Long-term non-prehensile planar manipulation is a challenging task for robot planning and feedback control. It is characterized by underactuation, hybrid control, and contact uncertainty. One main difficulty is to determine contact points and directions, which involves joint logic and geometrical reasoning in the modes of the dynamics model. To tackle this issue, we propose a demonstration-guided hierarchical optimization framework to achieve offline task and motion planning (TAMP). Our work extends the formulation of the dynamics model of the pusher-slider system to include separation mode with face switching cases, and solves a warm-started TAMP problem by exploiting human demonstrations. We show that our approach can cope well with the local minima problems currently present in the state-of-the-art solvers and determine a valid solution to the task. We validate our results in simulation and demonstrate its applicability on a pusher-slider system with real Franka Emika robot in the presence of external disturbances.

许多数值优化技术的收敛性对提供给求解器的初始猜测高度敏感。我们提出了一种基于张量方法的方法，以初始化靠近全局Optima的现有优化求解器。该方法仅使用成本函数的定义，不需要访问任何良好解决方案的数据库。我们首先将成本函数（这是任务参数和优化变量的函数）转换为概率密度函数。与将任务参数设置为常数的现有方法不同，我们将它们视为另一组随机变量，并使用替代概率模型近似任务参数的关节概率分布和优化变量。对于给定的任务，我们就给定的任务参数从条件分布中生成样本，并将其用作优化求解器的初始化。由于调节和来自任意密度函数的调节和采样具有挑战性，因此我们使用张量列车分解来获得替代概率模型，我们可以从中有效地获得条件模型和样品。该方法可以为给定任务产生来自不同模式的多个解决方案。我们首先通过将其应用于各种具有挑战性的基准函数来评估该方法以进行数值优化，这些功能很难使用基于梯度的优化求解器以幼稚的初始化来求解，这表明所提出的方法可以生成靠近全局优化的样品，并且来自多种模式。 。然后，我们通过将所提出的方法应用于7-DOF操纵器来证明框架的通用性及其与机器人技术的相关性。