Direct control of the endpoint of the manipulator under non-smooth uncertainty and reference trajectories

The problem of tracking the reference trajectory for the manipulator endpoint is considered under the following assumptions: the matrices of the mechanical system have uncertain parameters; external nonsmooth disturbances act on the system; and only the vector of generalized coordinates of the manipulator is measured. This vector is uniquely recalculated into the vector of positions of the endpoint. A direct method for the synthesis of a tracking system is proposed, which does not require solving the inverse position problem. The manipulator model is represented in the canonical input-output form considering the vector of the endpoint. The input is a vector of generalized moments developed by the actuators. The complexity of regulation consists of the uncertainty of the input matrix. To stabilize tracking errors under these conditions, a method of linearization by dynamic feedback has been developed. For estimating mixed variables and disturbances, an observer of the minimum possible dynamic order is proposed. A cascade procedure for tuning S-shaped smooth and nonlinear (sigmoid) corrective actions of the observer is presented. This procedure provides an estimation of non-smooth disturbances in a given time with a given accuracy. To smooth primitive trajectories that define, as a first approximation, the desired movement of the endpoint in the workspace, tracking differentiators with sigmoid local feedbacks are used. To tune a tracking differentiator of arbitrary dimension, a decomposition procedure is developed. This procedure considers physical constraints on the velocity and higher derivatives of the manipulator endpoint. The variables of such a differentiator generate smoothed trajectories and their derivatives of any desired order. These trajectories become achievable for the robot. They are used in the tracking