GEOMETRIC MODELING AND COMPLEXITY ANALYSIS OF ALGORITHMS FOR CALCULATING KINEMATIC PARAMETERS OF ROBOT MANIPULATION SYSTEMS

When analyzing the movement of robot manipulation systems, it becomes necessary to calculate the speeds and accelerations of the points selected on its links, which make up the set of kinematic parameters of a given mechanical system. Algorithms for calculating kinematic parameters of robot manipulation systems are based on vector-matrix equations, which can be obtained based on a geometric model describing the structure of a complex mechanism. The paper describes an original method for constructing a universal geometric model of the mechanisms of robot manipulation systems, based on linking two coordinate systems to each link of the mechanism and compiling linear operators corresponding to these systems – matrices (44) of homogeneous coordinate transformation. This made it possible to identify parts of the geometric model that are independent of the relative position of the links of the mechanism and exclude these parts from the computational process as quantities that change during the movement of the mechanism. In turn, the allocation of parts of the geometric model that change during the movement of the mechanism made it possible to use special differentiation matrices to calculate partial derivatives of homogeneous coordinate transformation matrices according to the corresponding generalized coordinates and ensured the universality of algorithms for modeling the movement of manipulation mechanisms created using them. An analysis of the complexity of the algorithms obtained on the basis of the geometric model was carried out by comparing the numbers of addition and multiplication operations used in the algorithms, which showed that only on the basis of the associativity property can computing efficiency be increased three times. A further increase in computational efficiency can be achieved by paralleling calculations.