Estimation and Control Methods for Position-Based Visual Servo Control using Dual Quaternions

In this work, a continuous time joint estimator-controller system is designed for the position based visual servo (PBVS) problem using a dual quaternion parametrization. A constrained extended Kalman filter (EKF) which provides pose estimates of an object of interest with respect to a camera is outlined. These pose estimates are then utilized in an exponentially stable proportional dual quaternion logarithmic controller to regulate the estimated pose to a desired pose. Proofs of stability for the controller and continuous time constrained EKF are provided individually, and then a nonlinear separation principle is used to prove the joint stability of the system. The proposed dual quaternion PBVS method is validated using a simulation, and a Monte Carlo simulation is used to evaluate the effectiveness of the dual quaternion parametrization in the estimation. The system is further verified in a robot experiment, where the end effector of a 7-DOF robot is guided to a desired position using feedback from a wrist-mounted camera.