Picking by Tilting: In-Hand Manipulation for Object Picking using Effector with Curved Form

In plain words

Some objects are too big for a robot gripper to close around, and a flat table is in the way of fingers sliding under them. This paper picks such an object up by letting it lean against a wall-like support first. A robot-held palm with a curved surface pushes the object up onto its edge, rolling along the palm as it tilts. Once the object is tilted, the palm slides its flat end into the gap underneath, and the object is then lifted, held between the palm and the table.

The idea is that the object does the work. The contacts with the table, the wall and the palm keep it from sliding away while it tilts, so the robot needs only simple hardware and simple control. The paper checks which tilt motions can be kept stable and then tests the method on a custom two-motor palm and on a standard robot arm with a rigid palm.

TL;DR

A curved, passive palm tilts a large object up against an inclined support, then tucks under it to get a grasp against gravity. The paper gives two tilt modes and a linear-programming force-closure test over (theta, delta) for planning. Experiments are author-reported and small: 5 trials per setting, 4 objects on the 2-DOF palm, 5 settings on the UR3 arm. Sensing is open-loop and no force/torque sensor is used.

Problem

Large objects cannot be taken by a parallel-jaw grasp, and a flat tabletop blocks the fingers from getting underneath §I. The paper treats the problem as a quasistatic planar task. The object sits on support #1 (perpendicular to gravity) and is blocked on one side by support #2, which may be inclined §III fig. 2. A friction contact is assumed at each of three points: A (support 1), B (support 2) and C (palm) §III. Without these supports the picking task is not feasible under the stated assumptions §III. The paper says that picking a thin object by tilting, or tilting with a force/torque sensor, is covered elsewhere §II.

Method

The task is split into four steps, shown in the picking sequence §V fig. 6a.

1. Approach. The palm touches the object at point X on its curved end §V.
2. Tilt. The palm moves up and presses the object against support #2 while reorienting, so that at the end of tilting the object is restrained from falling §V §IV-B. In the 2-DOF experiments the tilt is run in one of two ways: motion control (both motor angles commanded) or motion-force control (motor 1 angle increases monotonically while motor 2 holds a constant torque) §V-B fig. 6b.
3. Regrasp. The palm rotates about point Y, which now coincides with contact C, away from the robot base. Its flat far end slides into the space between the object and support #1 §V.
4. Lift. The palm is lifted and retracted to detach the object from both supports §V.

Two tilt modes are distinguished by the order of three points on the edge line that contains C. B'1 and B'2 are the images of B under the left and right edges of its friction cone §IV-A.

• Order B'1, C, B'2 (C inside segment B'1B'2): C lies in B's friction cone, so the contacts B and C see each other. The object is wedged, and an upward palm motion rotates it about B until contact A breaks §IV-A fig. 2a.
• Order C, B'1, B'2: three-contact tilt, with the object sliding on supports A and B. The gravity wrench can be balanced by the composite contact wrench §IV-A fig. 2b.
• Order B'1, B'2, C: gravity cannot be balanced unless contact C is sticky so that its force can point upward. The paper calls this less desirable because it needs large friction §IV-A fig. 2c.

The paper also argues that slender objects (large width-to-thickness ratio) tilt more easily §IV-A, and that inclining support #2 so that its contact normal points downward helps the three-contact mode §IV-A §V-C.

Planning uses the configuration (theta, delta): theta is the object's angular displacement and delta the position of contact C §IV-B fig. 3a. During tilting, theta increases while delta decreases monotonically §IV-B. The supports are set at 90 degrees in the model §IV-B.

# Force-closure map and straight-line tilt plan  [§IV-B] [fig. 3]
# Input:  palm profile, object profile, mu_A, mu_B, mu_C
# Output: a (theta, delta) path that stays force-closed

def plan_tilt(object, palm, mus):
    # Sample (theta, delta) on a grid  [§IV-B]
    grid = sample_configurations(theta_range, delta_range)
    # Mark each sample with a binary LP force-closure test  [§IV-B]
    closed = {c: lp_force_closure(c, object, palm, mus) for c in grid}
    # Start on the delta axis, target on the theta axis  [§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

At the target (delta = 0), the palm's first-order geometry matters. Reuleaux's method is used to find the rotation centres the object can use to ungrasp §IV-B fig. 4. The palm is oriented so that the contact normals at A, B and C do not allow a clockwise ungrasp §IV-B fig. 4b.

Hyperparameters

Only values stated in the paper are listed. The paper gives no controller gains, control rates or tilt torque values.

Results

Author-reported. Setup: a custom five-bar palm with two HT8108-J6 motors §V-A and a UR3 arm with a rigid palm §V-C. Five trials per setting. The 2-DOF palm results are in fig. 6c; the arm results are in tab. I.

2-DOF palm (teleoperated), average over trials, with the spread as printed:

UR3 arm (programmed trajectory):

The paper says the motion-force mode gives a more "gentle" grasp and needs fewer teleoperation commands than pure motion control §V-B. The text cites peak motor-2 torques of 2.05 Nm (motion) and 0.99 Nm (motion-force) for object #2 §V-B fig. 6b.

Paper vs code

No official code. The paper has no code link, and the arXiv metadata carries no comment field. The paper's links are a video attachment and a motor vendor page §V-A. A GitHub repository search for the title and for "curved palm in-hand manipulation tilting" found one repository, Danielsong001/Picking_by_tilting. Its README gives this paper's title and authors. Its owner is "Daniel Song", which matches none of the four authors, and it lists no license. It was not used, so no code is cited.

Pitfalls

• Torque sentence is ambiguous. The text says motion control produced much larger peak torque, then gives 2.41 Nm (motion) against 2.69 Nm (motion-force) for motor 1 §V-B. Read literally, motion-force is higher on motor 1, which contradicts "much larger". The peak values in fig. 6c are averages over trials and differ from the single-trial numbers in the text.
• The "±" and "average number of commands" are undefined. Whether the spread is a standard deviation, and what a "command" is, is not stated fig. 6c. Trial counts are small (5), so the success rates have wide uncertainty.
• Tilt end is manual. The experimenter decides when tilting stops and switches the controller off §V-B. No automatic criterion is given.
• Planning is open-loop and ignores palm geometry. The paper states the actual path in (theta, delta) differs from the planned one, and that palm geometry is ignored in the model §V-D. Stability is attributed to high friction on the palm §V-D.
• Force-closure depends on friction. The map is computed for mu_C of 0.1 and 0.2 with mu_A and mu_B at 0.1 fig. 3. The real friction values of the hardware are not stated, and the paper reports that a larger mu_C enlarges the feasible set §IV-B.
• Arm failure mode. With the steel box at 90 degrees the object is wedged, then falls onto the bottom support because the contact wrenches cannot balance gravity §V-C fig. 7a. The paper's fix is to incline support #2, which made the steel box succeed at 61 degrees §V-C fig. 7b.
• Arm inertia. The high reflected inertia of the UR3 made steady pressing difficult, and the paper ties this to the failure mode §V-C.
• Deformable objects. The cardboard box did not show the failure mode, and the paper hypothesises contact compliance explains this §V-C. This is untested.
• Object geometry. Slender objects are said to tilt more easily §IV-A, but no object sizes are given in the text. Object dimensions are not stated.
• Scope. The object model is a planar trapezoid extruded or revolved into an inverted truncated cone §III. Other shapes are not covered.
• Section and figure numbers here follow the IEEE conference class numbering as counted from the LaTeX source (roman sections, subsections lettered). Check against the PDF before quoting in a citation.

Lineage

• Builds on: the Reuleaux mobility method (cited key Mason__2001_3803) for rotation centres §IV-B §IV-A, and an LP force-closure test (cited key lynch2017modern) §IV-B. Both are cited methods, not new here.
• Compared against: a motion-force tilting method with a high-fidelity force/torque sensor (cited key 8794366), which the paper says reports a similar arm failure mode §II §V-C; a tilting picker for thin objects (cited key 9197493) §II; and zero-DOF end-effectors for picking (cited keys 973345, mucchiani2018object) §II.
• Superseded by: not stated.