Programming robots to perform complex manipulation tasks is difficult because many tasks require sophisticated controllers that may rely on data such as manipulability ellipsoids, stiffness/damping and inertia matrices. Such data are naturally represented as Symmetric Positive Definite (SPD) matrices to capture specific geometric characteristics of the data, which increases the complexity of hard-coding them. To alleviate this difficulty, the Learning from Demonstration (LfD) paradigm can be used in order to learn robot manipulation skills with specific geometric constraints encapsulated in SPD matrices.

Learned skills often need to be adapted when they are applied to new situations. While existing techniques can adapt Cartesian and joint space trajectories described by various desired points, the adaptation of motion skills encapsulated in SPD matrices remains an open problem. In this paper, we introduce a new LfD framework that can learn robot manipulation skills encapsulated in SPD matrices from expert demonstrations and adapt them to new situations defined by new start-, via- and end-matrices. The proposed approach leverages Kernelized Movement Primitives (KMPs) to generate SPD-based robot manipulation skills that smoothly adapt the demonstrations to conform to new constraints. We validate the proposed framework using a couple of simulations in addition to a real experiment scenario.

对机器人进行编程以执行复杂的操纵任务非常困难，因为许多任务需要复杂的控制器，这些控制器可能依赖于诸如可操纵性椭球，刚度/阻尼和惯性矩阵之类的数据。此类数据自然地表示为对称正定（SPD）矩阵，以捕获数据的特定几何特征，这增加了对其进行硬编码的复杂性。为了减轻这一困难，可以使用“从演示中学习”（LfD）范例来学习具有封装在SPD矩阵中的特定几何约束的机器人操作技能。

当将所学技能应用于新情况时，通常需要对其进行调整。尽管现有技术可以适应由各种期望点描述的笛卡尔和关节空间轨迹，但是封装在SPD矩阵中的运动技能的适应仍然是一个悬而未决的问题。在本文中，我们引入了一个新的LfD框架，该框架可以从专家演示中学习封装在SPD矩阵中的机器人操作技能，并使它们适应由新的开始，通过和结束矩阵定义的新情况。所提出的方法利用核化运动原语（KMP）生成基于SPD的机器人操作技能，该技能可以平滑地使演示适应新的约束。除了实际的实验场景外，我们还使用一些模拟来验证所提出的框架。