  Extrinsic manipulation, a technique that enables robots to leverage extrinsic
resources for object manipulation, presents practical yet challenging
scenarios. Particularly in the context of extrinsic manipulation on a
supporting plane, regrasping becomes essential for achieving the desired final
object poses. This process involves sequential operation steps and stable
placements of objects, which provide grasp space for the robot. To address this
challenge, we focus on predicting diverse placements of objects on the plane
using deep neural networks. A framework that comprises orientation generation,
placement refinement, and placement discrimination stages is proposed,
leveraging point clouds to obtain precise and diverse stable placements. To
facilitate training, a large-scale dataset is constructed, encompassing stable
object placements and contact information between objects. Through extensive
experiments, our approach is demonstrated to outperform the start-of-the-art,
achieving an accuracy rate of 90.4\% and a diversity rate of 81.3\% in
predicted placements. Furthermore, we validate the effectiveness of our
approach through real-robot experiments, demonstrating its capability to
compute sequential pick-and-place steps based on the predicted placements for
regrasping objects to goal poses that are not readily attainable within a
single step. Videos and dataset are available at
https://sites.google.com/view/pmvlr2022/.
