Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories; however, they have three shortcomings: a) the DS is assumed to have a single attractor, which limits the diversity of tasks it can achieve, b) state derivative information is assumed to be available in the learning process and c) the state of the DS is assumed to be measurable at inference time. We propose a class of provably stable latent DS with possibly multiple attractors, that inherit the training methods of Neural Ordinary Differential Equations, thus, dropping the dependency on state derivative information. A diffeomorphic mapping for the output and a loss that captures time-invariant trajectory similarity are proposed. We validate the efficacy of our approach through experiments conducted on a public dataset of handwritten shapes and within a simulated object manipulation task.

翻译：从示教中学习复杂轨迹的问题已通过利用动力系统（DS）得到有效解决。最先进的DS学习方法确保了生成轨迹的稳定性，但存在三个缺陷：a) 假设DS具有单一吸引子，这限制了其可完成任务的多样性；b) 假设学习过程中可获得状态导数信息；c) 假设推理时可测量DS状态。我们提出一类具有可能多个吸引子的可证明稳定隐式DS，其继承了神经常微分方程的训练方法，因此消除了对状态导数信息的依赖。我们提出了输出的微分同胚映射以及捕捉时间不变轨迹相似性的损失函数。通过在公开手写形状数据集和模拟物体操作任务上的实验，我们验证了所提方法的有效性。