This article discusses the issue of developing a system for copying control of a slave anthropomorphic manipulator using a master device in the form of an active exoskeleton that captures the movements of the operator's hand. The drives in the joints implement the force-torque feedback from the controlled manipulator. The tasks and requirements for the design of the master device, for the collection of information, and the speed of operation are considered. The issue of time delays in the control loop was considered. The question of the difference between the kinematic schemes of the exoskeleton and the manipulator is considered. A method is proposed for obtaining information about forces and torques through current information using an estimation system, a Kalman filter for a serial manipulator. For observation, an alternative description of the manipulator using a generalized momentum is given, which is well compatible with the set of parameters being measured. It also makes it possible not to use generalized accelerations and inversion of the mass-inertia matrix. The principle of the filter structure on the extended model is also used to estimate the external moments in the joints and the vector of forces applied to the end-effector. The computer experiments carried out in MATLAB Simulink showed an acceptable result and satisfactory quality of estimates of the external vector of forces and disturbing moments in the drives.