Algorithms are a fundamental component of robotic systems: they control or reason about motion and perception in the physical world. They receive input from noisy sensors, consider geometric and physical constraints, and operate on the world through imprecise actuators. The design and analysis of robot algorithms therefore raises a unique combination of questions in control theory, computational and differential geometry, and computer science. This book contains the proceedings from the 2006 Workshop on the Algorithmic Foundations of Robotics. This biannual workshop is a highly selective meeting of leading researchers in the field of algorithmic issues related to robotics. The 32 papers in this book span a wide variety of topics: from fundamental motion planning algorithms to applications in medicine and biology, but they have in common a foundation in the algorithmic problems of robotic systems.