Kinematic-Free Orientation Control for a Deformable Manipulator Based on the Geodesic in Rotation Group SO(3)

Abstract

Orientation control is an important topic with many applications including robotic manipulation, spacecraft control, etc. The orientation control is particularly challenging when the system model is unknown due to the fact that the rotation group is a nonlinear manifold. In this letter, we propose a kinematic-free orientation control method for a deformable manipulator whose kinematic parameters are unknown. We estimate the Jacobian matrix by independently and incrementally actuating each joint and observing their effects on the orientation of the affected end-effector. Considering the nonlinear property, we generate a temporary and anticipant target by cutting a small distance on the geodesic in each control period, instead of using the target orientation directly. The geodesic is from the current orientation to the target orientation in SO (3). Our method guarantees global convergence and can automatically adapt to drastic changes in kinematic parameters, which is very difficult for model-based methods. Our method is implemented to control a 4-DOF deformable manipulator. The simulation and experimental results demonstrate the effectiveness of our method.