Learning from Demonstration allows robots to mimic human actions. However, these methods do not model constraints crucial to ensure safety of the learned skill. Moreover, even when explicitly modelling constraints, they rely on the assumption of a known cost function, which limits their practical usability for task with unknown cost. In this work we propose a two-step optimization process that allow to estimate cost and constraints by decoupling the learning of cost functions from the identification of unknown constraints within the demonstrated trajectories. Initially, we identify the cost function by isolating the effect of constraints on parts of the demonstrations. Subsequently, a constraint leaning method is used to identify the unknown constraints. Our approach is validated both on simulated trajectories and a real robotic manipulation task. Our experiments show the impact that incorrect cost estimation has on the learned constraints and illustrate how the proposed method is able to infer unknown constraints, such as obstacles, from demonstrated trajectories without any initial knowledge of the cost.

翻译：从演示中学习使机器人能够模仿人类动作。然而，这些方法并未对确保所学技能安全性的关键约束进行建模。此外，即使显式建模约束，它们也依赖于已知成本函数的假设，这限制了其在成本未知任务中的实际可用性。本文提出一种两步优化过程，通过将成本函数的学习与演示轨迹中未知约束的识别解耦，从而估计成本与约束。首先，我们通过隔离约束对部分演示的影响来识别成本函数。随后，使用约束学习方法识别未知约束。我们的方法在仿真轨迹和真实机器人操作任务中均得到验证。实验表明，错误的成本估计对所学约束的影响，并展示了所提方法如何在没有任何成本先验知识的情况下，从演示轨迹中推断出障碍物等未知约束。