Efficient Event-Driven Forward Kinematics of Open Kinematic Chains with O(Log n) Complexity

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.