Title: Geometric Visual Servo Via Optimal Transport Show Chinese title

Title: 基于最优传输的几何视觉伺服

Abstract: 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. Show Chinese abstract

Abstract: 在为机器人系统开发控制律时，考察其性能的主要因素是选择能够实现平滑跟踪参考输入的输入。 在机器人操作的背景下，这涉及将物体或末端执行器从初始姿态移动到目标姿态。 机器人操作控制律经常使用视觉系统作为误差生成器来跟踪特征并产生控制输入。 然而，当前的控制算法并未考虑提取的概率特征，而是依赖于手工调整的特征提取方法。 此外，目标特征可能处于静态姿态，从而允许结合姿态和特征误差用于控制生成。 我们提出了一种几何控制律，用于解决机器人操作器的视觉伺服问题。 来自摄像机的输入构成了三维特殊欧几里得任务空间群上的概率测度，在该群中，当前姿态与期望姿态之间的 Wasserstein 距离类似于几何测地线。 基于此，我们开发了一种控制器，通过结合经典PD控制与重力补偿，并利用三维特殊欧几里得群上的测地流来最小化误差，从而实现了姿态和基于图像的视觉伺服。 我们在一组测试用例上展示了我们的结果，证明了我们的方法对多种初始位置的泛化能力。