Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a stable vector field that resembles the desired motion dynamics. This is challenging as the robot state does not evolve on a Euclidean space, and therefore the stability guarantees and vector field encoding need to account for the geometry arising from, for example, the orientation representation. To tackle this problem, we propose learning Riemannian stable dynamical systems (RSDS) from demonstrations, allowing us to account for different geometric constraints resulting from the dynamical system state representation. Our approach provides Lyapunov-stability guarantees on Riemannian manifolds that are enforced on the desired motion dynamics via diffeomorphisms built on neural manifold ODEs. We show that our Riemannian approach makes it possible to learn stable dynamical systems displaying complicated vector fields on both illustrative examples and real-world manipulation tasks, where Euclidean approximations fail.
翻译:远程和自主机器人应该能够巧妙地执行精心设计的动态动作。 学习技巧可以用来构建这种动态技能的模型。 为了实现这一点, 学习模型需要将一个与理想运动动态相似的稳定矢量场编码。 这具有挑战性, 因为机器人状态不会在欧几里德空间上演进, 因此, 稳定性保障和矢量场编码需要考虑到诸如定向代表法等产生的几何。 为了解决这个问题, 我们提议从演示中学习里曼尼亚稳定的动态系统( RSDS ), 以便让我们对动态系统状态代表制产生的不同几何限制进行核算。 我们的方法为里曼多维体模型提供了莱普诺维度的保证。 我们展示了我们的里曼方法可以学习稳定动态系统, 显示在演示示例和真实世界操纵任务中显示复杂的矢量场, 在那里, 欧几里德近似失败 。