Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose incorporating barrier certificates into an optimization problem to learn a stable and barrier-certified DS. Such optimization problem can be very complex or extremely conservative when the traditional linear parameter-varying formulation is used. Thus, different from previous approaches in the literature, we propose to use polynomial representations for DSs, which yields an optimization problem that can be tackled by sum-of-squares techniques. Finally, our approach can handle obstacle shapes that fall outside the scope of assumptions typically found in the literature concerning obstacle avoidance within the DS learning framework. Supplementary material can be found at the project webpage: https://martinschonger.github.io/abc-ds

翻译：现有让机器人从示范中学习的技术基于学习稳定的动力系统（DS）。为增强机器人在涉及静态障碍物避障任务中对抗扰动的韧性，我们提出将屏障证书整合到优化问题中，从而学习一个既稳定又带屏障证书的DS。当使用传统的线性参数变化表述时，此类优化问题可能极其复杂或极度保守。因此，不同于文献中的现有方法，我们提出使用DS的多项式表示，由此产生的优化问题可通过平方和技巧求解。最后，我们的方法能够处理超出DS学习框架中障碍物避障文献常见假设范围的障碍物形状。补充材料见项目网页：https://martinschonger.github.io/abc-ds