Nowadays the introduction of robotic systems is one of the most common forms of the technological operations automation in various spheres of human activity. Among the robotic systems a special place is occupied by sequential multi-link robotic manipulators (SRM). SRM have become widespread due to relatively small dimensions and high maneuverability, which makes their use indispensable to solve various tasks. In practice, the effectiveness of the functioning of the SRM can be influenced by various types of external environment fuzzy factors. Among the external factors there is a group affecting the ability to determine the exact target position. Such factors often affect technical vision systems. This problem is especially relevant for special purpose mobile robots operating in aggressive environmental conditions. A situation similar to the described one also occurs when a medical robot manipulator is used for minimally invasive surgery, when the role of the control and monitoring system is assumed by an operator. In this regard, the organization of effective control taking into account influence of the external fuzzy factors, that prevent the correct recognition of the target position of the SRM instrument, is an urgent problem. The authors consider the solution of the inverse kinematics problem for SRM based on the use of fuzzy numerical methods, taking into account the possible occurrence of singular configurations in the process of solving.