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：从演示中学习(LfD)是复制和普及人类提供演示的机器人技能的流行方法。在本文中,我们提议了一种新的基于优化的LfD方法,将演示编码为弹性图。弹性图是一个通过泉水网状连接的结点图。我们通过将弹性图与成套演示相配,来构建一个技能模型。我们的方法中的配制优化问题包括自然和物理解释的三个目标。主要术语是对笛卡尔斯坐标中的平均正方形错误的奖励。第二个术语惩罚了导致轨道总长度最佳的点的非等距离分布。第三个术语在惩罚非线性的同时奖励平滑。这些四边目标形成了一个可以与当地优化者高效解决的锥形问题。我们研究了9个构建和加权弹性图的方法,并研究了其在机器人任务中的性能。我们还评估了在使用UR5调控器进行的若干模拟和实际实验中的拟议方法,并将它与其他LfD方法进行了比较,以展示其效益和灵活性。