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.

翻译：在机器人系统控制律的开发过程中，评估其性能的核心因素是选择能使系统平滑跟踪参考输入的输入量。在机器人操作场景中，这涉及将物体或末端执行器从初始位姿转换到目标位姿。机器人操作控制律常利用视觉系统作为误差生成器来追踪特征并产生控制输入。然而，当前控制算法并未考虑所提取特征的概率特性，而是依赖人工调参的特征提取方法。此外，目标特征可能存在于静态位姿中，从而允许将位姿误差与特征误差相结合用于控制生成。我们针对机器人操作臂的视觉伺服问题提出了一种几何控制律。来自相机的输入构成三维特殊欧几里得任务空间群上的概率测度，其中当前位姿与目标位姿之间的Wasserstein距离类似于几何测地线。由此，我们通过将经典PD控制与重力补偿相结合，并利用三维特殊欧几里得群上的测地流实现误差最小化，开发了一种同时支持位姿基和图像基视觉伺服的控制器。我们在多个测试案例上展示了该方法对多种初始位置的泛化能力。