A dynamic version of the Inverse Kinematics problem addresses the two main objectives: One objective is to find a configuration of joints such that a desired pose and orientation can be reached by a robotic arm. Another one is to preserve this state in a continuously changing environment. In this paper a reaching goal in dynamic constrained Inverse Kinematics is considered where either a target point to be reached or locations of obstacles or both can change in time. The Infeasibility Driven Evolutionary Algorithm is applied for an exploration of the set of possible joint angles configurations in every moment. Additionally, the anticipation mechanism based on Auto-Regressive Integrated Moving Average Model is used in order to speed up an adaptation process so that a population of candidate solutions can be directed in advance towards the most probable future global optima.