Jan Wolter

A combinatorial analysis of enumerative data structures for assembly planning

Current assembly planning systems have used different definitions of an assembly plan and applied different restrictions to the planning process. This report surveys, analyzes, and compares several key aspects of assembly planning systems. The most common restrictions applied to assembly plans-sequentiality, monotonicity, and coherence-are defined and discussed. Three distinct definitions of an assembly plan are described and compared. Several enumerative data structures designed to represent large sets of assembly plans are analyzed and compared.<<ETX>>

Automatic selection of fixture points for frictionless assemblies

During the assembly of a product, it is vital that the partially completed assembly be stable. If the assembly is unstable, then it must be fixtured to stabilize it before retrieving the next part or subassembly This paper presents a stability test and a new approach to automatically generating the positions of a small set of fixture elements (fixels) that will stabilize an assembly. The stability test and the fixel positioning approach consider both the translational and rotational degrees of freedom of each part. Since all the relevant mechanical constraints are linear functions of the contact force magnitudes and the components of the velocities of the parts, linear programming techniques can be used with great efficiency.<<ETX>>

Mating constraint languages for assembly sequence planning

The authors analyze the most commonly used form of constraint languages for assembly planning: mating constraint languages. These constraints are typically composed of relations asserting that a certain pair of parts must be mated before some other pair of parts may be mated. However there are many significant differences between the forms of these constraints used by different authors. It is proven that some of these forms, such as those based on less-than relations and those based on less-than-or-equal-to relations, are equivalent. A variety of theorems that address which kinds of mating constraint languages are able to represent which kinds of sets of plans are included.<<ETX>>

A hierarchical approach to assembly planning

This paper describes a fundamentally new approach to assembly sequence planning which views an assembly as a hierarchy of standard structures and uses a strategy of merging partial plans for structures to derive a plan for the whole assembly. Such a planner has been implemented on a Sun Sparc Station 1. It generates a plan in which there are no subassemblies, if such a plan exists, given as a partial order in terms of the sequence of part insertion and their trajectories. The planning algorithm is shown to be correct and complete and the methodology is shown to lessen considerably the combinatorial problems encountered by current planners working on large real world problems.<<ETX>>

Toward assembly sequence planning with flexible parts

A wide range of different approaches to assembly sequence planning has been described in the literature, but, to date, primarily assemblies of rigid parts have been considered. Yet flexible parts of all sorts are common in real world assemblies. This paper considers the special characteristics of operations on flexible parts in general and string-like parts (wires, cables, hoses, ropes, etc.) in particular. Different types of operations are discussed, and knowledge representation techniques for assembly states and operations are described, together with basic algorithms for queries on string-like assemblies.

The Centroid of Points with Approximate Weights

Let S be a set of points in ℝd, each with a weight that is not known precisely, only known to fall within some range. What is the locus of the centroid of S? We prove that this locus is a convex polytope, the projection of a zonotope in ℝd+1. We derive complexity bounds and algorithms for the construction of these “centroid polytopes”.

A concept for a constraint-based representation of functional and geometric design knowledge

Welter ancl Periannan Chandrasekaran Department of Computer Science Texas A&M University Pure geometric modeling systems are effective as drafting tools, but of limited utility in conceptual design. A design system which explicitly represents functional requirements and ties this to a geometric model could more effectively support the design process and provide a richer database to be used by production planning and design optimization tools. To achieve this goal more flexible ways of structuring geometric knowledge are needed. This paper describes the basic ideas behind a feature-oriented functional design system currently under study. Geometry is represented through a hierarchy of geometrical structures called geornes each of which represent some underconstrained set of geometrical elements. Models are represented by a constraint network that is generated by the instantiation and unification of geomes. Possible methods for providing a graphical user interface to this type of system are also briefly discussed.

Model-based understanding of uncertain observational data for oil spill tracking

Oil spill tracking is essential in oil spill clean-up. Usually, the oil spill tracking is treated by employing a mathematical oil spill model which describes the fate and transport behavior of an oil-spill. Before a model can predict where the spilled oil will go in the future, it must have a reasonably accurate understanding about what happened in the past. Typically, the input to the model such as wind, current, etc. is unreliable or sometimes not completely available so that interpolating the past behavior of an oil spill becomes extremely difficult. In this paper, we regard the oil spill tracking as a control problem in which we reduce the errors between the oil observations and the model outputs by iteratively adjusting the model inputs and cope with the uncertainty of the model inputs by using fuzzy logic techniques. Through the process, we can construct a plausible history of the oil spill that is consistent with our observations and can be effectively extrapolated into the future.<<ETX>>

Assembly planning with intermediate states

The nonmonotonicity of assembly planning in different states is characterized and used to represent the three-dimensional geometric constraints of assembly operations in the form of blocking states. A subsumption mechanism based on the blocking states is used to reduce the search space so that a feasible plan can be efficiently found. An algorithm, NOMOL, which can generate nonmonotonic and nonlinear plans is presented and shown to be correct and complete.<<ETX>>

A constraint-based approach to planning with subassemblies

The XAP/1 assembly planner used an opportunistic, constraint-based approach to generate plans for the manufacture of mechanical assemblies. Extensions to that system to allow the generation of plans with subassemblies are described. This is done by extending the set of constraints to allow the generation of subassembly trees, while maintaining the flexibility of the original planner