Constrained Search in Continuous Time and Space

As we recall from Chap. 4, search applications might require the consideration of constraints on the agility of the searcher. For example, in the development of real-time controllers for autonomous systems it becomes essential to account for their often limited speed, turn radii, and other performance characteristics. When such systems need to be controlled on a very fine time scale, it becomes natural to formulate these problems in continuous time. Consequently, we are faced with the problem of optimal search in continuous time and space subject to constraints. This chapter provides an introduction to the subject through the formulation of several search situations as uncertain optimal control problems. Although there are computational challenges associated with the solution of uncertain optimal control problems, they are not unsurmountable. In fact, we include a section with examples that illustrate today’s capabilities and demonstrate that practically useful solutions can be obtained in tens of minutes by standard optimization solvers. We also provide an introduction to the theory supporting such problems.