A geometric solver for calibrated stereo egomotion

This paper introduces a novel geometrical solution for the pose estimation of a stereo camera system as commonly used in robotics, where the camera system balances between coverage and overlap. The proposed approach considers a set of features observed, respectively, in four, three and two views. In contrast to most algebraic solutions our constraints are geometrically meaningful. Initially, we use a four view feature to restrict our translation vector to lie on the surface of a sphere while setting orientation as a function of translation up to a single rotational degree of freedom. Next, we use a three view feature to restrict the translation vector to lie on a circle on the sphere, while completely defining orientation as a function of translation. Finally, we use a two view feature to determine the translation vector lying on the intersection of the circle and one of the generator lines of a doubly ruled quadric. We show how for this final step, the problem can be reduced to the intersection of two coplanar circles. We also analyze the degenerate configurations of the proposed solver and perform an experimental evaluation.