Making Waves: A Membrane-Coupled Delta Array for Manipulating Objects Below the Actuator Spacing

Bailey Dacre; Andrés Faíña; Oliver Kroemer; Zeynep Temel

cs.ROSep 30, 2026

Making Waves: A Membrane-Coupled Delta Array for Manipulating Objects Below the Actuator Spacing

Authors: Bailey Dacre, Andrés Faíña, Oliver Kroemer, Zeynep Temel

Abstract

Distributed manipulator systems manipulate objects through the coordinated motion of many actuators. However, an object must be supported by several actuators at once, so the centre-to-centre actuator spacing imposes a hard lower bound on manipulable object size. We remove this bound by coupling the end-effectors of an 8 x 8 array of three degrees-of-freedom delta robots with a stretchable fabric, turning 64 discrete contacts into a continuous surface capable of manipulating objects smaller than the actuator spacing. Viewing the array as a displacement field over that surface, we investigate local quasi-static and cyclic fields as manipulation primitives. These primitives can be applied globally across the array or locally confined around each tracked object to independently manipulate several objects in parallel. We then train a policy acting on low-order discrete cosine transform coefficients: at equal action dimension, commanding a nineteen-delta neighbourhood halves the placement error of commanding the whole array. The policy transfers to hardware without adaptation at 76% success. The platform manipulates objects from 15mm-90mm, a six-fold range spanning both sides of the actuator spacing, 43.3mm, on a single surface.

Figures & tables

Fig. 3 : Single delta Workspace slice at $z=$133\text{\,}\mathrm{mm}$$ , coloured by the maximum membrane strain between one delta and its six neighbours, all held at their neutral poses (black triangles). — Fig. 3 : Single delta Workspace slice at $z=$ 133\text{,}\mathrm{mm}$$ , coloured by the maximum membrane strain between one delta and its six neighbours, all held at their neutral poses (black triangles).

Fig. 4 : Strain over all $4.9\times 10^{11}$ pose pairs of an adjacent delta pair, from the workspace autocorrelation at $1\text{\,}\mathrm{mm}$ resolution. (a) Histogram in $10\text{\,}\mathrm{\%}$ bands. (b) Admissible fraction of the joint workspace under $\varepsilon\leq\varepsilon_{\max}$ , with the $70\text{\,}\mathrm{\%}$ limit of the membrane used marked.

Mode	Basis	DoF
Out-of-plane ( $\mathbf{v}=\mathbf{0}$ ): $w=$
Heave	$h$	1
Tilt	$gX\;\mid\;gY$	2
Parabola	$\tfrac{1}{2}\kappa\,(X^{2}+Y^{2})$	1
Saddle	$\tfrac{1}{2}\kappa\,(X^{2}-Y^{2})\;\mid\;\kappa XY$	2
In-plane ( $w=0$ ): $\mathbf{v}=$

TABLE I : The twelve quasi-static shape modes, each an in-plane displacement

\mathbf{v}

or out-of-plane displacement

w

of a delta at

\mathbf{r}=(X,Y)

from the field centre. Amplitudes: heave

h

[m], gradient

g

, curvature

\kappa

[m -1 ], offset

c

[m], dilation

\beta

, rotation

\Omega

[rad], shear

\gamma

. Two-DoF modes are listed as a basis pair; their combination sets magnitude and orientation.

Fig. 5 : A central delta and its ring-1 neighbourhood, $R_{1}$ . Purple marks the unit cell of the reciprocal lattice and $\lambda_{\min}$ in the principal directions. Inter-cell primitives - edge ( $P_{0}$ , red), node ( $P_{1}$ , blue) and deflect ( $P_{2}$ , green) - transfer an object between cells, $C_{n}$ , triangular regions of fabric between adjacent deltas.

Fig. 6 : Translation of a disc ( $\diameter=$70\text{\,}\mathrm{mm}$,\frac{3d}{2}<\diameter<\sqrt{3}d$ ) across the array using an elliptical gait with $\hat{\mathbf{d}}=[1,0]$ , averaged (bold line) over five trials (faint). Red: wave vector $\mathbf{k}$ aligned with $\hat{\mathbf{d}}$ ; blue: $\mathbf{k}$ perpendicular, showing a greater translational velocity. Each uses the shortest wavelength available at that heading, $\lambda_{\min}^{\theta}$ . — Fig. 6 : Translation of a disc ( $\diameter=$ 70\text{,}\mathrm{mm} $,\frac{3d}{2}<\diameter<\sqrt{3}d$ ) across the array using an elliptical gait with $\hat{\mathbf{d}}=[1,0]$ , averaged (bold line) over five trials (faint). Red: wave vector $\mathbf{k}$ aligned with $\hat{\mathbf{d}}$ ; blue: $\mathbf{k}$ perpendicular, showing a greater translational velocity. Each uses the shortest wavelength available at that heading, $\lambda_{\min}^{\theta}$ .

Fig. 7 : Assembly and orientation of magnetic blocks, localised by AprilTag. (a) Blocks assembled with the $R_{1}$ tilt primitive. (b) A local cyclic wave rotates and centres the assembly. (c) Final desired pose.

$P_{0}$ edge: $C_{0}\!\to\!C_{1}$				$P_{1}$ node: $C_{0}\!\to\!C_{2}$				$P_{2}$ deflect: $C_{0}\!\to\!C_{3}$
Delta	$\hat{a}$	$\hat{c}$	$\hat{z}$	Delta	$\hat{a}$	$\hat{c}$	$\hat{z}$	Delta	$\hat{a}$	$\hat{c}$	$\hat{z}$
$\Delta_{3}$	$-5$	$0$	$+15$	$\Delta_{1}$	$-3$	$+10$	$+25$	$\Delta_{1}$	$-5$	$0$	$+15$
$\Delta_{1}$	$0$	$+15$	$-10$	$\Delta_{3}$	$-3$	$-10$	$+25$	$\Delta_{3}$	$-10$	$-17.3$	$-10$
$\Delta_{0}$	$0$	$-15$	$-10$	$\Delta_{0}$	$0$	$0$	$-20$	$\Delta_{0}$	$0$	$+20$	$-10$
$\Delta_{2}$	$-10$	$0$	$-30$	$\Delta_{4}$	$-10$	$-10$	$-25$	$\Delta_{5}$	$+10$	$-17.3$	$-20$
				$\Delta_{6}$	$-10$	$+10$	$-25$	$\Delta_{6}$	$-10$	$0$	$-30$

TABLE II: Cell primitives of Fig. 5 , all moving from

C_{0}

. Each row is a delta’s tip offset from neutral (mm), expressed in a frame attached to the primitive:

\hat{a}

points from

C_{0}

toward the target cell,

\hat{z}

up, and

\hat{c}=\hat{z}\times\hat{a}

to left of travel. For deflection,

\hat{c}

is taken toward

\Delta_{0}

; the mirror variant follows by symmetry.

Fig. 8 : Colour sorting task with $15\text{\,}\mathrm{mm}$ cubes using cell primitives. Objects route dynamically to colour-matched targets (⌀= $50\text{\,}\mathrm{mm}$ ), traversing the array simultaneously without conflict.

Action space	Ch.	Suc (%)	Med (mm)	p90 (mm)
$R_{2}$ , 19 deltas	$xyz$	95.1	3.5	8.4
$R_{2}$ , 19 deltas	$z$	95.2	4.0	10.2
$R_{1}$ , 7 deltas	$xyz$	83.9	7.1	61.1
Whole array, 64 deltas	$xyz$	93.5	6.5	14.2

TABLE III : Test-set performance on holdout by action space and commanded channels. Suc is the rate of reaching the

20\text{\,}\mathrm{mm}

target; Med and p90 are the median and 90th-percentile final in-plane error.

R_{n}

denotes the ring-

n

neighbourhood.

Fig. 9 : Labelled EGAD [ 15 ] objects used for sim-to-real translation experiments. Objects range from $30\text{\,}\mathrm{mm}90\text{\,}\mathrm{mm}$ in bounding box edge length, $S_{e}$ .

Object, $S_{e}$	Real	Sim	Real	Sim	Real	Sim
	Success (%)		Final (mm)		Closest (mm)
A1, 30mm	80	100	18.8	3.5	14.7	0.8
B2, 45mm	90	100	11.4	3.6	4.6	0.4
C3, 60mm	70	100	25.3	3.6	18.3	0.3
D4, 75mm	80	100	16.4	3.3	6.3	0.3
E5, 90mm	60	100	24.9	3.3	15.6	0.6

TABLE IV: Sim-to-real transfer of the

R_{2}

xyz

policy without fine-tuning: ten start–goal pairs per object on hardware, with identical pairs replayed in simulation. Trials end at

100

steps (

20\text{\,}\mathrm{s}

); success is a final error below

20\text{\,}\mathrm{mm}

. Final and Closest give the mean planar error at the end of the trial and at nearest approach. Objects labelled by EGAD [ 15 ] identifier and

S_{e}

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ComManip: Overfitting Manipulation Policies to Comfortable Regions

Yidan Lai, Xinyi Chen, Shuquan Man, Huiping Zhuang

South China University of Technology, Guangzhou, China · Nanyang Technological University, Singapore

Robotic Manipulation Policies Improved Generalization

Open paper AskPDF arXiv

Training robot manipulation policies relies on costly robot demonstrations, making large-scale data collection impractical. Meanwhile, to improve policy generalization, existing approaches seek greater diversity in visual observations by varying object placements, viewpoints, and robot configurations during data collection. However, under a limited demonstration budget, this strategy forces the policy to model diverse visual observations, providing insufficient supervision to learn reliable observation-action correspondences under similar local conditions. Our study reveals that policies trained under this strategy achieve lower task success rates than those trained within a compact, visually and kinematically stable region. We refer to these stable regions as comfortable manipulation regions. To exploit this finding, we propose ComManip, a learning paradigm that specializes manipulation policies to comfortable manipulation regions. During inference, ComManip repositions the mobile base until the detected target center enters the familiar image-space range estimated from comfortable-region demonstrations. It then executes the same manipulation policy, enabling effective manipulation across diverse target locations. We conduct extensive experiments across multiple manipulation tasks, demonstration budgets, and policy families including ACT,

π_{0.5}

, RDT, OpenVLA-OFT, and SmolVLA. The results demonstrate that ComManip improves task success by roughly 20 percentage points or more across different policy architectures in large workspaces under limited demonstration budgets, suggesting that specializing manipulation policies to comfortable regions provides a more data-efficient learning paradigm for manipulation.

Abstract

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