Non-prehensile manipulation: pushing, flipping, sliding

Most robot manipulation literature is about grasping — pinch, lift, place. Real-world dexterity is broader. Sliding a coin off a table edge, nudging a package into a tight slot, flipping a pancake — the object moves but never leaves the surface. Non-prehensile manipulation is the term, and it's where some of the prettiest robotics math hides.

Why bother

You'd grasp if you could. But sometimes you can't:

• Object is too heavy for the gripper.
• Object is fragile (eggs, electronics).
• Object is in a cluttered environment where the gripper doesn't fit.
• Object is too thin or large to wrap fingers around.
• You only need to nudge, not transport.

Examples: aligning a part on an assembly line, pushing a box onto a shelf, flipping food in a pan, separating a stack of papers. All everyday tasks where humans don't grasp.

The pushing model (Mason, 1986)

The canonical analysis. A flat object on a surface; a pusher contacts it at a single point with a known direction. Where does the object go?

Three competing physics:

• Pusher pushes with force F at the contact point.
• Friction resists motion at every point on the contact patch with the surface.
• Object mass stores momentum.

Mason proved that for quasi-static pushing (slow enough to ignore inertia), the object's motion is determined by the limit surface of friction — a 3D shape relating the applied wrench (force + torque) to the resulting velocity (linear + angular).

Key result: depending on where you push (relative to the object's center of friction), the object either translates straight, rotates while translating, or rotates in place. There's a region of "left of center / right of center" pushes that produce predictable straight-line motion.

This is what lets a robot push a box across the floor reliably.

The friction cone again

A finger pushing a block: the resulting motion depends on the friction coefficient at the contact. If the push direction lies inside the friction cone (covered in the grasp-analysis lesson), the contact sticks; the object follows. If outside, the contact slips; results get unpredictable.

Practical implication: push along the contact normal whenever possible. If lateral, expect the contact to slip and plan accordingly.

Common non-prehensile primitives

Single-point pushing

One contact, push to a target pose. The math (Mason, Lynch) gives a closed-form mapping from push direction to object motion. Production: pre-compute the mapping, plan as if the object follows the prediction, monitor for slip.

Two-finger sliding

Two contacts at the same height squeeze and slide an object along its plane. Useful for precise positioning of small flat parts.

Tipping / pivoting

Push hard enough at the top of an object that it tips over a far edge. Used to flip orientations.

Flipping

Use a tool (spatula, paddle) to lift, rotate, and reset an object. The pancake-flip problem: timing the impulse to land in the desired orientation.

Throwing / catching

Release with controlled velocity to land at a distant target. Done by drone-mounted arms and athletic robots like Boston Dynamics Atlas.

Toppling and rolling

Combine pushing with shape: a cylinder on its side rolls; a brick stays put. Use the shape to your advantage.

Why this is hard

• Friction is unmodeled-or-poorly-modeled. The coefficient changes with surface contamination, temperature, micro-scratches.
• Physics is non-smooth. Stick-slip transitions are discontinuous, hard to differentiate, hard to optimize through.
• Many degrees of freedom emerge — every contact is a degree of freedom.
• Sensitivity to initial conditions. A 1 mm offset in pushing point can change which way the object rotates.

Classical analytical methods give you the framework but not the precise predictions. Real systems combine analysis with measurement (force sensing, vision tracking) and re-planning.

The 2024+ learning approach

Reinforcement learning and imitation learning have eaten a lot of the "hard" non-prehensile problems:

• Push-T — pushing a T-shaped object to a target pose. Diffusion policy from teleop demos solved it.
• Pancake flipping — multiple papers demonstrate learned policies that beat scripted ones.
• Pile manipulation — moving multiple objects with single contacts. Used by warehouse-robot vendors.
• Catching — agile motion with high-speed cameras. Demonstrated on KUKA LBR.

The 2026 production pattern: classical analysis to set up the problem (what's the goal pose, what motion is feasible), learned policy for the actual control. The math gives structure; the network gives robustness.

When non-prehensile is the right answer

• Small adjustments: nudging an object 5 mm into place is faster than re-grasping.
• Large or awkward parts: when grasping isn't feasible.
• Singulation: separating items from a cluster (warehouse bin-picking).
• Speed: throwing or sliding can move things faster than carrying.
• Tool-mediated tasks: spatula, broom, plunger — humans use these all the time.

The simulation gap is real

Non-prehensile policies trained in MuJoCo or PyBullet often fail to transfer because friction models in simulation are approximations. Recipes that work for sim-to-real:

• Domain randomization on friction coefficient (range 0.3–1.5).
• Add observation noise to object pose tracking.
• Include force perturbations during training.
• Fine-tune with a few real-world demos (50–100 episodes).

This is more involved than sim-to-real for grasping, where contact dynamics matter less. Budget extra time.

Production examples in 2026

• Amazon Robotics: warehouse robots singulating packages with non-prehensile push-pull motions.
• Sushi-folding robots: in some Japanese factories — fully non-prehensile, end-to-end.
• Liquid-handling lab robots: pipetting + tube-tilting often involves non-prehensile motion.
• Cobot demos: domino-toppling, pancake-flipping; mostly viral marketing, but the technology is real.

Where the math still wins

For repeatable industrial tasks (push this part 10 mm to the right), classical analytical pushing models give you precision and explainability that learned policies don't. Pick the tool to fit the task; combine when it helps.

Exercise

In MuJoCo, set up a flat puck on a table with a robot arm. Implement single-point pushing: command the arm to push the puck along a straight line. Vary the contact point relative to the puck's center of friction; observe how the puck rotates. The friction model in MuJoCo isn't perfectly accurate, but you'll see Mason's predictions qualitatively.

Next

Dexterous manipulation — multi-fingered hands, in-hand reorientation, and why the field is still mostly open.