Nonprehensile manipulation

Overview

Some objects are too large for a parallel-jaw grasp, and a flat table blocks the fingers from getting under them 2411.16055 §I. The one card on this concept handles that case by using the environment. The object is tilted against a support so that it stays in contact with a table, a second support and the palm, and the palm then slides under it 2411.16055 §III §V.

The invariant is that the object must stay restrained while it moves. In the planner this is a force-closure condition that has to hold at every sample along the tilt path 2411.16055 §IV-B. The variants below differ in the order of contacts and in how the palm is driven.

The card's tags file this method under nonprehensile manipulation. The card's text does not discuss the term itself, so the scope here is the method on that card.

Variants

Wedged tilt

The palm contact lies inside the friction cone at the contact with the second support, so the two contacts see each other and the object is wedged. An upward palm motion then rotates the object about the contact with the table until that contact breaks 2411.16055 §IV-A fig. 2a.

Three-contact tilt

The palm contact is outside the friction cone, and the object slides on the two supports. The gravity load can be balanced by the combined contact wrench 2411.16055 §IV-A fig. 2b. The card does not say which contact order the physical trials followed.

Sticky-contact tilt

The palm contact is placed so that gravity can only be balanced if the palm contact is sticky enough to push upward. The paper calls this less desirable, because it needs large friction 2411.16055 §IV-A fig. 2c.

Motion control and motion-force control

These are two ways to drive the two-motor palm, not two contact geometries. In motion control both motor angles are commanded. In motion-force control, motor 1 follows a monotonic angle while motor 2 holds a constant torque 2411.16055 §V-B fig. 6b. The paper calls motion-force gentler and says it needed fewer teleoperation commands 2411.16055 §V-B.

When to use which

All success counts are from 5 trials per setting. The table picks a setup, not a ranking.

Implementation sketch

The planning step from the paper's model. The grid, the force-closure test and the straight-line check are as the paper describes them. The grid resolution and the LP solver are not stated.

# Plan a tilt path in (theta, delta) that stays force-closed  [arxiv:2411.16055 §IV-B]
# Input:  object and palm profiles, friction mu_A, mu_B, mu_C  [fig. 3]
# Output: a path, or None if no straight line stays force-closed

def plan_tilt(object, palm, mus):
    # Sample configurations on a grid  [§IV-B]
    grid = sample_configurations(theta_range, delta_range)
    # Test each sample with a binary LP force-closure check  [§IV-B]
    closed = {c: lp_force_closure(c, object, palm, mus) for c in grid}
    # Start on the delta axis and end on the theta axis at delta = 0  [§IV-B]
    start = pick_feasible_on_delta_axis(closed)
    target = pick_feasible_on_theta_axis(closed)
    # Accept the straight line only if every sample on it is force-closed  [§IV-B]
    path = straight_line(start, target)
    if all(closed[c] for c in path):
        return path
    return None

The paper reports that a larger friction at the palm enlarges the feasible set 2411.16055 §IV-B. In the grid, friction values of 0.1 and 0.2 at the palm contact were plotted, with 0.1 at the two supports fig. 3.

Contradictions

• Torque wording. The paper says motion control gave much larger peak torque on motor 1. The numbers it then gives are 2.41 Nm for motion control and 2.69 Nm for motion-force control 2411.16055 §V-B. Read literally, the second is larger, so the sentence and the numbers do not agree. The averaged peaks in the figure differ again fig. 6c. Not resolved here.
• Slender objects. The paper says slender objects tilt more easily, but it gives no object sizes 2411.16055 §IV-A fig. 5c.

Papers

• Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form: tilts a large object against two supports with a curved passive palm, then tucks the palm under it.