Learning from Demonstration (LfD) is a popular method of reproducing and generalizing robot skills from human-provided demonstrations. In this paper, we propose a novel optimization-based LfD method that encodes demonstrations as elastic maps. An elastic map is a graph of nodes connected through a mesh of springs. We build a skill model by fitting an elastic map to the set of demonstrations. The formulated optimization problem in our approach includes three objectives with natural and physical interpretations. The main term rewards the mean squared error in the Cartesian coordinate. The second term penalizes the non-equidistant distribution of points resulting in the optimum total length of the trajectory. The third term rewards smoothness while penalizing nonlinearity. These quadratic objectives form a convex problem that can be solved efficiently with local optimizers. We examine nine methods for constructing and weighting the elastic maps and study their performance in robotic tasks. We also evaluate the proposed method in several simulated and real-world experiments using a UR5e manipulator arm, and compare it to other LfD approaches to demonstrate its benefits and flexibility across a variety of metrics.

翻译：示教学习（LfD）是一种通过人类提供的示教数据复现并泛化机器人技能的常用方法。本文提出一种新颖的基于优化的示教学习方法，该方法将示教数据编码为弹性地图。弹性地图是通过弹簧网格连接的节点图。我们通过将弹性地图拟合到示教数据集来构建技能模型。本方法构建的优化问题包含三个具有自然物理意义的优化目标：主目标项奖励笛卡尔坐标系中的均方误差；第二项惩罚点分布的非等距性，从而得到轨迹的最优总长度；第三项奖励平滑性同时惩罚非线性。这些二次型目标构成了一个凸优化问题，可通过局部优化器高效求解。我们研究了九种构建和加权弹性地图的方法，并分析了它们在机器人任务中的性能。同时，我们在仿真和真实环境中使用UR5e机械臂进行了多组实验评估，并通过与其它示教学习方法的对比，验证了所提方法在多项指标上的优势与灵活性。