arbitrary positive δ . We improve this bound if we allow in addition a different kind of approximation for the optimal radius. We also give bounds when d is not a constant. Received November 14, 1996; revised June 20, 1997, and January 9, 1998.     

New bounds on the number of frictionless fingers requied to immobilize

Using a novel second-order mobility theory that was recently developed by the authors, this article develops new lower bounds on the number of frictionless fingers required to immobilize generic planar objects. We show that any generic smooth or polygonal planar object can be immobilized with three convex fingers or fixtures that have sufficiently flat curvature. Further, if it is possible to specify the fingertip curvature, then any generic smooth or polygonal object can be immobilized with two, possibly concave, fingers. © 1995 John Wiley & Sons, Inc.     

Power grasp force distribution control using artificial neural networks

In this article, methods for force distribution control of power grasp are developed. A power grasp is characterized by multiple points of contact between the object grasped and the surfaces of the fingers and palm. The grasp is highly stable because of form closure. However, modeling power grasps is difficult because of the resulting closed kinematic structure and the complexity of multiple contacts. The first method used to obtain the desired force distribution is based on linear programming. In particular, a model of the DIGITS grasping system, under development at The Ohio State University, is used, and constraint equations are formulated for force balance and actuator torque limits. Supervisory control of the desired forces at the contacts is achieved by prescribing a desired clinch level. The objective function is designed to achieve the desired clinch level, except in cases where the specified force is inadequate to stably hold the object. Although this method yields the desired force distribution, a second method based on artificial neural networks (ANNs) is developed to achieve constant-time solutions. Linear programming solutions are used to generate training data for a set of ANNs. Two techniques, modular networks and adaptive slopes, are also developed and employed in the training to improve the training time and accuracy of the ANNs. The results show that the ANNs learn the appropriate nonlinear mapping for the force distribution and provide stable grasp over a wide range of object sizes and clinch levels.     

Contributions and co-ordination of individual fingers in multiple finger prehension

The contributions and co-ordination of external ringer grip forces were examined during a lifting task with a precision grip using multiple fingers. The subjects ( n = 10) lifted a force transducer-equipped grip apparatus. Grip force from each of the five fingers was continuously measured under different object weight (200 g, 400 g, and 800 g) and surface structure (plastic and sandpaper) conditions. The effect of five-, four-, and three-finger grip modes was also examined. It was found that variation of object weight or surface friction resulted in change of the total grip force magnitude; the largest change in finger force, was that for the index finger, followed by the middle, ring, and little fingers. Percentage contribution of static grip force to the total grip force for the index, middle, ring, and little fingers was 420%, 27·4%, 17·6% and 12·9%, respectively. These values were fairly constant for all object weight conditions, as well as for all surface friction conditions, suggesting that all individual finger force adjustments for light loads less than 800 g are controlled comprehensively simply by using a single common scaling value. A higher surface friction provided faster lifting initiation and required lesser grip force exertion, indicating advantageous effect of a non-slippery surface over a slippery surface. The results indicate that nearly 40% force reduction can be obtained when a non-slippery surface is used. Variation in grip mode changed the total grip force, i.e., the fewer the number of fingers, the greater the total grip force. The percent value of static grip force for the index, middle, and ring fingers in the four-finger grip mode was 42·7%, 32·5%, and 24·7%, respectively, and that for the index and middle fingers in the three-finger grip mode was 43·0% and 56·9%, respectively. Therefore, the grip mode was found to influence the force contributions of the middle and ring fingers, but not of the index finger.     

Randomized competitive algorithms for the list update problem

We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constantd. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful.A preliminary version of these results appeared in a joint paper with S. Irani in theProceedings of the 2nd Symposium on Discrete Algorithms, 1991 [17].This research was partially supported by NSF Grants CCR-8808949 and CCR-8958528.This research was partially supported by NSF Grant CCR-9009753.This research was supported in part by the National Science Foundation under Grant CCR-8658139, by DIMACS, a National Science Foundation Science and Technology center, Grant No. NSF-STC88-09648.     

基于六维力传感器的工业机器人末端负载受力感知研究

针对工业机器人末端负载与外界环境接触力的感知需求,在机器人法兰与负载之间设置六维力传感器,并研究一套标定与计算方法,综合考虑负载重力作用、传感器零点、机器人安装倾角等因素,利用不少于3个机器人姿态下的力传感器数据,可求得传感器零点、机器人安装倾角、负载重力大小、负载重心坐标等参数,进一步可消除传感器零点及负载重力对受力感知的影响,精确得到机器人末端负载所受的外部作用力与力矩.实验得到对于重量从320N到1917N的负载,在静态条件下,感知外力的误差在负载重力的0.28%以内,感知外力矩的误差在负载对传感器力矩的0.59%以内.