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Cloth manipulation is a category of deformable object manipulation of greatinterest to the robotics community, from applications of automatedlaundry-folding and home organizing and cleaning to textiles and flexiblemanufacturing. Despite the desire for automated cloth manipulation, thethin-shell dynamics and under-actuation nature of cloth present significantchallenges for robots to effectively interact with them. Many recent works omitexplicit modeling in favor of learning-based methods that may yield controlpolicies directly. However, these methods require large training sets that mustbe collected and curated. In this regard, we create a framework fordifferentiable modeling of cloth dynamics leveraging an Extended Position-basedDynamics (XPBD) algorithm. Together with the desired control objective,physics-aware regularization terms are designed for better results, includingtrajectory smoothness and elastic potential energy. In addition, safetyconstraints, such as avoiding obstacles, can be specified using signed distancefunctions (SDFs). We formulate the cloth manipulation task with safetyconstraints as a constrained optimization problem, which can be effectivelysolved by mainstream gradient-based optimizers thanks to the end-to-enddifferentiability of our framework. Finally, we assess the proposed frameworkfor manipulation tasks with various safety thresholds and demonstrate thefeasibility of result trajectories on a surgical robot. The effects of theregularization terms are analyzed in an additional ablation study.

Achieving Autonomous Cloth Manipulation with Optimal Control via Differentiable Physics-Aware Regularization and Safety Constraints