Deformable object manipulation is critical to many real-world robotic applications, ranging from surgical robotics and soft material handling in manufacturing to household tasks like laundry folding. At the core of this important robotic field is shape servoing, a task focused on controlling deformable objects into desired shapes. The shape servoing formulation requires the specification of a goal shape. However, most prior works in shape servoing rely on impractical goal shape acquisition methods, such as laborious domain-knowledge engineering or manual manipulation. DefGoalNet previously posed the current state-of-the-art solution to this problem, which learns deformable object goal shapes directly from a small number of human demonstrations. However, it significantly struggles in multi-modal settings, where multiple distinct goal shapes can all lead to successful task completion. As a deterministic model, DefGoalNet collapses these possibilities into a single averaged solution, often resulting in an unusable goal. In this paper, we address this problem by developing DefFusionNet, a novel neural network that leverages the diffusion probabilistic model to learn a distribution over all valid goal shapes rather than predicting a single deterministic outcome. This enables the generation of diverse goal shapes and avoids the averaging artifacts. We demonstrate our method's effectiveness on robotic tasks inspired by both manufacturing and surgical applications, both in simulation and on a physical robot. Our work is the first generative model capable of producing a diverse, multi-modal set of deformable object goals for real-world robotic applications.

Shape servoing, a robotic task dedicated to controlling objects to desired goal shapes, is a promising approach to deformable object manipulation. An issue arises, however, with the reliance on the specification of a goal shape. This goal has been obtained either by a laborious domain knowledge engineering process or by manually manipulating the object into the desired shape and capturing the goal shape at that specific moment, both of which are impractical in various robotic applications. In this paper, we solve this problem by developing a novel neural network DefGoalNet, which learns deformable object goal shapes directly from a small number of human demonstrations. We demonstrate our method's effectiveness on various robotic tasks, both in simulation and on a physical robot. Notably, in the surgical retraction task, even when trained with as few as 10 demonstrations, our method achieves a median success percentage of nearly 90%. These results mark a substantial advancement in enabling shape servoing methods to bring deformable object manipulation closer to practical, real-world applications.