Learning from humans allows non-experts to program robots with ease, lowering the resources required to build complex robotic solutions. Nevertheless, such data-driven approaches often lack the ability to provide guarantees regarding their learned behaviors, which is critical for avoiding failures and/or accidents. In this work, we focus on reaching/point-to-point motions, where robots must always reach their goal, independently of their initial state. This can be achieved by modeling motions as dynamical systems and ensuring that they are globally asymptotically stable. Hence, we introduce a novel Contrastive Learning loss for training Deep Neural Networks (DNN) that, when used together with an Imitation Learning loss, enforces the aforementioned stability in the learned motions. Differently from previous work, our method does not restrict the structure of its function approximator, enabling its use with arbitrary DNNs and allowing it to learn complex motions with high accuracy. We validate it using datasets and a real robot. In the former case, motions are 2 and 4 dimensional, modeled as first- and second-order dynamical systems. In the latter, motions are 3, 4, and 6 dimensional, of first and second order, and are used to control a 7DoF robot manipulator in its end effector space and joint space. More details regarding the real-world experiments are presented in: \url{https://youtu.be/OM-2edHBRfc}.

翻译：通过人类示范进行学习使非专家用户能够轻松编程机器人，从而降低构建复杂机器人解决方案所需的资源。然而，这类数据驱动方法往往无法对其学习到的行为提供保证，这对避免故障和/或事故至关重要。本研究聚焦于到达/点对点运动任务——机器人必须始终从任意初始状态抵达目标位置。该目标可通过将运动建模为动力学系统并确保其全局渐近稳定性来实现。为此，我们提出一种新型对比学习损失函数用于训练深度神经网络（DNN），当该损失函数与模仿学习损失函数协同使用时，能强制所学运动具备上述稳定性。与以往研究不同，本方法不限制函数逼近器的结构，因此可适配任意深度神经网络，并支持以高精度学习复杂运动。我们通过数据集仿真与实际机器人实验验证了该方法的有效性。在仿真实验中，运动任务为2维和4维空间，分别建模为一阶和二阶动力学系统。在实际机器人实验中，运动任务涵盖3维、4维和6维空间（含一阶与二阶系统），并用于控制七自由度机器人操作臂的末端执行器空间与关节空间运动。更多真实实验细节参见：\url{https://youtu.be/OM-2edHBRfc}。