Analysis of the Computational Complexity of the Method of Iterative Dimensional-Linear Generation of the Trajectory of Motion of the Three-Line Anthropomorphic Manipulator in the Volume Space With Obstruction

Abstract

Energy efficiency is an actual problem of the present, including in the field of robotics. Existing methods for planning the trajectory of motion of manipulators with excessive mobility face a number of problems, one of which is the impossibility of working in real time mode due to the high complexity of the scheduling algorithm. Moreover, the existing algorithms that work in real time are significantly inferior to the accuracy of the target operations. Therefore, earlier, in the author's articles, an iterative method of piecewise linear generation of the manipulator's trajectory was developed. In this paper, we analyze the computational complexity of the numerical method of iterative piecewise linear generation of the trajectory of a three-link anthropomorphic manipulator with 7 degrees of mobility in a volume space with an obstacle, an approximated hypersphere, in real time. A short description of the proposed method of planning the trajectory of motion is given. To move between the waypoints, the Denavite-Hartenberg representation used, with the formulation and solution of the problem of nonlinear optimization with the objective function of minimizing energy consumption when the manipulator moved to the target point. The initial generalized algorithm of the path planning method described. The number of operations that must performed in the process of execution of a recursive algorithm is considered. Parallelizing the branching recursive algorithm allows you to reduce the execution time to the time of executing a non-branching recursive algorithm with the same computational complexity and depth. A formula developed that allows you to select the values of variable parameters of the algorithm based on the available computational power and the allowable calculation time, and to determine the requirements for the manipulator computer system at the development stage.

Energy-Efficient Path Planning: Designed Software Implementation

“…The component "Optimization" is intended to provide optimal solution to inverse kinematics problem for determining the final position of the anthropomorphic robotic arm [2,4].…”

“…To calculate the manipulator's final position in the workspace with obstacle, we used the optimization method for the inverse kinematics problem based on the Denavit-Hartenberg representation and the generalized reduced gradient method where the condition for finding the optimal value of the function intends the condition for minimizing the energy consumed by manipulator engines. [4].…”