一种用于可形变对象操作的动力学模型隐式求解方法

An Implicit Solution to the Dynamic Model for Deformable Object Manipulation

  • 摘要: 机器人操作可形变对象在多类场景中具有重要的应用需求。然而,对象复杂的高维动力学模型导致难以准确、快速地计算其形变。本文建立了一种基于交替方向乘子法的对象形变动力学模型快速、准确、隐式优化求解方法。该方法以通用对象几何模型为输入创建有限元模型,并分别构建材料本构势能函数和操作及碰撞交互单元的位置约束能量函数。随后,采用动力学投影方法构建基于交替方向乘子法的两项优化求解问题,最终快速、准确地计算对象在机器人操作下的形变。数值实验表明,所提出的方法能够在保证相对形变计算误差低于5%的条件下,实现高于24帧/秒的物理形态更新。针对实际应用场景,对所提出的方法开展了从形变仿真预测到在线操作执行的量化评估以及全局约束环境下的离线规划和仿真应用验证。

     

    Abstract: The demands for robotic manipulation of deformable objects is increasing in many fields. However, it is difficult to accurately and efficiently compute the deformation of deformable objects, due to their high-dimensional and complex dynamic model. Based on the alternating direction multiplier method (ADMM), this paper proposes an efficient and accurate implicit optimization solution to the object deformation dynamic model. This method takes the geometric model of a general object as input to generate a finite element model, then respectively constructs a material constitutive potential energy function and a positional constraint energy function of the manipulation and collision interaction elements. After that, a two-term optimization problem based on ADMM is constructed by utilizing a projective dynamics strategy, to calculate the object deformation under robotic manipulation accurately and efficiently. Numerical experiments show that the proposed method can achieve an updating rate greater than 24 frames per second for physical deformation calculation while guaranteeing a relative deformation error less than 5%. Some experiments from deformation simulation to online manipulation are also conducted in an actual application scenario for quantitative evaluation of the proposed method, and offline planning and simulation application in globally constrained environments are demonstrated.

     

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