Geometric Visual Servo Via Optimal Transport

When developing control laws for robotic systems, the principle factor when examining their performance is choosing inputs that allow smooth tracking to a reference input. In the context of robotic manipulation, this involves translating an object or end-effector from an initial pose to a target pose. Robotic manipulation control laws frequently use vision systems as an error generator to track features and produce control inputs. However, current control algorithms don't take into account the probabilistic features that are extracted and instead rely on hand-tuned feature extraction methods. Furthermore, the target features can exist in a static pose thus allowing a combined pose and feature error for control generation. We present a geometric control law for the visual servoing problem for robotic manipulators. The input from the camera constitutes a probability measure on the 3-dimensional Special Euclidean task-space group, where the Wasserstein distance between the current and desired poses is analogous with the geometric geodesic. From this, we develop a controller that allows for both pose and image-based visual servoing by combining classical PD control with gravity compensation with error minimization through the use of geodesic flows on a 3-dimensional Special Euclidean group. We present our results on a set of test cases demonstrating the generalisation ability of our approach to a variety of initial positions.