Algebraic-Trigonometric Nonlinear Analytical Inverse Kinematic Modeling and Simulation for Robotic Manipulator Arm Motion Control

Abstract

Robotic manipulator arm has to endure certain challenges of actual applications that regularly affect its motion behavior incorporating end-effector positional accuracy and repeatability, degree-of-freedom constraint, redundant movement, heavy payload uplifting, long reach stretching, and other complications. This study works on finding inverse kinematic (IK) solutions to facilitate the robotic arm motion control with algebraic-trigonometric nonlinear analytical models. The nonlinear analytical models acquired from the extensive manipulation of trigonometric rules, specifically sum-and-difference and Pythagorean identities and algebraic arithmetic in pursuit of determining the reachable actuating joint configurations are experimented for applicability on the fundamental structure of two-segmented manipulator arm. For verification, the precision of the IK solutions yielded by the models are cross-referenced with the manipulator’s direct kinematics and tested with the statistical performance measure of minimum squared error while tracking cubic Hermite spline, cubic Bezier, and cubic B-spline curves. For validation, an interactive spreadsheet-based IK application utilizing built-in front-end capabilities including Visual Basic for Applications, Math and Trig Function Library, Name Manager, Data Validation, ActiveX Controls, and Charts is developed to accommodate these models and simulate the feasible joint angles and orientations of robot arm. The application visualizes (1) the robotic linkage motion on xz plane according to the links lengths, end-effector position, and base position specified and (2) the robotic curves trajectory tracking of cubic Hermite spline, cubic Bezier, and cubic B-spline. The algebraic-trigonometric nonlinear analytical models proposed provide alternative practical IK solutions for the two-segmented robotic manipulator arm.