Motion Control Along Spatial Curves for Robot Manipulators: A Noninertial Frame Approach

This paper presents an innovative approach to robot motion control that utilizes a noninertial tool frame with a specific parametrization to maintain a constant tool speed. The approach employs an efficient numerical technique that generates the constant-speed trajectory, correlating time with the curve's arc length. The robot motion equations are derived along the curve using two types of noninertial frames: (1) a rotation-minimizing frame (Bishop frame) which leverages its minimal twist property to simplify the motion equations and facilitates stable kinematics at trajectory inflection points and (2) a Darboux frame which is employed for paths given by spatial curves on surfaces. These motion equations are developed by projecting the trajectory tracking error onto the tangential, binormal, and normal directions of the moving frames. Feedback control laws are then developed for the motion equations in these projected (or transformed) coordinates to ensure stable trajectory error convergence to zero. Pertinent discussions are provided related to the advantages of using a moving frame over a fixed frame for enhanced precision in robotic motion control. The proposed approach facilitates precise spatial trajectory tracking, which is validated through real-time experiments with a Kuka iiwa robot, demonstrating its benefits in robot motion control for a wide variety of applications.