O (logn) algorithm for forward kinematics under asynchronous sensory input

Abstract

This paper presents a new algorithm for forward kinematics, called Asynchronous Forward Kinematics (AFK). The algorithm has the complexity of O(log n) for updating one joint angle, and O(logn) for obtaining a homogeneous transformation matrix between links. AFK enables computation for efficient forward kinematics under asynchronous sensory data. Moreover, AFK peovides localise computational resources at sensitive joints to the position of the endpoint (e.g. a fingertip), like a root joint. We provide comparative results including computation time, evaluating AFK against the conventional forward kinematics (CFK). The results showed that the computation time is well adequate for real-time computation. Computation time for 100 links takes less than 20 us for 1 query. Moreover, computation time with over 50000 links takes less than 35 us for 1 query.