Robot motion planning has become a major focus of robotics. Research findings can be applied not only to robotics but to planning routes on circuit boards, directing digital actors in computer graphics, robot-assisted surgery and medicine, and in novel areas such as drug design and protein folding. This text reflects the great advances that have taken place in the last ten years, including sensor-based planning, probabalistic planning, localization and mapping, and motion planning for dynamic and nonholonomic systems. Its presentation makes the mathematical underpinnings of robot motion accessible to students of computer science and engineering, rleating low-level implementation details to high-level algorithmic concepts. Howie Choset is Associate Professor in the Robotics Institute at Carnegie Mellon University. Kevin M. Lynch is Associate Professor in the Mechanical Engineering Department, Northwestern University. Seth Hutchinson is Professor in the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign. George Kantor is Project Scientist in the Center for the Foundations of Robotics, Robotics Institute, Carnegie Mellon University. Wolfram Burgard is Associate Professor and Head of the Autonomous Intelligent Systems Research Lab in the Department of Computer Science at the University of Freiburg. Lydia E. Kavraki is Professor of Computer Science and Bioengineering, Rice University. Sebastian Thrun is Associate Professor in the Computer Science Department at Stanford University and Director of the Stanford AI Lab.