The paper concentrates on the development and control of the humanoid robot arm iSoRA, intended for operation in a dynamic unstructured environment. Optical torque sensors integrated into each joint enable measurement of contacting forces along the entire manipulator surface. A variable admittance control strategy was elaborated to increase the robot functionality and to achieve the human-like dynamics of interaction. The experimental results show that the proposed approach not only provides safe interaction of the robot arm with a person, but also improves the effectiveness of contact task performance. The paper also presents a novel concept of avoidance of an obstacle of unknown shape. The tactile sensory ability of the developed manipulator allows robot links to follow the object contour and to perform motion planning in the dynamic environment. The information on the applied normal force vector, object shape and target point coordinates is supplied to the motion planning system. The algorithms for contact point detection, object geometry recognition, and estimation of contacting object stiffness are detailed. The numerical simulation elicits a capability of the proposed method to approximate various object shapes precisely. The experimental results showed that the local admittance control and motion planner allowed the end-effector to follow the object contour in a very smooth, consistent manner while reaching the target point.