Pose and motion estimation from vision using dual quaternion-based extended Kalman filtering

Determination of relative three-dimensional (3-D) position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to this problem that uses two-dimensional (2-D), intensity images from a single camera is desirable for real-time applications. Where the object geometry is unknown, the estimation of structure is also required. A single camera is advantageous because a standard video camera is low in cost, setup and calibration are simple, physical space requirements are small, reliability is high, and low-cost hardware is available for digitizing and processing the images. A difficulty in performing this measurement is the process of projecting 3-D object features to 2-D images, a nonlinear transformation. Noise is present in the form of perturbations to the assumed process dynamics, imperfections in system modeling, and errors in the feature locations extracted from the 2-D images. This dissertation presents solutions to the remote measurement problem for a dynamic system given a sequence of 2-D intensity images of an object where feature positions of the object are known relative to a base reference frame and where the feature positions are unknown relative to a base reference frame. The 3-D transformation is modeled as a nonlinear stochastic system with the state estimate providing six degree-of-freedom motion and position values. The stochastic model uses the iterated extended Kalman filter as an estimator and as a screw representation of the 3-D transformation based on dual quaternions. Dual quaternions provide a means to represent both rotation and translation in a unified notation. The method has been implemented and tested with both simulated and actual experimental data. Simulation results are provided along with comparisons to a point-based method using rotation and translation to show the relative advantages of the proposed method. Experimental test results using a camera mounted on the end effector of a robot arm to demonstrate relative motion and position control are also presented.