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：机器人教授方法众多，其中最具代表性的是示范学习（LfD）。许多LfD表示可转化为约束优化问题。我们提出了一个新颖的凸优化框架，将LfD问题表示为弹性映射模型，将技能再现建模为一系列串联弹簧。借助强对偶性以及约束优化问题的扰动分析性质，我们构建了置信度度量指标。该方法允许以不同置信水平再现示范技能，从而产生不同级别的平滑度与灵活性。基于置信度的方法能在给定约束条件下生成更优的技能再现结果。通过分析约束，该方法还可移除冗余约束。我们使用Jaco2七自由度机械臂进行了多项仿真与真实实验验证。