---
kind: concept
slug: nonprehensile-manipulation
title: Nonprehensile manipulation
summary: >-
  Moving an object without a closed grip, here by tilting it against two supports with a curved palm and then tucking the palm under it. Only one card so far, so the page covers one method. Its contact order decides whether the tilt is feasible, and planning uses a force-closure test over (theta, delta). Author-reported, with 5 trials per setting.
tags: [manipulation, nonprehensile, in-hand, picking, force-closure]
papers: ["2411.16055"]
related: [in-hand-manipulation, manipulation-taxonomy, robotic-grasp-generation]
status: draft
updated_at: 2026-10-25
---

## Overview

Some objects are too large for a parallel-jaw grasp, and a flat table blocks
the fingers from getting under them [arxiv: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 [arxiv: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 [arxiv: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
[arxiv: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
[arxiv: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 [arxiv: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
[arxiv:2411.16055 §V-B] [fig. 6b]. The paper calls motion-force gentler and
says it needed fewer teleoperation commands [arxiv:2411.16055 §V-B].

## When to use which

| Situation | Use | Why |
|---|---|---|
| Large object, a flat surface and a support or wall near it, no force sensing | Tilt against supports | The paper's open-loop tests on the 2-DOF palm succeeded 4 to 5 of 5 times [arxiv:2411.16055 fig. 6c] |
| Rigid palm on an arm, and the support corner is 90 degrees | Incline the second support | The steel box failed 0 of 5 at 90 degrees and succeeded 5 of 5 at 61 degrees on one object [arxiv:2411.16055 tab. I]. Another steel box succeeded only 3 of 5 at 61 degrees [tab. I] |
| Soft or compliant object | Not established | The cardboard box succeeded at 90 degrees, and the paper suggests compliance explains it, but this was not tested [arxiv:2411.16055 §V-C] |
| Need an automatic stop of the tilt | Not available here | The experimenter ends the tilt by hand [arxiv:2411.16055 §V-B] |
| Need the executed path to match the plan | Not available here | The paper reports that the actual path differs from the planned one [arxiv:2411.16055 §V-D] |

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.

```pseudocode
# 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 [arxiv: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 [arxiv: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 [arxiv:2411.16055 §IV-A] [fig. 5c].

## Papers

- [Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form](/papers/2411.16055): tilts a large object against two supports with a curved passive palm, then tucks the palm under it.