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The paper is devoted to the construction of a mathematical model of the dynamics of a parallel structure manipulator with three controlled degrees of freedom, based on the reduction of the kinetic energy of the manipulator to a quadratic form relative to three independent generalized coordinates, comparative results of mathematical modeling are presented.

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.

Algorithm for synthesis of control voltages of electric motor at movement of working element of manipulator of parallel structure based on tripod from initial position to specified final position at fixed time of movement from condition of minimum criterion characterizing heating of electric motor is developed.

Synthesis methods for program displacements are developed for executive cylinders of the manipulator of a parallel-sequential structure, that ensure implementation of the required trajectories of the executive device of a manipulator. Program displacements of executive cylinders are interpolated by a finite collection of third-order and fourth-order splines. At each point of the trajectory of the executive device, the manipulator configuration is determined by resolving an optimization problem with the minimum condition of the generalized energy criterion.

The article considers the development of a control algorithm for the actuating links of a manipulator with a parallel-serial structure. The authors suggest a two-stage procedure for resolving the problem of controlling the robot operating body motion into a set neighborhood of the final state for a set time. The first stage covers the process of solving the problem of defining the manipulator generalized coordinates at the set coordinates of the operating body. Then the problem of determining the laws of the formation of reference influences for the actuators is solved, which ensures the movement of the working body in the vicinity of a given point. 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 laws of change in control voltages are obtained. The results of numerical modeling are presented, confirming the efficiency of the proposed algorithm on the example of a specific manipulator.

The mathematical model of dynamics of the electric-power DC drive for actuating links of tripod manipulator with self-breaking transmission has been considered. Analytical conditions of lack of dynamic jamming the drive have been obtained.

Method of synthesis of kinematic algorithm of stabilization of spatial position of manipulator gripper of parallel-serial structure relative to given position is described in work. Coordinates and speeds and accelerations of generalized coordinates of manipulator are taken as control parameters. Analytical ratios of the control signals of the drive electric motors are obtained, which ensure the movement of the working body of the manipulator in the vicinity of the designated point. Numerical examples of the implementation of the obtained control laws are given.

Design features of manipulators of a parallel-serial structure based on a tripod are considered. kinematic diagram of a manipulator-tripod on a rotary base is presented, consisting of two series-connected manipulators - a manipulator-tripod of a parallel structure and a manipulator of a serial structure, and its configuration is considered, which is determined by solving an optimization problem from the condition of a minimum criterion of generalized energy. The sequential manipulator acts as a gripper. The number of degrees of freedom of the manipulator is seven. As actuating links, links with electric DC drive (actuators) are used. All actuators are equipped with an integrated analog displacement sensor. In the structure of the manipulator, the axes of the drive links of linear movement geometrically converge at one point by means of a spherical five-movable hinge assembly, which eliminates the appearance of bending moments in them from external loads from the side of the gripping device. The results of the implementation of the algorithm for constructing the service area of a manipulator of a parallel-sequential structure with a grip are presented.

A tripod-based parallel structure manipulator is considered in the article. The movement of the working body from a known position to a given final position is realized by changing the lengths of the tripod end points. Linear links with an electric DC drive are used as end points. The algorithm was developed for the synthesis of the electric motor control voltages when moving the parallel structure manipulator working body based on the tripod from the initial position to the specified final position of the fixed travel time from the minimum criterion characterizing heating of the electric motor. The mathematical model of the manipulator controlled movements is described by linear differential equations of the second order. The static characteristic of the motor is used. The resistance force is taken proportional to the working body movement speed. The problem is solved by the methods of classical calculus of variations. The results of numerical modeling are presented, confirming the effectiveness of the proposed algorithm for determining the working body movement optimal laws.

A mathematical model was developed for dynamics of spatial controlled movements of end-effector being a multi-mass electromechanical system.

The motion of a mobile robot with orthogonal walking drives is considered. The problem of reducing power consumption of drive motors for overcoming the forces of linear viscous resistance and nonlinear forces of dry friction in the case of straight motion of the robot is considered. Methods of variational calculus are used to determine the optimal program law of motion from the condition of minimum thermal losses of drive electric motors.

We consider the problem of control of motion of a many-legged statically stable locomotion machine ensuring the choice of a minimal-power motor. We show that the machine frame can be used as a kinetic energy recuperator, thus providing a significant decrease in the reactive power.

The walking machines of ground practicability are under consideration. The methods of calculations of the dynamic movement characteristics have been elaborated. The real walking machine has been designed, produced and tested on the basis of proposed methods of calculations.

Multilegged statically stable walking machines of soil cross-country capability with propellers on the basis of cycle mechanisms are under consideration. The turn both of existing and elaborating walking machines moving on comparativelly flat surface with poor carrying ability was learned out. Methods of parameters calculations of the kinematic scheme and control system for the new elaborating walking machine providing stable motion has been developed.