WRAP: Fixtureless Wrench-aware Multi-Robot Assembly Planning

Valentin N. Hartmann; Huang Su; Yijiang Huang; Stelian Coros

cs.ROSep 24, 2026

WRAP: Fixtureless Wrench-aware Multi-Robot Assembly Planning

Authors: Valentin N. Hartmann, Huang Su, Yijiang Huang, Stelian Coros

Organizations: Computational Robotics Lab, ETH Zurich, CH

Abstract

Assembly using robots often requires specially designed fixtures, or relies on top-down only assembly strategies. Using multiple robots, we can avoid using fixtures and make robotic assembly more flexible. Planning assembly sequences for multiple robots is challenging due to the high number of possible task assignments and orders. In addition, we need to reason over forces that occur during the assembly process, e.g., to decide if multiple robots are required for support, or if external support such as a table should be used. We present Wrap, a multi-robot assembly planner for multi-part assemblies, given the inter-part ordering-dependencies, the part meshes, and their initial state. We formulate a linear program to reason about valid grasps for supporting the forces that occur during assembly. The search leverages the assembly sequence, and greedily finds a feasible solution per assembly step by computing a heuristic via a cheap backwards search, and using the heuristic in the more expensive forward search. We then solve the multi-robot, multi-goal motion planning problem, and for execution, we split the plan into contact-rich assembly skills, and free space motion. We benchmark the planner on a variety of multi-part assemblies, and apply the planner to groups of robots differing in size and kinematics. We validate the work both in a physics simulation, and in real. Videos and code are available at https://www.vhartmann.com/wrap.

Figures & tables

Panel of Figure 1 — Fig. 1 : Multi-robot assembly: (left) Two OpenArm robots assembling a toy car. (right) Two UR5e arms collaborating to assemble a bench.

Fig. 2 : System overview: The input to our algorithm is part meshes, the initial state of the scene, and assembly dependencies, and mating wrenches. It then computes grasps, and stable rest orientations. After, it plans discrete robot-action sequences and their corresponding continuous configurations. The plan is then checked by a kinematic motion planner, and depending on feasibility of the path, replanning the plan is required. We then optimize the keyframes, and finally, we postprocess the path to make it dynamically feasible, and execute it.

Fig. 3 : (left) Illustration of an assembly action and (right) the force constraints that we introduce.

Fig. 4 : New assemblies from left to right: Stool, Chair, Cross, Cube.

Env.	Robots	DoF	EE	# parts	Dep. type
Stool	4 UR5e	24	Mixed	5	DAG
Chair	4 UR5e	24	Mixed	8	DAG
Cross	4 UR5e	24	2F	7	Sequence
Cube	4 UR10e	24	Vac.	8	Sequence
Fabrica (7 assemblies)	4 UR5e	24	2F	5–9	DAG

TABLE I : Overview of the scenarios used to test our planner.

Solver	Metric	Cross	Stool	Chair	F. Beam	F. Plumber block	F. Car	F. Gamepad	F. Cooling Manifold	F. Duct	F. Stool
Optimistic	$t_{\mathrm{init}}$	$11.25\pm\pm 0.15$	$14.42\pm\pm 0.09$	timeout	$13.01\pm\pm 0.03$	$9.73\pm\pm 0.05$	$49.29\pm\pm 0.23$	$115.13\pm\pm 0.28$	$60.65\pm\pm 0.08$	$51.46\pm\pm 0.09$	20.59 ± 0.04
Optimistic	cost	22	20	timeout	14	14	18	19	26	25	24
Ours	$t_{\mathrm{init}}$	$2.01\pm\pm 0.02$	1.60 ± 0.02	$8.93\pm\pm 0.03$	9.73 ± 0.05	$7.87\pm\pm 0.02$	$19.71\pm\pm 0.03$	$82.25\pm\pm 0.13$	19.11 ± 0.11	17.74 ± 0.26	$27.70\pm\pm 0.07$
Ours	cost	22	$32$	$43$	$16$	14	18	$23$	$46$	25	$30$
Flat lazy	$t_{\mathrm{init}}$	OOM	OOM	OOM	OOM	OOM	OOM	OOM	OOM	OOM	$45.12\pm\pm 0.08$
Flat lazy	cost	OOM	OOM	OOM	OOM	OOM	OOM	OOM	OOM	OOM	24

TABLE II : Comparison of search times and costs for different algorithms. We report the mean and standard deviation of 10 runs.

		Backwards		Forward		Motion
Object	$t_{\text{grasp}}$	$t_{\text{bwd search}}$	$t_{\text{force LP}}$	$t_{\text{fwd search}}$	$t_{\text{IK}}$	$t_{\text{MP init}}$
Cross	$0.48\pm\pm 0.01$	$0.77\pm\pm 0.02$	$0.19\pm\pm 0.00$	$0.66\pm\pm 0.01$	$0.40\pm\pm 0.00$	$7.67\pm\pm 0.57$
Stool	$2.43\pm\pm 0.02$	$0.35\pm\pm 0.00$	$0.05\pm\pm 0.00$	$0.70\pm\pm 0.02$	$0.50\pm\pm 0.00$	$9.65\pm\pm 0.46$
Chair	$11.81\pm\pm 0.05$	$1.27\pm\pm 0.01$	$0.40\pm\pm 0.00$	$3.46\pm\pm 0.03$	$3.80\pm\pm 0.00$	$14.31\pm\pm 0.68$
F. Beam	$8.99\pm\pm 0.10$	$0.10\pm\pm 0.01$	$0.05\pm\pm 0.00$	$9.28\pm\pm 0.05$	$0.30\pm\pm 0.00$	$3.14\pm\pm 0.20$
F. Plumb. block	$5.49\pm\pm 0.03$	$0.64\pm\pm 0.01$	$0.09\pm\pm 0.00$	$5.24\pm\pm 0.03$	$1.89\pm\pm 0.03$	$44.36\pm\pm 3.05$

TABLE III : Breakdown of where time is spent in Wrap . We report mean and standard deviation from 10 runs.

Panel of Figure 8 — Fig. 5 : Scaling comparison for two objects and different wrench models for ( left ) two, ( middle ) three, and ( right ) four robots. $\lambda$ is a scaling factor on the required assembly force.

Panel of Figure 9 — Fig. 6 : Cost convergence plot for (left) Cross, (middle) Stool and (right) Chair.

Env.	Model	Succ.	Tasks	Fail.	Transport util.		Insertion util.
		[%]			2F	Vac.	2F	Vac.
Cross	w/o wrench	0	11/26	no support (10)	10	–	18	–
	Gravity	0	11/26	no support (10)	10	–	18	–
	Full	100	22/22	–	25	–	21	–
Cube	w/o wrench	0	1.4/21	no support (10)	–	8	–	34
	Gravity	0	1.4/21	no support (10)	–	8	–	34

TABLE IV : Simulation success of plans computed with different support models. We report success and mean peak support utilization over 10 runs for the successful part of the trajectory. Utilization is split by execution phase and gripper type; bold values exceed the limit. – denotes an absent gripper type.

Parameter	Adopted (measured)		Assembly measured	Transport measured
	Two-finger gripper		Vacuum gripper
$F_{x}$ [ $\mathrm{N}$ ]	50	(95.3)	0	67.4
$F_{y}$ [ $\mathrm{N}$ ]	39.7	(39.7)	0	67.4
$F_{z}$ [ $\mathrm{N}$ ]	50	(80.4)	110.0	110.0
$M_{x}$ [ $\mathrm{N}\text{\,}\mathrm{m}$ ]	4.7	(4.7)	0	5.0
$M_{y}$ [ $\mathrm{N}\text{\,}\mathrm{m}$ ]	4.5	(4.5)	0	5.0

TABLE V : Wrench limits used during assembly and transport. Two-finger values are the minimum of the manufacturer limit and the measured slippage load (in parentheses). The same limits apply to assembly and transport. For the vacuum gripper, only a

z

-force is allowed during assembly, since deflection otherwise occurs.

Fig. 7 : Robot calibration (left and middle) and closeup of the snap fit (right) that we use in the stool model.

Panel of Figure 13 — Fig. 8 : Snapshots from simulation, from left to right: Duct, 2x2x3 Cube, Cross with OpenArm, Car, Half-Stool with Husky.

Panel of Figure 14 — Fig. 9 : Sequence from the real robot execution of the stool assembly with two UR5e arms on a stationary Husky base. From left to right: initial configuration, handing over the first leg, grasping the seat, inserting a leg into the seat held in mid-air, grasping the second leg, and insertion, and placing the assembled stool on the table.

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