Robust second order sliding mode control for 6D position based visual servoing with a redundant mobile manipulator

This paper presents a second order sliding mode controller for Position-Based Visual Servoing. The pose of a 7 DoF robot arm is controlled in position and orientation using visual information from a monocular camera. To handle large errors produced by the initial error condition or by occlusions in the field of view an additional bias function is introduced. The bias prevents the system from generating large overshoots in the joint efforts which exceed the maximum joint torques of the robot when the error condition is high. Even if the distance between current and desired pose is large, the end effector is moving smoothly to regain tracking. After occlusions the bias reduces the torques from peaks of 45 Nm to a maximum of 7 Nm. While in many researches the camera is used in an eye-in-hand configuration, this approach uses an observing camera in the head of the robot. To control the redundant robot with joint efforts, the Moore-Penrose pseudoinverse maps the desired cartesian velocities to joint velocities. Additionally a nullspace analysis is used with a secondary fixed pose task to suppress undesired motions. We validate our control approach on a real PR2 robot.