Planning Algorithms

By Steven M. LaValle
This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensor-based planning, visibility, decision-theoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Planning to Plan
Planning is a term that means different things to different groups of people. Robotics addresses the automation of mechanical systems that have sensing, actuation, and computation capabilities (similar terms, such as autonomous systems are also used). A fundamental need in robotics 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. Most of us have encountered similar problems when moving a sofa or mattress up a set of stairs. Robot 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 robot motion planning algorithm and determining how to move along the solution in a way that respects the mechanical limitations of the robot.