Robust Nonprehensile Object Transportation with Uncertain Inertial Parameters

TL;DR

This work tackles nonprehensile object transportation on a tray when the transported object's inertial parameters—particularly the CoM and inertia—are uncertain. It introduces robust sticking constraints embedded in an offline optimization framework, and uses moment-relaxation realizability checks (Lasserre hierarchy) to certify that planned trajectories remain feasible for all physically realizable inertial parameters, including inertia. In simulation and real hardware, the proposed method reliably transports tall objects (e.g., 56 cm) under substantial inertia uncertainty, outperforming baseline Center/Top constraint strategies that can drop the object. An open-source planner is provided to enable practical adoption and benchmarking of robust nonprehensile transportation under inertial uncertainty.

Abstract

We consider the nonprehensile object transportation task known as the waiter's problem - in which a robot must move an object on a tray from one location to another - when the transported object has uncertain inertial parameters. In contrast to existing approaches that completely ignore uncertainty in the inertia matrix or which only consider small parameter errors, we are interested in pushing the limits of the amount of inertial parameter uncertainty that can be handled. We first show how constraints that are robust to inertial parameter uncertainty can be incorporated into an optimization-based motion planning framework to transport objects while moving quickly. Next, we develop necessary conditions for the inertial parameters to be realizable on a bounding shape based on moment relaxations, allowing us to verify whether a trajectory will violate the constraints for any realizable inertial parameters. Finally, we demonstrate our approach on a mobile manipulator in simulations and real hardware experiments: our proposed robust constraints consistently successfully transport a 56 cm tall object with substantial inertial parameter uncertainty in the real world, while the baseline approaches drop the object while transporting it.

Figures (7)

• Figure 1: The goal of this work is to move an object on a tray to a desired position without dropping it, despite the inertial parameters of the object being uncertain. Here our mobile manipulator is transporting a tall box with uncertain contents. A video of our experiments is available at http://tiny.cc/upright-robust.
• Figure 2: A box (red) on a tray, with four contact points $C_1$--$C_4$ located at the vertices of the base. We assume that the box's center of mass (CoM) is not known exactly, but rather only known to lie inside some polyhedral set (green).
• Figure 3: We transport a cuboid-shaped object $\mathcal{K}$ (red) with an uncertain CoM contained in $\mathcal{C}$ (green). We test three variations of the sticking constraints: assume the CoM is at the object's centroid (Center), assume it is centered at the top of the object (Top), and Robust, in which the controller enforces sticking constraints for eight different objects, where each has its CoM at one of the vertices of $\mathcal{C}$.
• Figure 4: Success rate of the different types of sticking constraints for all 135 combinations of desired positions, CoMs, and inertias for each object height and constraint method (1620 total runs). The Robust constraints always successfully transport the object, while the other constraint types result in an increasing number of failures as the object height increases; the rate varies slightly with the number of SQP iterations $n_s$. Here the bar shows $n_s=3$ and the black dot $n_s=10$.
• Figure 5: Our transported objects are boxes containing a bottle filled with sugar to offset the CoM and to make the task of balancing more difficult. One cannot tell how the box is packed (and therefore what its mass distribution is) just by looking at it. Box2 (shown on the right) consists of two boxes attached together; Box1 is a single box. A firm base board (green) is attached to the bottom box to provide a consistent contact area with the tray.