利用視覺特征確定抓取點(diǎn)外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯
利用視覺特征確定抓取點(diǎn)外文文獻(xiàn)翻譯、中英文翻譯、外文翻譯,利用,視覺,特征,確定,抓取,外文,文獻(xiàn),翻譯,中英文
Grasping Points Determination Using Visual Features
Madjid Boudaba1 , Alicia Casals2 and Heinz Woern3
1 Design Center, TES Electronic Solutions GmbH, Stuttgart
2 GRINS: Research Group On Intelligent Robots and Systems,Technical University of
Catalonia, Barcelona
3 Institute of Process Control and Robotics (IPR), University of Karlsruhe
Introduction
This paper discusses some issues for generating point of contact using visual features. To address these issues, the paper is divided into two sections: visual features extraction and grasp planning. In order to provide a suitable description of object contour, a method for grouping visual features is proposed. A very important aspect of this method is the way knowledge about grasping regions are represented in the extraction process, which is used also as filtering process to exclude all undesirable grasping point (unstable points) and all line segments that do not fit to the fingertip position. Fingertips are modelled as point contact with friction using the theory of polyhedral convex cones. Our approach uses three-finger contact for grasping planar objects. Each set of three candidate of grasping points is formu- lated as linear constraints and solved using linear programming solvers. Finally, we briefly describe
some experiments on a humanoid robot with a stereo camera head and an anthropomorphic robot hand within the ”Centre of excellence on Humanoid Robots: Learning and co-operating.Systems” at the University of Karlsruhe and Forchungszentrum Karlsruhe.
Related work
Grasping by multi-fingered robot hands has been an active research area in the last years. Several important studies including grasp planning, manipulation and stability analysis have been done. Most of these researches assume that the geometry of the object to be grasped is known, the fingertip touches the object in a point contact without rolling, and the position of the contact points are estimated based on the geometrical constraints of the 2.Madjid Boudaba, Alicia Casals and Heinz Woern grasping system. These assumptions reduce the complexity of the mathema.tical model of the grasp (see [Park and Starr, 1992], [Ferrari and Canny, 1992], [Ponce and Faverjon, 1995], [Bicchi and Kumar, 2000], [J. W. Li and Liu, 2003]). A few work, however has been done in integrating vision-sensors for grasping and manipulation tasks. To place our approach in perspective, we review existence methods for sensor based grasp planning. The existing literature can be broadly classified in two categories; vision based and tactile based. For both categories, the extracted image features are of concern which are vary from geometric primitives such as edges, lines,
vertices, and circles to optical flow estimates. The first category uses visual features to estimate the robot’s motion with respect to the object pose [Maekawa et al., 1995], [Smith and Papanikolopoulos, 1996], [Allen et al., 1999]. Once the robot hands is already aligned with object, then it needs only to know where the fingers are placed on the object. The second category of sensor uses tactile features to estimate the touch sensing area that in contact with the object [Berger and Khosla, 1991], [Chen et al., 1995], [Lee and Nicholls, 1999]. A practical drawback is that the grasp execution is hardly reactive to sensing errors such as finger positioning errors. A vision sensor, meanwhile, is unable to handle occlusions. Since an object is grasped according to its CAD model [Koller et al., 1993], [Wunsch et al., 1997], [Sanz et al., 1998], [N. Giordana and Spindler, 2000], [Kragic et al., 2001], an image also contains redundant information that could become a source of errors and ineffciency in the processing.
This paper is an extension of our previous works [Boudaba and Casals, 2005], [Boudaba et al., 2005], and [Boudaba and Casals, 2006] on grasp planning using visual features. In this work, we demonstrate its utility in the context of grasp (or fingers) positioning. Consider the problem of selecting and executing a grasp. In most tasks, one can expect various uncertainties. To grasp an object implies building a relationship between the robot hand and object model. The latter is often unavailable or poorly known. So selecting a grasp position from such model can be unprecise or unpracticable in real time applications. In our approach, we avoid to use any object model and instead it works directly from image features. In order to avoid fingers positioning error, a set of grasping regions is defined that represents the features of grasping contact point. This not only avoids detection/localization errors but also saves computations that could affect the reliability of the system. Our approach can play the critical role of forcing the fingers to a desired positions before the task of grasping is executed.
The proposed work can be highlighted in two major phases:
1. Visual information phase: In this phase, a set of visual features such as object size, center of mass, main axis for orientation, and object’s boundary are extracted. For the purpose of grasping region determination, extracting straight segments are of concern using the basic results from contour based shape representation techniques. We will focus on the class techniques that attempt to represent object’s contour into a model graph, which preserves the topological relationships between features.
2. Grasp planning phase: The grasping points are generated in the planning task taking as input these visual features extracted from the first phase. So a relationship between visual features and grasp planning is proposed. Then a set of geometrical functions is analysed to find a feasible solution for grasping. The result of grasp planning is a database contains a list of:
l Valid grasps. all grasps that fulfill the condition of grasp.
l Best Grasps. a criterion for measuring a grasp quality is used to evaluate the best grasps from a list of valid grasps.
l Reject grasps. those grasps that do not fulfill the condition of grasp.
The remainder of this chapter is organized as follows: Section 3 gives some background for grasping in this direction. The friction cone modeling and condition of force-closure grasps are discussed. In section 4, a vision system framework is presented. The vision system is divided into two parts: the first part concerning to 2D grasping and the second part concerning 3D grasping. we first discuss the extracted visual information we have integrated in grasp planning, generation of grasping regions by using curves fitting and merging techniques, and discuss the method of selecting valid grasps using the condition of force-closure grasp. We then discuss the algorithm for computing feasible solutions for grasping in section 5. We verify our algorithm by presenting experimental results of 2D object grasping with three-fingers. Finally, we discuss the result of our approach, and future work in section 6.
Grasp Background
Our discussion is based on [Hirai, 2002]. Given a grasp which is characterized by a set of contact points and the associated contact models, determine if the grasp has a force-closure. For point contact, a commonly used model is point contact with friction (PCWF). In this model, fingers can exert any force pointing into friction cone at the edge of contacts (We use edge contact instead of point contact and can be described as the convex sum of proper point contacts). To fully analyze the grasp feasibility, we need to examine the full space of forces acting on the object. Forming the convex hull of this space is diffcult due to the nonlinear friction cone constraints imposed by the contact models. In this section, we only focus in precision grasps, where only the fingertips are in contact with the object. After discussing the friction cone modeling, a form alizme is used for analysing the force closure grasps using the theory of polyhedral convex cones.
Modeling the Point of Contac
A point of contact with friction (sometimes referred to as a hard-finger) im- poses non linear constraints on the force inside of its friction cones. For the analysis of the contact forces in planar grasps, we simplify the problem by modeling the friction cones as a convex polytopes using the theory of polyhedral convex cones attributed to [Goldman and Tucker, 1956]. In order to construct the convex polytope from the primitive contact forces, the following theorem states that a polyhedral convex cone (PCC) can be generated by a set of basic directional vectors.
Figure 1. Point Contact Modelling
Theorem 1. A convex cone is a polyhedral if and only if it is finitely generated, that is, the cone is generated by a finite number of vectors v1,v2,?,vm
where the coeffcients αiare all non negative. Since vectors ui through um span the cone, we write 1 simply by C=span {u1, u2, ..., um}. The cone spanned by a set of vectors is the set of all nonnegative linear combinations of its vectors. A proof of this theorem can be found in [Goldman and Tucker, 1956]. Given a polyhedral convex set C, let vert(P)={u1, u2, ..., um} stand for vertices of a polytope P,while face(P)={F1, ..., FM} denotes its faces. In the plane, a cone has the appearance as shown in Figure 1(b). This means that we can reduce the number of cone sides, m = 6 to one face, Ci.Let’s denote by P, the convex polytopes of a modelled cone, and {u1, u2, u3} its three vertices. We can define such polytope as
where ui denotes the i-th vertex of P, and up is the total number of vertices.
n=2 in the case of a 2D plane.
Force-Closure Grasps
The force-closure of a grasp is evaluated by analysing its convex cone. For a set of friction cone intersection, the full space can be defined by
where k is the number of grasping contacts. Note that the result of is a set of polytopes intersections and produces either an empty set or a bounded convex polytopes. Therefore, the solution of (3) can be expressed in terms of its extreme vertices
where vp is the total number of extreme vertices.
Figure 2. Feasible solution of a three-fingered grasp
Figure 2 illustrates an example of feasible solution of and its grasp space represented by its extreme vertices P = {v1,v2,?,vm}. From this figure, two observations can be suggested: first, if the location of a fingertip is not a solution to the grasp, it is possible to move along its grasping region. Such displacement is defined byui=ui0+βitiwhere βi is constrained by 0≤βi≤li and ui b e a p o i n t ed v e r t e x o f Ci. Second, we define a ray passing through the pointed vertex ui, by a function. The vector vci=[vcix,vciy]∈R2 varies from the lower to the upper side of the spanned cone Ci. This allows us to check whether the feasible solution remains for all Vci in the cone spanned by u2 and u3 (see Figure 1(b)).Testing the force-closure of a grasp now becomes the problem of finding the solutions to (4). In other words, finding the parameters of (3) that the (4) is a bounded convex polytopes
System Description
We are currently developing a robotic system that can operate autonomously in an unknown environment. In this case, the main objective is the capability of the system to (1) locate and measure objects, (2) plan its own actions, and (3) self adaptable grasping execution. The architecture of the whole system is organized into several modules, which are embedded in a distributed object communication framework. There are mainly three modules which are concerned in this development: the extraction of visual information and its interpretation, grasp planning using the robot hand, the control and execution of grasps.
(a) Experimental setup (b) Stereo vision head
Figure 3. Robotic system framework. (a) An humanoid robot arm (7DOF) and an antropomorphic robot hand (10DOF). (b) Stereo vision system
1.1 The Robot Hand
The prototype of the anthropomorphic robot hands (see [Schulz et al. 2001]) has a 7 degrees of freedom (DOF) arm (see Fig. 3(a)). This first prototype is currently driven pneumatically and is able to control the 10 DOF separately, but the joints can only be fully opened or closed. The robot's task involve controlling the hand for collision-free grasping and manipulation of objects in the three dimensional space. The system is guided solely by visual information extracted by the vision system.
1.2 The Vision System
The vision system shown in Fig. 3(b) consists of a stereo camera (MEGA-D from Videre Design) mounted on pan-tilt heads equipped with a pair of 4.8 mm lenses and has a fixed baseline of about 9 cm. The pan-tilt head provides two additional degrees of freedom for the cameras, both of them rotational. The MEGA-D stereo head uses a IEEE 1394 firewire interface to connect to a workstation and has a SRI's Small Vision System (SVS) software for calibration and stereo correlation (see [Konolige, 1997]).
For its complexity, the flow diagram of visual information has been divided into two parts. The first part provides details of 2D visual features extraction. The second part is dedicated to 3D visual features retrieval. The image acquisition primarily aims at the conversion of visual information to electrical signals, suitable for computer interfacing. Then, the incoming image is subjected to processing having in mind two purposes: (1) removal of image noise via low-pass filtering by using Gaussian filters due to its computational simplicity and (2) extraction of prominent edges via high-pass filtering by using the Sobel operator. This information is finally used to group pixels into lines, or any other edge primitive (circles, contours, etc). This is the basis of the extensively used Canny's algorithm [Canny, 1986]. So, the basic step is to identify the main pixels that may preserve the object shape. As we are visually determining grasping points, the following sections provide some details of what we need for our approach.
Contour Based Shape Representation
Due to their semantically rich nature, contours are one of the most commonly used shape descriptors, and various methods for representing the contours of 2D objects have been proposed in the literature [Costa and Cesar, 2001]. Extracting meaningful features from digital curves, finding lines or segments in an image is highly significant in grasping application. Most of the available methods are variations of the dominant point detection algorithms [M. Marji, 2003]. The advantage of using dominant points is that both, high data compression and feature extraction can be achieve. Other works prefer the method of polygonal approximation using linking and merging algorithms [Rosin, 1997] and curvature scale space (CSS) [Mokhtarian and Mackworth, 1986].
A function regrouping parameters of visual features together can be defined by
Where vlist=(V1,V2,?,Vm) is a list of consecutive contour’s vertices with Vi=(xi, yi) that represents the location of relative to the center of mass of the object, com=(xc, yc). slist={S1, S2，···，Sm } is a list of consecutive contour’s segments. Both lists and slist are labelled counter-clockwise (ccw) order about the center of mass. During the processing, the boundary of the object, B is maintained as a doubly linked list of vertices and intervening segments as V1S1V2,?,VmSmV1. The first segment S1, connecting vertices V1 and V2, the last segment Sm, connecting vertices Vm and V1. A vertex Viis called reflex if the internal angle at Vi is greater than 180 degrees, and convex otherwise. llist is a list that contains the parameters of correspondent segments. Additional to the local features determined above, an algorithm for contour following is integrated. This algorithm follows the object’s boundary from a starting point determined previously and goes counter-clockwise around the contour by ordering successively its vertices/edge points into a double linked list. The algorithm stops when the starting point is reached for the second time. The aim of this stage is to determine that all vertices/segments belong to the object’s boundary which we will need further for the determination of the grasping points position.
(a) Binary object
(b) Visual features extraction
Figure 4. Object shape representation. (a) Images from original industrial objects (b) Extraction of grasping regions
Extraction of Grasping Regions
Grasping regions are determined by grouping consecutive edge points from a binary edge image. This is usually a preliminary step before grasping takes place, and may not be as time critical as the task of grasping points determination. We deal with (5), the list vlist=(V1,V2,?,Vm) is the result that forms an ordered list of connected boundary vertices. We then need to store the parameters of these primitives instead of discrete points (or vertices) to fit a line segment to a set of vertices points that lie along a line segment. The aim of this step is to determine all salient segments that preserve the shape of the object contour. Figure 4(b) shows grasp regions on the object’s contour. Afterwards, each grasping region is extracted as straight segment. The size of the grasping regions should be long enough for positioning the robot fingers. The curve fitting (as shown in Figure 5(a)) describes the process of finding a minimum set of curve segments to approximate the object’s contour to a set of line segments with minimum distortion. Once the line segments have been approximated, the merging method (as shown in Figure 5(b)) is used to merge two lines segment that satisfied the merging threshold.
The final result of the algorithm is a list of consecutive line segments with a specified tolerance which preserve the object’s contour. Briefly, merging methods, (1) use the first two vertices points to define a line segment (2) add a new vertex if it does not deviate too much from the current line segment (3) update the parameters of the line segment using least-squares measure (4) start a new line segment when edge points deviate too much from the line segment. The final result of the algorithm is a list of consecutive line segments with a specified tolerance which preserve the object’s contour. We define such list by
where a segment Si is defined by its ending vertices Vi=(xi, yi)and Vi+1=(xi+1, yi+1) that represent the location of a segment in the plane. m is the number of segments containing the list slist.
(a) Curve fitting (b) Segment merging
Figure 5. Curve fitting and merging methods.
Critical Grasping Points
(a) Critical points (b) Finger displacement
Figure 6. (a) Critical grasping point
To assure the robustness of contact placement, we make some assumptions in (6): First assumption, to avoid undesirable contacts at convex vertices and convex corners (see the position of finger f1, f2 in Figure 6(a)) which are not generally robust due to small uncertainty during the grasping phase. We also avoid the concave vertices having a size of concavity smaller than the size of the fingertip using the reachability conditions (see the position of finger f3in Figure 6(a)).
Second assumption, we estimate a fingertip as a sphere with radius fr (see Figure 6). the grasping regions must be large enough for positioning the fingertip on it. Hence, a preprocessing (or prefiltering) is necessary in (6) to discard those segments with length less than the diameter of the sphere.
Based on both assumption, we define a small margin value at the endpoint of each segment by as shown in Figure 6 with ε=fr If a segment si contains all possible contact points fromVi to Vi+1 then any grasping points must satisfy
Using the grasp criteria of (7) including the condition that the size of the grasp region must be large enough to place a finger on it, gi≤2fr( (see Figure 6). Equation (6) becomes
where glist is a linked list ordered in counterclockwise direction (see Figure 6(b)) and updated from the condition of
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