Constraint resolution using optimisation techniques

Abstract

Constraint-based CAD systems are useful for handling design applications in which the precise rules are not known beforehand. The designer can introduce new constraints as these become apparent as the design task proceeds. A variety of ways for resolving constraints currently exist. This paper considers the use of a direct search optimisation approach. It is shown that this has the advantage of being able to handle a variety of different applications and that problems of under- or over-constrained systems no longer exist. A software system using this approach is introduced and its application to a number of areas is illustrated, including typical problems from computer-aided sketching, assembling modelling and mechanism simulation.

Introduction

Computer aided design (CAD) systems have found uses in a large number of application areas. Since commercial systems tend to be general purpose engines, there have been a number of attempts to tailor them to more specific applications. Many of these have relied on the underlying user language of the system and the use of parametrics is one such case [1], [2]. When the application area is well understood, rule-based expert systems provide a means for capturing that information for the less experienced user [3], [4]. These can be used to control the CAD system via its user language.

In the more general design situation, a designer is often meeting a task for the first time. In such cases the precise rules which apply are not immediately obvious. What are clear are some of the constraints which bound what can be done. These might include limitations on weight or size or allowable forces. As the design proceeds more and more constraints emerge. These are often in conflict and the designer's skill is in deciding which can be comprised with reasonable safety.

The use of constraint-based systems has emerged recently [5], [6], [7], [8]. Often these systems underlie sketching software and the constraints relate to the geometry involved particularly in relation to the underlying cartesian coordinates of points. A range of solution techniques exist.

It is generally acknowledged that there is a range of constraints that need to be considered, ranging from the purely geometric to more complex engineering considerations. However, the constraint resolvers employed do not generally seem designed to handle this range satisfactorily.

This paper proposes that resolution techniques based upon mathematical optimisation provide a means for handling all the various different types of constraint within a single unified approach. While more sophisticated means of solution certainly exist, they depend upon specific forms of constraint. Optimisation strategies, particularly those based on direct search techniques, require only the ability to be able to evaluate the imposed constraints. Problems of too many or too few constraints are not a problem and indeed the optimisation approach allows best compromise solutions to be obtained when constraints are in conflict. Furthermore, as the speed of computing equipment increases, numerical methods can afford to be less efficient in speed and cruder but more robust techniques become acceptable. The approach using optimisation is demonstrated using a constraint modelling system called SWORDS.

In the next section, related research in the area of constraint-based systems is reviewed and this is followed with some background from optimisation theory. The structure of the SWORDS system is described and is then applied as an example to a typical problem arising in sketching systems. In the following sections, techniques for addressing applications in assembly and mechanisms are discussed including the use of solid models. Finally conclusions are presented.