Planning Algorithms

What is a planning algorithm? This is a difficult question, and a precise mathematical definition will not be given in this book. Instead, the general idea will be explained, along with many examples of planning algorithms. Planning is a term that means different things to different groups of people. A fundamental need in any process of automation is to have algorithms that convert high-level specifications of tasks from humans into low-level descriptions of how to move. The terms motion planning and trajectory planning are often used for these kinds of problems. A classical version of motion planning is sometimes referred to as the Piano Mover’s Problem. Imagine giving a precise computer-aided design (CAD) model of a house and a piano as input to an algorithm. The algorithm must determine how to move the piano from one room to another in the house without hitting anything. Motion planning usually ignores dynamics and other differential constraints and focuses primarily on the translations and rotations required to move the piano. Recent work, however, does consider other aspects, such as uncertainties, differential constraints, modeling errors, and optimality. Trajectory planning usually refers to the problem of taking the solution from a motion planning algorithm and determining how to move along the solution in a way that respects the limitations of the automation. Why study planning algorithms? There are at least two good reasons. First, it is fun to try to get machines to solve problems for which even humans have great difficulty. This involves exciting challenges in modeling planning problems, designing efficient algorithms, and developing robust implementations. Second, planning algorithms have achieved widespread successes in several industries and academic disciplines, including robotics, manufacturing, drug design, and aerospace applications. The rapid growth in recent years indicates that many more fascinating applications may be on the horizon. These are exciting times to study planning algorithms and contribute to their development and use.