Dynamic Manipulation of Deformable Objects with Implicit Integration

Due to their complex dynamics and high-dimensional configuration spaces, non-rigid objects such as cables, garments, bedding and various food items remain notoriously challenging for robots to manipulate effectively. In this letter, we therefore develop, validate and analyze model-based optimal control techniques for dynamic manipulation of deformable objects. We study, in particular, the application of both the batch Newton method and the stagewise Differential Dynamic Programming (DDP) approach to this challenging problem domain. On a technical level, we derive analytic formulations for all necessary derivatives, noting that numerically stable simulation of deformable objects demands implicit integration schemes, which do not have closed form solutions. While both DDP and Newton's method converge quadratically, our experiments and analysis show that the relative overall performance of these two approaches depends heavily on the dimensions of the control problems being solved. We demonstrate the efficacy of our trajectory optimization formulations through a variety of simulation and real-world experiments.