Setpoint regulation of continuum robots using a fixed camera

We investigate the problem of measuring the shape of a continuum robot using visual information from a fixed camera. Specifically, we capture the motion of a set of fictitious planes, each formed by four feature points, defined at various strategic locations along the body of the robot. Then, utilizing expressions for the robot forward kinematics as well as the decomposition of a homography relating a reference image of the robot to the actual robot image, we obtain the three dimensional shape information continuously. We then use this information to demonstrate the development of a kinematic controller to regulate the end-effector of the robot to a constant desired position and orientation, while at the same time using its kinematic redundancy to satisfy a subtask objective such as obstacle avoidance.