Several methods exist for teaching robots, with one of the most prominent being Learning from Demonstration (LfD). Many LfD representations can be formulated as constrained optimization problems. We propose a novel convex formulation of the LfD problem represented as elastic maps, which models reproductions as a series of connected springs. Relying on the properties of strong duality and perturbation analysis of the constrained optimization problem, we create a confidence metric. Our method allows the demonstrated skill to be reproduced with varying confidence level yielding different levels of smoothness and flexibility. Our confidence-based method provides reproductions of the skill that perform better for a given set of constraints. By analyzing the constraints, our method can also remove unnecessary constraints. We validate our approach using several simulated and real-world experiments using a Jaco2 7DOF manipulator arm.

翻译：机器人教学存在多种方法，其中最具代表性的方法之一是从演示中学习（LfD）。许多LfD表示可被构建为约束优化问题。我们提出了一种新颖的LfD问题凸优化表示形式，将其建模为弹性映射，该模型将技能复现过程描述为一系列相互连接的弹簧系统。基于约束优化问题的强对偶性与扰动分析特性，我们构建了一种置信度度量指标。本方法能够以不同置信度水平复现演示技能，从而产生不同级别的平滑度与灵活性。这种基于置信度的方法能够在给定约束条件下生成性能更优的技能复现结果。通过分析约束条件，本方法还能消除不必要的约束。我们通过使用Jaco2七自由度机械臂进行的多组仿真与真实世界实验验证了所提方法的有效性。