Solving the problem of stabilizing a given position and programmed motion of an anthropomorphic robotic arm

A three-link anthropomorphic robotic arm moving in a vertical plane with viscous friction in the joints is considered. The problems of stabilizing a given position and a programmed motion are solved under the condition that only the joint angles are measured. For position stabilization, a nonlinear PI controller with feedback on the signs of half the error angles is proposed. Using Lyapunov functions, explicit conditions on the gains and the damping coefficient are obtained under which the position is stabilized for any initial deviations. For piecewise-constant sampled-data control, a bound on the admissible sampling period is found. For tracking a programmed motion, a control law with a dynamic filter replacing velocity measurement is constructed. It is proved that, under the conditions found, the tracking error tends to zero modulo 2π for any initial conditions. The results are confirmed by numerical simulation.