This paper presents novel event-driven forward kinematics algorithms for open kinematic chains with O(log n) complexity. This event-driven algorithm can efficiently update forward kinematics only when new sensory data comes. This will also contribute to localization of computational resources at sensitive joints to the position of the endpoint (e.g. a fingertip), like a root joint. We constructed 3 event-driven FK algorithms. We proved that the algorithms have the complexity of O(logn) for updating 1 joint angle, and O(logn) for obtaining a homogeneous transformation matrix between links. We compared the 3 algorithms with a conventional forward kinematics algorithm in the viewpoint of complexity, computation time, time-variance and algebraic structures. The results showed that the computation time is well adequate for real-time computation. Computation time is less than 2 us per 1 query, for 40,000 kinematic chains.

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.