This paper considers the development of gripping algorithm to grasp different objects by a two-finger manipulator of an anthropomorphic robot using a composite array of pressure and proximity capacitance sensors. The developed algorithm of link motion utilizes data from the composite array of pressure and proximity sensors, controlling the process of grip approach in the small neighborhood of gripping point through setting of position and orientation, required for grip, with specified accuracy levels. Based on the two-finger manipulator grip and on the data from the composite sensor arrays, embedded into robot fingers, several experiments were performed, using the developed algorithm of object grip. Dependencies for successful object grip were obtained, derived from orientation-related accuracy parameters and from finger configuration during grasp. It was revealed in process of testing of the developed algorithm that by optimal values of the specified parameters, the probability of successful grip was 97%. The proposed algorithm with certain modifications, which comply with the problem in question, is applicable for gait control of walking and anthropomorphic robots, as well for secure human-machine interactions, involving multi-link robotic systems.