We study the feasibility of design for a layer-deposition manufacturing process called stereolithography which works by controlling a vertical laser beam which when targeted on a photocurable liquid causes the liquid to harden. In order to better understand the power as well as the limitations of this manufacturing process, we define a mathematical model of stereolithography (referred to as vertical stereolithography) and analyze the class of objects that can be constructed under the assumptions of the model. Given an object (modelled as a polygon or a polyhedron), we give algorithms that decide in O(n) time (where n is the number of vertices in the polygon or polyhedron) whether or not the object can be constructed by vertical stereolithography. If the answer is in the affirmative, the algorithm reports a description of all the orientations in which the object can be made. We also show that the objects built with vertical stereolithography are precisely those that can be made with a 3-axis NC machine.

We study the problem of grasping an unknown 2- 1 2 D object with constant horizontal cross section using three types of robot hands. We consider a three fingered hand, a two fingered hand and a standard parallel jaw gripper and equip these with distance and angle sensors that are located at the fingers or jaws. The sensors used are simple, provide only limited information, but allow us to reactively find a good grasp on an unknown convex object. When grasped the forces applied will be normal to the object boundary. Furthermore the object is not disturbed as the grasping points are being sought. 1 Introduction In the past, the usual approach to grasping has been to assume an accurate model of the object to be grasped and from such a model, an off-line geometric algorithm determines a set of grip points, where the fingers are then placed. (See Mishra et. al. [MSS87] and Mishra and Teichmann [MT92], Stam et. al. [SPF92]). Once the grip points have been determined, the geometry of the ob...

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We study the problem of grasping an unknown object with constant cross section using various “reactive ” robot hands. In the simplest example, we equip a standard parallel jaw gripper with several light-beam sensors (close to each jaw) and implement a reactive algorithm for grasping polygonal objects with this architecture. Extending these ideas further, we also devise two and three fingered reactive hands for objects with smooth boundary and equip these with distance and angle sensors that are located at the finger tips. The sensors used are simple, provide only limited and immediate information, but allow us to reactively find a good grasp on an object of unknown geometry and dynamics. When grasped the forces applied will be normal to the object boundary. Furthermore, in all cases, the object is not disturbed as the grasping points are being sought. Various approaches to dextrous manipulation can be categorized into two groups: object-priority approaches and finger-priority approaches. This classification was first

Abstruct- This article presents a new theorem and an algorithm for fast synthesis of two-fingered force-closure grasps for arbitrary polygonal objects. The polygonal objects are allowed to be of arbitrary shape, in the sense that there is no restriction that the objects he convex. Moreover, each edge of the polygon is allowed to have different frictional characteristics. Our novel formulation results in a simple and efficient algorithm that finds grasps that tolerate the largest positioning errors for each of the fingertips at the contact points. The algorithm is both complete and correct, meaning that if any force-closure grasp exists for the object, the algorithm will find it; furthermore, all the grasps synthesized by the algorithm are guaranteed to be valid force-closure grasps. I.

In this paper, we study various algorithmic questions regarding the computation of an optimal three finger planar grasp. We present a novel O(n² log n)-time algorithm to compute such an optimal grasp for an arbitrary simple n-gon. This algorithm can be used for finding "good" immobilizing sets. We also discuss several variations on the problem and many intriguing open questions in the area that remain unsolved.

We consider the problem of grasping an unknown polygonal flat object using a parallel jaw gripper. Our design equips a standard gripper with several light-beam sensors (close to each jaw) and employs a control scheme based on a reactive grasping algorithm. This is done by probing the object to locate a good grasp position, and then grasping, without moving the object significantly. The goal is to do as little motion as possible to find a grasp. In this paper, we discuss an implementation of this device using NYU's MOSAIC robot, following a quick overview of the underlying reactivity principle.

A key problem in robot grasping is that of positioning the manipulator contacts so that an object can be grasped. In unstructured environments, contact positions are typically planned based on range or visual measurements that are used to reconstruct object geometry. However, because it is difficult to measure the complete object geometry precisely in common grasp scenarios, it is useful to employ additional techniques to adjust or refine the grasp using only local information. In particular, grasp control techniques can be used to improve a grasp by adjusting the contact configuration after making initial contact with an object by using measurements of local object geometry at the contacts. This paper proposes three variations on null space grasp control, an approach that combines multiple grasp objectives to improve a grasp. Two of these variations are theoretically demonstrated to converge to force closure configurations for arbitrary convex objects when grasping with two contacts. All variations are found to converge in simulation. Robot grasping experiments are reported that show the approach to be useful in practice.

Creating force domain behavior requires control processes that optimize manipulator contact configuration based on the forces that can be applied. In the case of grasping, contact configuration must be optimized for grasp quality measures. If robust controllers can be defined that converge to good grasp configurations, even over limited domains of attraction, then these controllers can be sequenced or combined to create robust behavior over larger domains. This chapter focuses on defining controllers that control grasp quality. Starting with Coelho’s force and moment residual control primitives, a composite grasp controller is defined that executes both of these control primitives concurrently [60]. Next, a hybrid position and force controller is defined that acts in concert with the grasp controller to slide the contacts to good grasp configurations [61]. Finally, the set of potential grasp controllers is expanded by allowing controllers to be parameterized by virtual contacts that correspond to contact groups [57]. Experimental results are presented that demonstrate these controllers to be a practical and effective way of synthesizing grasps in poorly modeled domains. 4.1 Background The control-based approach to solving force-domain problems taken in this thesis rests heavily upon Coelho’s force and moment residual controllers. These controllers minimize grasp error functions by displacing contacts on the surface of an object in response to local tactile feedback at the contacts. This section describes different approaches to tactile sensing and a method for displacing contacts on the surface of an object that acquires tactile feedback, called probing. Next, Coelho’s force residual and moment residual controllers that displace contacts into quality grasp configurations based on local tactile feedback are described. 4.1.1 Sensing for Grasp Control Grasp controllers assume that it is possible to sense local surface geometry in the neighborhood of each contact. This may be accomplished in a number of ways. For example, it may be possible to use computer vision to extract the relationship between object surface and grasp contact [1]. Notice that this vision problem is significantly easier than the general problem of reconstructing full object geometry. Unfortunately, it can be difficult to use vision for the purpose of “tactile sensing ” without placing

manufacturing, experienced a mathematical rebirth in the mid 80’s, when this nascent field established many beautiful connections to convexity theory and computational geometry. Jack Schwartz played a seminal role in its inception and development. Here, I speculate on where Jack might have liked this field to go in the future.