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the controls approaches). To cover these there will have to be a New and Advanced Topics classification. This does not indicate a shortcoming in the representations, but a lack of definition in the areas included.

40.4.3 OPTIMIZATION TECHNIQUES

40.4.3.1 - SPATIAL PLANNING

40.4.3.2 - TRANSFORMED SPACE

40.4.3.3 - FIELD METHODS

40.4.3.4 - NEW AND ADVANCED TOPICS

40.4.4 INTERNAL REPRESENTATIONS

Most problem solving techniques need some internal method of dealing with the problem. These methods all have their various advantages. Most of these internal representations depend upon the method of world modelling used in the setup. These may be converted inside the program. There are factors to consider when choosing between various internal representations. For example if arrays are used they are very large and, the updating procedure is very slow, but the lookup is very swift. This technique is of best use when, the obstacles do not move, and the arrays are set up off-line to be used on line. With the current advances in computer hardware (i.e.. Vector Processing and Memory) special hardware may become available that will make the arrays based methods very fast, thus they should not be discarded, but shelved.

The next technique of interest is lists. These are mainly an efficient way to store linked data. This may vary from an oct-tree representation of some object to a simple list of boxes in space. These are efficient with space, but there is storage overhead, and lookups are slower than the array.

Functions are very space efficient, but they are subject to inflexibility. Functions may represent a variety of execution speeds from quite fast for a simple problem to very slow for a complex problem. It should be noted that functions may grow exponentially with increased environment complexity. This function should be used with discretion.