This book is the second volume of two that present research advances on algorithmic robotics written by leading experts in the field. 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, computer science and machine learning. Advances in this area have a wide range of applications in manufacturing, computational biology, medical robotics, sensor networks, human-robot interaction, virtual environments, and many other areas. These results were presented at the 16th edition of the International Workshop on the Algorithmic Foundations of Robotics (WAFR) held October 7-9, 2024 at the University of Illinois Discovery Partners Institute in the City of Chicago, Illinois, USA. This edition of WAFR also marked 30 years since its creation in 1994 as a small workshop. Since then, WAFR has established a reputation of being one of the most important venues for presenting cutting-edge research on algorithmic problems in robotics.  Each of the 47 chapters in these two volumes presents an exciting contribution in algorithmic robotics spanning motion and task planning, geometry, multi-robot systems, game theoretic algorithms, control, reinforcement learning,  robot design and dynamics, planning with beliefs, minimalism, manipulation, planning with ``interesting'' goals, and perception, localization, and communication.