Abstract Trajectory planning through dynamical systems (DS) provides robust control for robots and has found numerous applications from locomotion to manipulation. However, to date, DS for controlling rhythmic patterns are distinct from DS used to control point to point motion and current approaches switch at run time across these to enable multiple behaviors. This switching can be brittle and subject to instabilities. We present an approach to embed cyclic and point to point dynamics in a single DS. We offer a method to learn the parameters of complete DS through a two-step optimization. By exploiting Hopf bifurcations, we can explicitly and smoothly transit across periodic and non-periodic phases, linear and nonlinear limit cycles, and non-periodic phases, in addition to changing the equilibrium’s location and the limit cycle’s amplitude. We use diffeomorphism and learn a mapping to modify the learned limit cycle to generate nonlinear limit cycles. The approach is validated with a real 7 DOF KUKA LWR 4+ manipulator to control wiping and with a humanoid robot in simulation.

中文翻译：

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学习具有分叉的动力系统

摘要 通过动态系统 (DS) 进行的轨迹规划为机器人提供了稳健的控制，并且已经发现了从运动到操纵的众多应用。然而，迄今为止，用于控制节奏模式的 DS 与用于控制点对点运动的 DS 不同，当前方法在运行时切换这些模式以实现多种行为。这种切换可能很脆弱并且容易不稳定。我们提出了一种在单个 DS 中嵌入循环和点对点动态的方法。我们提供了一种通过两步优化来学习完整 DS 参数的方法。通过利用 Hopf 分岔，除了改变平衡点的位置和极限环的幅度之外，我们还可以明确且平滑地跨越周期和非周期相位、线性和非线性极限环以及非周期相位。我们使用微分同胚并学习映射来修改学习到的极限环以生成非线性极限环。该方法通过真正的 7 DOF KUKA LWR 4+ 机械手来控制擦拭，并在仿真中使用仿人机器人进行验证。