Robotic Boomerang Throwing via Model-Based Release Design

Yang Liu; Colin Jones; Aude Billard

cs.ROOct 7, 2026

Robotic Boomerang Throwing via Model-Based Release Design

Authors: Yang Liu, Colin Jones, Aude Billard

Organizations: Learning Algorithms and Systems Lab (LASA), EPFL, Switzerland · Automatic Control Lab, EPFL, Switzerland

Abstract

Throwing objects that generate aerodynamic lift can greatly extend robot throwing beyond ballistic flight. A returning boomerang is a challenging example because its flight depends strongly on the release velocity, attitude, and spin, while robotic manipulators cannot readily reproduce the rapid motions used in human throwing. We present a model-based framework for robotic boomerang throwing centered on the release state. We identify the boomerang flight dynamics in stages to predict how flight changes across design variations. To systematically design the robot throwing motion, we screen candidate parameters according to how strongly and consistently they control release spin under uncertain contact conditions. These models are then used to design the throwing motion and boomerang for a 6-DoF manipulator with limited joint speeds. To our knowledge, this is the first robotic manipulator to generate a returning boomerang flight. In the demonstrated returning trial, the boomerang is released at 51 rad/s (8.1 rev/s), reaches 2.03 m from the robot base, and returns to touch down 0.31 m from the base. The successful release differs significantly from the measured human throws, showing that a robot need not imitate human throwing motion to achieve a returning flight. The project page is available at https://robot-boomerang.github.io

Figures & tables

Fig. 1 : Robot throws a boomerang with a returning flight.

Fig. 2 : Boomerang frames and variable definitions.

Fig. 3 : Transient release during an overhead throw. The boomerang is initially pinch-grasped. As the gripper opens and the normal force decreases, it pivots and slides in hand, gaining spin before detachment.

Fig. 4 : Three tested boomerangs. Left to right: nominal ( $0.6\,\mathrm{mm}$ thick), thin ( $0.4\,\mathrm{mm}$ ), and large ( $0.6\,\mathrm{mm}$ ).

variant	thickness (mm)	radius (mm)	$m$ (g)	$I_{3}$ ( $\mathrm{g\,cm^{2}}$ )
nominal	0.6	85.00	6.000	1.4617
thin	0.4	85.00	4.000	0.9745
large	0.6	106.25	9.375	3.5686

TABLE I : Boomerang variants used in the experiments.

class	#par.	DTW (m)	landing (m)	$Z_{\max}$ (m)
wind-tunnel prior	0	0.63 $\pm$ 0.18	2.09 $\pm$ 0.50	0.46 $\pm$ 0.11
scaled wind-tunnel prior	6	0.31 $\pm$ 0.13	0.37 $\pm$ 0.23	0.27 $\pm$ 0.09
direct polynomial fit	60	29 $\pm$ 60	80 $\pm$ 163	12 $\pm$ 28
staged fit (ours)	16	0.29 $\pm$ 0.19	0.55 $\pm$ 0.38	0.08 $\pm$ 0.06

TABLE II : Flight-reconstruction error by model class on the nominal boomerang (MAE

\pm

STD over

N{=}9

trials). Boldface indicates the lowest MAE for each metric.

Fig. 5 : Reconstruction of a representative nominal flight by model class: top view (top), height above release (bottom left), and spin rate (bottom right).

Fig. 6 : Measured and predicted cross-design trajectories at closely matched release states in a release-aligned frame. Relative to the nominal design, the thin variant turns more tightly and the large variant more widely; the transferred staged fit predicts both changes without refitting.

Panel of Figure 9 — Fig. 7 : Illustration of the grasp angle $\theta_{g}$ .

group	variable	range
release state	throw-plane pitch offset [rad]	$[-0.2,0.2]$
	elbow release velocity [rad/s]	$[-7,-6]$
	wrist release velocity [rad/s]	$[-14,-13]$
	hardware delay [s]	$[0.01,0.02]$
gripper force	peak force $F_{\max}$ [N]	$[60,90]$
	switching force $F_{s}$ [N]	$[5,15]$

TABLE III : 12 uncertain operating variables and their prescribed ranges, covering the operating envelope of the setup.

Fig. 8 : Two-stage normal-force profile used in the release simulation. The nominal profile is parameterized by the peak force

F_{\max}

, switching force

F_{s}

, and phase durations

T_{1},T_{2}

; the shaded region shows the range sampled during screening.

parameter	span	$A$ [rad/s]	$c$	$\omega_{\max}$ [rad/s]
$\theta_{g}$ [deg]	$[0,120]$	15.0	0.81	53.4
$a_{e}$ [rad/s 2 ]	$[0,30]$	2.43	0.90	49.1
$a_{w}$ [rad/s 2 ]	$[0,60]$	1.00	0.69	47.3
$t_{d}$ [s]	$[0.03,0.08]$	0.45	0.09	48.3

TABLE IV : Simulation screening over the 512 fixed uncertain operating conditions.

A

: spin authority over the parameter span.

c

: consistency of the local steering gain across parameter levels and operating conditions.

\omega_{\max}

: largest simulated release spin during the sweep.

Fig. 9 : Simulated release-spin response for the four candidate motion parameters. Each curve shows

\omega_{0}

as one parameter is swept under a fixed operating condition; the bold curve is the ensemble mean and the shaded band shows the range. The overall change of the mean reflects spin authority

A

, while consistent local slopes across parameter levels and operating conditions correspond to high consistency

c

. Twelve conditions are shown for legibility.

Fig. 10 : Measured release-spin response on the robot for the three motion parameters retained after simulation screening. Each curve corresponds to one boomerang variant while one motion parameter is varied and the remaining parameters are held at the operating point.

Fig. 11 : Measured robot flights illustrating the design procedure. Increasing the grasp angle raises the nominal variant’s release spin and produces a clear turn, but the boomerang does not return. The thin variant returns at a similar release spin. For each throw, the release configuration is chosen so that the end-effector velocity is approximately horizontal.

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