Robotic Motion Planning Using the Jacobian Matrix-Based Inverse Kinematics Algorithm

Abstract

Planning a robot’s motion once meant mapping a static room; now it means sending a fragile drone through the living room and kitchen without leaving a dent. This work investigates Jacobian-Matrix-Based Inverse Kinematics as a toolbox for that job, testing how well it steers, stops, and resets robotic arms that must mimic human manipulation. The Jacobian acts like the machine’s translator, converting tiny wrist-fed velocity orders into joint twists almost instantaneously. When arms sport a dozen servos, though, that translation hides in gnarly nonlinear equations with no tidy algebraic answer. The iterative Jacobian trick sidesteps the mess by flattening the curve at every loop, nudging the hardware closer to the goal without a crystal ball. The paper spells out the Jacobian, plays with its pseudoinverse, and wraps a damping blanket around both to dodge singular corners and jittery solvers. Synthetic runs on a six-jointed testbed, then measures how straight the end effector walks, how many processor ticks each substep steals, and whether prints settle to a target within a human-acceptable blink. The experiments show that the Jacobian method minds the budget even in excess-joint kinematics, wraps movement in curves rather than corners, and adapts on the run when workspace furniture shifts or speed orders change. The paper also examines optimization procedures paired with the Jacobian technique to reduce both energy use and overall joint motion. Experiments that task the robot with avoiding obstacles and rearranging its path provide additional evidence of the method's robustness. Because it delivers the needed accuracy and flexibility, the approach is well-suited to industrial automation lines, surgical robots, and service platforms alike. In summary, the work positions Jacobian-based inverse kinematics as a broadly applicable strategy for high-performance robotic motion control