A criterion

This encodes the desired outcome of a plan in terms of the state and actions that are executed. There are generally two different kinds of planning concerns based on the type of criterion:
  1. [1.] Feasibility: Find a plan that causes arrival at a goal state, regardless of its efficiency.
  2. [2.] Optimality: Find a feasible plan that optimizes performance in some carefully specified manner, in addition to arriving in a goal state.
For most of the problems considered in this book, feasibility is already challenging enough; achieving optimality is considerably harder for most problems. Therefore, much of the focus is on finding feasible solutions to problems, as opposed to optimal solutions. The majority of literature in robotics, control theory, and related fields focuses on optimality, but this is not necessarily important for many problems of interest. In many applications, it is difficult to even formulate the right criterion to optimize. Even if a desirable criterion can be formulated, it may be impossible to obtain a practical algorithm that computes optimal plans. In such cases, feasible solutions are certainly preferable to having no solutions at all. Fortunately, for many algorithms the solutions produced are not too far from optimal in practice. This reduces some of the motivation for finding optimal solutions. For problems that involve probabilistic uncertainty, however, optimization arises more frequently. The probabilities are often utilized to obtain the best performance in terms of expected costs. Feasibility is often associated with performing a worst-case analysis of uncertainties.

Steven M LaValle 2020-08-14