Sacks and Joskowicz: Computational Kine- Kine-matics

Research on \Computational Kinematics" [25] by Sacks and Joskowicz shares many features in common with AMES; however, their focus was much more specialized.

The goal of that project was to create kinematic models of mechanical devices. This is dierent from the scope of AMES' task since AMES deals with unconstrained congurations of objects, and uses complete reasoning about dynamics.

The methods that Sacks and Joskowicz developed can generate mathematical models that describe the motions of the parts of a wide variety of mechanisms from their geometry. Another similarity to AMES, in approach, is that they create models of systems by composing models of their components' behaviors (for mechanism kine-matics, these behaviors are pairwise motion constraints). Furthermore, like AMES, their methods handle the changes in models that result from change in mechanical part contact congurations.

Since the domain of mechanism kinematics, though complex, is a highly con-strained subset of mechanics, the methods they used are dicult to compare to AMES except at the highest level. Reasoning eciently about mechanism kinematics

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requires special exploitation of the constraints that engineers design into their ma-chines. Therefore, while the approach used in AMES is quite general, it is impractical for reasoning about the types of the problems that Sacks and Joskowicz attacked in their project. Conversely, methods for reasoning about machine kinematics are too specialized to be of much use in reasoning about unconstrained classical mechanics problems.

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Chapter 6 Conclusions

In my opinion, this thesis contributes to the eld of physical reasoning in two ways.

First, it presents a powerful paradigm for predicting physical behaviors that addresses some of the most important limitations in the qualitative reasoning methods that have become popular in recent years. Second, this project oers several insights into formally representing knowledge about mechanics.

The algebraic simulation paradigm demonstrated in AMES is signicant in several ways. One of its most important contributions is that it oers a fresh perspective on the roles of quantitative and qualitative reasoning. Qualitative reasoning in algebraic simulation is a method for constructing mathematical models, while quantitative reasoning handles inferences about systems' evolution. This architecture allows pro-grams to reason about highly complex interactions, without the crippling ambiguity that purely qualitative approaches typically encounter. At the same, time, algebraic simulation retains many of the key benets of qualitative reasoning. For example, al-gebraic methods allows alal-gebraic simulations to abstract over ambiguities in scenario descriptions, and generalize over ranges of parameter values.

Another signicant contribution of the algebraic simulation paradigm is that it presents a method for constructing mathematical descriptions of physical systems in domains, like mechanics, that cannot be described by xed topology networks of lumped parameter elements. The features of algebraic simulation that support this power include: a modular decomposition of physical knowledge that reects the

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structure of mathematical models in the reasoning domain; and the ability to both predict the limits of scenario models and update them when their evolution crosses these boundaries.

In terms of the signicance of this thesis in providing insights into eectively capturing mechanics domain knowledge, perhaps the most important contribution is the model component representational framework. Lucid representations result from the demands of both describing physical behaviors in a modular fashion, and using these descriptions to construct mathematical models of physical systems. Model components make explicit the situations in which represented behaviors arise, the system attributes that such behaviors inuence, and the precise relationship that exists between those attributes.

In addition, the discussion surrounding the AMES program oers several specic ideas for capturing and organizing mechanics knowledge. The program's knowledge-base, in particular, gives special insight into characterizing rigid body dynamics: an important subset of the domain.

Looking toward the future, work on this project has raised a large number of issues in physical reasoning, especially the automated analysis of mechanics. In the immediate future, an interesting project would be to construct a program that in-corporates many of the suggestions for improvement to AMES. Such a project would be able to evaluate and expand upon the suggestions this thesis makes for represent-ing additional mechanics knowledge; examine eciency issues in reasonrepresent-ing about the mathematical models that simulations generate; and explore how to apply simulation to various classes of problem solving. Other areas for future exploration could include model selection, problem decomposition, and applications of simulation in design.

To conclude, therefore, this thesis presents an initial look at a paradigm for phys-ical reasoning that combines qualitative and quantitative reasoning in a somewhat novel fashion that oers interesting advantages over methods that are currently pop-ular. This technique is especially useful for reasoning about the complex interactions present in domains such as classical mechanics, and research on this project has gen-erated several suggestions for how knowledge about that domain can be represented

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in an eective manner.

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