Inverse Kinematic Manipulation Control and Trajectory Tracking of Robotic Arm Using Trigonometric Tangential Mathematical Models

Abstract

Industrial robot is forced to sustain certain complications of real-world applications that continually influence its motion competency embracing end-effector positional accuracy and repeatability, degree-of-freedom limitation, redundant movement, heavy payload uplifting, long horizontal reach stretching, and others. This work focuses on devising inverse kinematic (IK) solutions to assist the robotic arm motion control using trigonometric tangential mathematical models. The nonlinear mathematical models acquired from the extensive manipulation of trigonometric rules, specifically sum, Pythagorean, and tangent quotient 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 randomly benchmarked 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 robotic arm. The application visualizes (1) the robotic linkage motion on xz plane according to the links lengths, end-effector position, and base position stipulated and (2) the robotic curves trajectory tracking of cubic Hermite spline, cubic Bezier, and cubic B-spline. The trigonometric tangential mathematical models suggested afford a credible and practical IK solution alternative for the manipulation control and trajectory tracking of two-segmented robotic manipulator arm.