Diagrammatic Teaching is a paradigm for robots to acquire novel skills, whereby the user provides 2D sketches over images of the scene to shape the robot's motion. In this work, we tackle the problem of teaching a robot to approach a surface and then follow cyclic motion on it, where the cycle of the motion can be arbitrarily specified by a single user-provided sketch over an image from the robot's camera. Accordingly, we introduce the \emph{Stable Diffeomorphic Diagrammatic Teaching} (SDDT) framework. SDDT models the robot's motion as an \emph{Orbitally Asymptotically Stable} (O.A.S.) dynamical system that learns to follow the user-specified sketch. This is achieved by applying a \emph{diffeomorphism}, i.e. a differentiable and invertible function, to morph a known O.A.S. system. The parameterised diffeomorphism is then optimised with respect to the Hausdorff distance between the limit cycle of our modelled system and the sketch, to produce the desired robot motion. We provide theoretical insight into the behaviour of the optimised system and also empirically evaluate SDDT, both in simulation and on a quadruped with a mounted 6-DOF manipulator. Results show that we can diagrammatically teach complex cyclic motion patterns with a high degree of accuracy.

该研究介绍了一种名为"图解教学"的机器人获得新技能的范式，通过用户在场景图像上提供二维示意图来控制机器人的运动，并通过应用一种可微分且可逆函数（diffeomorphism）优化模型，实现对机器人运动的精确控制。实验证明，在模拟和实体机器人上，图解教学系统能够准确地教授复杂的循环运动模式。

学习轨道稳定系统以图示方式教学