Pushing Everything Everywhere All At Once: Probabilistic Prehensile Pushing

TL;DR

The paper tackles prehensile pushing by formulating a nonlinear trajectory optimization that originally involves mixed-integer variables for pushers. By recasting pushers as a discrete probability distribution and adding an entropy penalty, the authors convert the problem into an efficient NLP that can leverage gradient-based optimization while still preferring a single active pusher at execution. Empirical results show an ~8× speedup and ~20× cost reduction over a state-of-the-art sampling-based baseline, with successful validation in simulation and on a real Franka Panda robot. The approach offers flexible objective design (e.g., pusher-switch minimization) and demonstrates robustness to friction variations, making it a practical planning method for extrusion of manipulative tasks that leverage environmental contacts.

Abstract

We address prehensile pushing, the problem of manipulating a grasped object by pushing against the environment. Our solution is an efficient nonlinear trajectory optimization problem relaxed from an exact mixed integer non-linear trajectory optimization formulation. The critical insight is recasting the external pushers (environment) as a discrete probability distribution instead of binary variables and minimizing the entropy of the distribution. The probabilistic reformulation allows all pushers to be used simultaneously, but at the optimum, the probability mass concentrates onto one due to the entropy minimization. We numerically compare our method against a state-of-the-art sampling-based baseline on a prehensile pushing task. The results demonstrate that our method finds trajectories 8 times faster and at a 20 times lower cost than the baseline. Finally, we demonstrate that a simulated and real Franka Panda robot can successfully manipulate different objects following the trajectories proposed by our method. Supplementary materials are available at https://probabilistic-prehensile-pushing.github.io/.

Figures (7)

• Figure 1: A real-world prehensile pushing example. The trajectory the robot followed is based on our method. As indicated by the arrows, the robot only translates in the three leftmost images, while it translates and rotates in the three rightmost images.
• Figure 2: Visual description for calculating mc. (a) Shows the pusher (P) pushing the rectangular object (O), which slides inside the gripper (G). Together, the convex hull of the generalized friction cones (b), the limit surface (c), and the gravity acting on the object (d) result in the motion resolution (e). The final polyhedral approximation of the motion cone is shown in (f). The axes labels in (b), (c), (e), and (f) follow the convention in (d), where forces act along the x- and z-axis and torque around the y-axis (best viewed in color).
• Figure 3: The smoothed non-convex state constraint for the T-shaped object. Here, $\alpha=200$ and $\hat{x}_0=0.02$.
• Figure 4: (\ref{['fig:random_sampling']}) shows the uniformly sampled start and goal positions while (\ref{['fig:example_trajectory']}) shows an optimized trajectory.
• Figure 5: The relationship between the goal distance and the computational budget. T stands for the T-shaped and L for the L-shaped object.