Multi-scale 3-D Surface Description: Open and Closed Surfaces

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed automatically and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. Our technique was applied to closed as well as open 3-D surfaces and the results are presented here

Multi-Scale Free-Form Surface Description and Curvature Estimation

A novel technique for multi-scale smoothing of a free-form 3-D surface is presented. Complete triangulated models of 3-D objects are constructed at our center [4] and using a local parametrization technique, are then smoothed using a 2-D Gaussian filter. Our method for local parametrization makes use of semigeodesic coordinates as a natural and efficient way of sampling the local surface shape. The smoothing eliminates the surface noise together with high curvature regions such as sharp edges, therefore, sharp corners become rounded as the object is smoothed iteratively. Our technique for free-form 3-D multi-scale surface smoothing is independent of the underlying triangulation. It is also argued that the proposed technique is preferrable to volumetric smoothing or level set methods since it is applicable to incomplete surface data which occurs during occlusion. The technique was applied to simple and complex 3-D objects and the results are presented here

Polyhedral computational geometry for averaging metric phylogenetic trees

This paper investigates the computational geometry relevant to calculations of the Frechet mean and variance for probability distributions on the phylogenetic tree space of Billera, Holmes and Vogtmann, using the theory of probability measures on spaces of nonpositive curvature developed by Sturm. We show that the combinatorics of geodesics with a specified fixed endpoint in tree space are determined by the location of the varying endpoint in a certain polyhedral subdivision of tree space. The variance function associated to a finite subset of tree space has a fixed $C^\infty$ algebraic formula within each cell of the corresponding subdivision, and is continuously differentiable in the interior of each orthant of tree space. We use this subdivision to establish two iterative methods for producing sequences that converge to the Frechet mean: one based on Sturm's Law of Large Numbers, and another based on descent algorithms for finding optima of smooth functions on convex polyhedra. We present properties and biological applications of Frechet means and extend our main results to more general globally nonpositively curved spaces composed of Euclidean orthants.Comment: 43 pages, 6 figures; v2: fixed typos, shortened Sections 1 and 5, added counter example for polyhedrality of vistal subdivision in general CAT(0) cubical complexes; v1: 43 pages, 5 figure

Using automatic robot programming for space telerobotics

The interpreter of a task level robot programming system called Handey is described. Handey is a system that can recognize, manipulate and assemble polyhedral parts when given only a specification of the goal. To perform an assembly, Handey makes use of a recognition module, a gross motion planner, a grasp planner, a local approach planner and is capable of planning part re-orientation. The possibility of including these modules in a telerobotics work-station is discussed

A systems engineering approach to robotic bin picking

In recent times the presence of vision and robotic systems in industry has become common place, but in spite of many achievements a large range of industrial tasks still remain unsolved due to the lack of flexibility of the vision systems when dealing with highly adaptive manufacturing environments. An important task found across a broad range of modern flexible manufacturing environments is the need to present parts to automated machinery from a supply bin. In order to carry out grasping and manipulation operations safely and efficiently we need to know the identity, location and spatial orientation of the objects that lie in an unstructured heap in a bin. Historically, the bin picking problem was tackled using mechanical vibratory feeders where the vision feedback was unavailable. This solution has certain problems with parts jamming and more important they are highly dedicated. In this regard if a change in the manufacturing process is required, the changeover may include an extensive re-tooling and a total revision of the system control strategy (Kelley et al., 1982). Due to these disadvantages modern bin picking systems perform grasping and manipulation operations using vision feedback (Yoshimi & Allen, 1994). Vision based robotic bin picking has been the subject of research since the introduction of the automated vision controlled processes in industry and a review of existing systems indicates that none of the proposed solutions were able to solve this classic vision problem in its generality. One of the main challenges facing such a bin picking system is its ability to deal with overlapping objects. The object recognition in cluttered scenes is the main objective of these systems and early approaches attempted to perform bin picking operations for similar objects that are jumbled together in an unstructured heap using no knowledge about the pose or geometry of the parts (Birk et al., 1981). While these assumptions may be acceptable for a restricted number of applications, in most practical cases a flexible system must deal with more than one type of object with a wide scale of shapes. A flexible bin picking system has to address three difficult problems: scene interpretation, object recognition and pose estimation. Initial approaches to these tasks were based on modeling parts using the 2D surface representations. Typical 2D representations include invariant shape descriptors (Zisserman et al., 1994), algebraic curves (Tarel & Cooper, 2000), 2 Name of the book (Header position 1,5) conics (Bolles & Horaud, 1986; Forsyth et al., 1991) and appearance based models (Murase & Nayar, 1995; Ohba & Ikeuchi, 1997). These systems are generally better suited to planar object recognition and they are not able to deal with severe viewpoint distortions or objects with complex shapes/textures. Also the spatial orientation cannot be robustly estimated for objects with free-form contours. To address this limitation most bin picking systems attempt to recognize the scene objects and estimate their spatial orientation using the 3D information (Fan et al., 1989; Faugeras & Hebert, 1986). Notable approaches include the use of 3D local descriptors (Ansar & Daniilidis, 2003; Campbell & Flynn, 2001; Kim & Kak, 1991), polyhedra (Rothwell & Stern, 1996), generalized cylinders (Ponce et al., 1989; Zerroug & Nevatia, 1996), super-quadrics (Blane et al., 2000) and visual learning methods (Johnson & Hebert, 1999; Mittrapiyanuruk et al., 2004). The most difficult problem for 3D bin picking systems that are based on a structural description of the objects (local descriptors or 3D primitives) is the complex procedure required to perform the scene to model feature matching. This procedure is usually based on complex graph-searching techniques and is increasingly more difficult when dealing with object occlusions, a situation when the structural description of the scene objects is incomplete. Visual learning methods based on eigenimage analysis have been proposed as an alternative solution to address the object recognition and pose estimation for objects with complex appearances. In this regard, Johnson and Hebert (Johnson & Hebert, 1999) developed an object recognition scheme that is able to identify multiple 3D objects in scenes affected by clutter and occlusion. They proposed an eigenimage analysis approach that is applied to match surface points using the spin image representation. The main attraction of this approach resides in the use of spin images that are local surface descriptors; hence they can be easily identified in real scenes that contain clutter and occlusions. This approach returns accurate results but the pose estimation cannot be inferred, as the spin images are local descriptors and they are not robust to capture the object orientation. In general the pose sampling for visual learning methods is a problem difficult to solve as the numbers of views required to sample the full 6 degree of freedom for object pose is prohibitive. This issue was addressed in the paper by Edwards (Edwards, 1996) when he applied eigenimage analysis to a one-object scene and his approach was able to estimate the pose only in cases where the tilt angle was limited to 30 degrees with respect to the optical axis of the sensor. In this chapter we describe the implementation of a vision sensor for robotic bin picking where we attempt to eliminate the main problem faced by the visual learning methods, namely the pose sampling problem. This paper is organized as follows. Section 2 outlines the overall system. Section 3 describes the implementation of the range sensor while Section 4 details the edge-based segmentation algorithm. Section 5 presents the viewpoint correction algorithm that is applied to align the detected object surfaces perpendicular on the optical axis of the sensor. Section 6 describes the object recognition algorithm. This is followed in Section 7 by an outline of the pose estimation algorithm. Section 8 presents a number of experimental results illustrating the benefits of the approach outlined in this chapter

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation

A generic computer simulation for manipulator systems (ROBSIM) was implemented and the specific technologies necessary to increase the role of automation in various missions were developed. The specific items developed are: (1) capability for definition of a manipulator system consisting of multiple arms, load objects, and an environment; (2) capability for kinematic analysis, requirements analysis, and response simulation of manipulator motion; (3) postprocessing options such as graphic replay of simulated motion and manipulator parameter plotting; (4) investigation and simulation of various control methods including manual force/torque and active compliances control; (5) evaluation and implementation of three obstacle avoidance methods; (6) video simulation and edge detection; and (7) software simulation validation

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered