An Implicit Solution to the Dynamic Model for Deformable Object Manipulation

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.