Trajectory Generation and LQR Control of a Three-Degree-of-Freedom Robotic Manipulator for Industrial Applications

Industrial automation involves developing efficient algorithms for both trajectory generation and robotic manipulator control. Robotic manipulators can be used for various applications, such as assembly, welding, and painting. This paper presents the modeling, trajectory planning, and control of a three-degree-of-freedom robotic manipulator with a revolute kinematic structure, typically employed for diverse industrial engineering applications. The kinematic model of the robotic arm is derived using the Denavit-Hartenberg formulation, and its dynamic behavior is obtained using the Lagrange equations of the second kind. A Cartesian trajectory of the end effector based on cubic spline interpolation is defined and transformed into joint space via inverse kinematics. Control is achieved using an inverse-dynamics feedforward approach combined with a Linear Quadratic Regulator (LQR) feedback controller. A comparative analysis of open-loop, closed-loop, and combined control strategies shows that the superimposed feedforward-feedback scheme improves tracking accuracy, robustness, and overall system performance.