On the motion stabilization of a three-link robotic manipulator with incomplete measurement

Abstract

Abstract. This paper considers a mathematical model of a manipulator which consists of a vertical column, two links, connected to it in series, and a gripper with a load. The column resting on a fixed base can rotate around its vertical axis. The links are connected by cylindrical hinges allowing them to rotate in the same vertical plane. The column and the links are modeled as rigid bodies with the links having unequal principal moments of inertia. The position of the manipulator in space is determined by three rotation angles of the column and the links. The manipulator can have several types of steady-state program movements. When gravitational torques are compensated by control torques applied in the cylindrical hinges, the manipulator has a program equilibrium position. The manipulator can also have a program motion when the column rotates at a given constant angular velocity, and the links have given relative equilibrium positions in their plane. The stabilization problem of manipulator motion is investigated by means of control torques with feedback when only the rotation angles of the column and links are measured. The problem posed is solved in the form of a nonlinear proportional-integral controller taking into account the cylindrical phase space of the manipulator's mathematical model. The solution includes construction of a Lyapunov functional with a semi-definite derivative and application of the corresponding theorems on the asymptotic stability of non-autonomous functional differential retarded-type equations. The obtained conditions for the program motion stabilization are robust with respect to the mass-inertial parameters of the manipulator. The numerical simulation results demonstrate global attraction to its given position in cylindrical phase space.