Control of a multi-fingered robotic hand is usually based on the theoretical analysis for kinematics and dynamics of fingers and of object. However, the implementation of such analyses to robotic hands is difficult because of errors and uncertainties in the real situations. This article presents the control method for estimating the kinematic constraint of an unknown object by active sensing. The experimental system has a two-fingered robotic hand suspended vertically for manipulation in the vertical plane. The fingers with three degrees-of-freedom are driven by wires directly connected to voice-coil motors without reduction gears. The fingers are equipped with three-axis force sensors and with dynamic tactile sensors that detect slippage between the fingertip surfaces and the object. In order to make an accurate estimation for the kinematic constraint of the unknown object, i.e. the constraint direction and the constraint center, four kinds of the active sensing and feedback control algorithm were developed: two position-based algorithms and two force-based algorithms. Furthermore, the compound and effective algorithm was also developed by combining two algorithms. Force sensors are mainly used to adapt errors and uncertainties encountered during the constraint estimation. Several experimental results involving the motion of lifting a finger off an unknown object are presented.