Dynamic Synthesis of Parallel-Sequential Structure Manipulator Control Algorithms

The paper is devoted to the development of an algorithm for the dynamic synthesis of control signals of actuators ensuring the required paths and application of motion laws of the manipulator’s effector. A parallel-sequential structure (hybrid) manipulator has been considered, which consists of a manipulator-tripod on a rotary base and a sequential structure manipulator with three controlled degrees of freedom. The effector moves from a known position to a given final one by changing the lengths of the tripod executive links and the rotation angles of the sequential structure manipulator links. Nonlinear dynamic equations obtained using the Lagrange equations with undetermined multipliers and additional holonomic constraints have been considered as a mathematical model of the controlled manipulator motions. The manipulator motions are determined by the nature of the process operation performed. In the paper, the issue of implementing the program effector paths predetermined in a parametric form has been resolved. First, the manipulator joint trajectories satisfying the given boundary conditions are determined. To do this, the effector motion laws are presented in a discrete form, and a point set characterizing the successive positions of the tripod actuators is determined by solving the optimization problem for the manipulator configuration (positional problem) providing minimum changes in the executive link lengths at each point of the effector path. Then, these values are interpolated by either a finite set of third and fourth-order splines or interpolation of the first and last path sections by fifth-order splines and the technique of point-based quadratic approximation of the intermediate path sections. The technique for the synthesis of dynamic algorithms for stabilizing the effector relative to a given position and implementing the program paths is based on generating the control signals of actuators by solving the inverse dynamic problem using a control signal generation algorithm provided that deviations from the current program path values are the solutions of a second-order differential equation. The actuator control circuits are synthesized when building the trajectory control algorithm. The numerical simulation results have been given that confirm the operability of the algorithm proposed on an example of the effector translation.

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