Fast Planning for Multi-object Multi-target Throwing

Zhengming Zhu; Yang Liu; Xiao Gao; Aude Billard

cs.ROOct 6, 2026

Fast Planning for Multi-object Multi-target Throwing

Authors: Zhengming Zhu, Yang Liu, Xiao Gao, Aude Billard

Organizations: Learning Algorithms and Systems Laboratory (LASA), EPFL, Switzerland

Abstract

Robot throwing has emerged as a promising technique for improving efficiency in logistics and warehouse automation, by enlarging the workspace and speeding up the process. To significantly increase the throwing system's throughput, we develop strategies for throwing multiple objects in one swipe. Such multi-object multi-target throwing (MOMT) leverages the large degrees of freedom of anthropomorphic hands. The key is to quickly generate fast and feasible throwing motions, which involves a complex trade-off between short trajectory duration and short planning time. We solve this problem in two stages. Offline, we build a model of the feasible set by combining object's inverted flying dynamics and the robot's kinematics and dynamics. Online, we generate feasible throws through fast solution matching and filtering of object's valid detach state and robot's feasible state that can compose sequences of throws in less than 5 ms. We validate the framework on a 7-DoF manipulator equipped with a multi-fingered hand. In simulation, coordinated two-object throwing reduces execution time by up to 46% compared to independent single-object planning, and this improvement is maintained when scaling to three objects. Real-world experiments with two objects confirm a 29% reduction; the remaining gap to the theoretical 50% is attributed to inter-throw transition overhead. When target positions are randomly changed mid-execution, the system re-plans and successfully reaches the new targets within 100 ms latency without stopping the robot. These results establish the first unified planning framework for MOMT throwing -- demonstrating scalability to multiple objects in simulation and real-world feasibility on two-object tasks -- advancing the frontier of high-throughput robotic manipulation. A video summarizing the method and the hardware experiments is available at https://liuyangdh.github.io/momt-video

Figures & tables

Fig. 1 : Multi-object multi-target throwing with a Kuka iiwa 7 robot equipped with an Allegro hand. The robot grasps two objects simultaneously and throws them to different target boxes in a single continuous motion, demonstrating the efficiency of our unified planning framework.

Symbol	Description
$(q,\dot{q})\in\mathbb{R}^{2n}$	Joint release state for n-DoF robot
${}^{A}p^{B}\in\mathbb{R}^{3}$	Target position in robot frame
${}^{A}p^{E}\in\mathbb{R}^{3}$	Object position at release in robot frame
$\mathbf{v}\in\mathbb{R}^{3}$	Object velocity at release
$d_{E}$	Horizontal distance from $E$ to robot base $A$
$d_{B}$	Horizontal distance from $B$ to robot base $A$

TABLE I : Notation for geometric modeling

Fig. 3 : The Backward Reachable Tube (BRT) is the set of release states whose trajectories reach the landing target set $\mathcal{X}$ .

Fig. 4 : Visualization of the BRT. At each spatial position, arrows show valid release velocities.

Fig. 5 : Visualization of the maximum velocity dictionary for the Kuka iiwa 7. The surface shows the maximum achievable end-effector velocity as a function of throwing direction $(\phi,\gamma)$ at a fixed height and distance.

Fig. 6 : Motivation for multi-throw coordination. The single-target planner yields multiple valid configurations per target (red for Target 1, blue for Target 2). Choosing configurations independently may result in large joint-space transitions (dashed arc), while coordinated selection minimizes total execution time (solid arrow).

Fig. 7 : Multi-target coordinator: Given multiple targets, the single-target throwing planner generates candidate solutions for each. The coordinator searches for the best combination minimizing total execution time.

Method	Computation (s)	Execution (s)	Energy (J)
Naive ( $K=1$ )	$0.06\pm 0.01$	$6.38\pm 1.69$	$87.46\pm 58.74$
Greedy- $K5$	$0.06\pm 0.01$	$5.10\pm 1.08$	$62.56\pm 40.52$
Greedy- $K10$	$0.06\pm 0.01$	$4.40\pm 0.70$	$53.56\pm 36.68$
Greedy- $K20$	$0.07\pm 0.01$	$4.21\pm 0.68$	$43.50\pm 24.63$
Greedy- $K50$	$0.12\pm 0.01$	$3.61\pm 0.41$	$42.39\pm 20.37$
Greedy- $K80$	$0.19\pm 0.01$	$3.51\pm 0.25$	$47.38\pm 21.90$

TABLE II : Planning-execution trade-off for two objects (simulation)

Method	Computation (s)	Execution (s)	Energy (J)
Naive ( $K=1$ )	$0.11\pm 0.01$	$9.57\pm 1.58$	$128.74\pm 74.57$
Greedy- $K5$	$0.10\pm 0.01$	$6.98\pm 0.84$	$73.08\pm 34.82$
Greedy- $K10$	$0.12\pm 0.01$	$6.41\pm 0.56$	$73.42\pm 23.51$
Greedy- $K20$	$0.29\pm 0.01$	$5.85\pm 0.33$	$62.78\pm 19.99$
Greedy- $K50$	$2.81\pm 0.06$	$5.45\pm 0.26$	$67.35\pm 18.84$
Greedy- $K80$	$11.11\pm 0.22$	$5.27\pm 0.21$	$76.26\pm 21.03$

TABLE III : Planning-execution trade-off for three objects (simulation)

Method	Computation (s)	Execution (s)	Energy (J)
Naive ( $K=1$ )	$0.15\pm 0.01$	$13.59\pm 1.96$	$195.11\pm 66.86$
Greedy- $K5$	$0.15\pm 0.01$	$9.54\pm 1.05$	$95.19\pm 41.76$
Greedy- $K10$	$0.40\pm 0.01$	$8.95\pm 0.82$	$94.79\pm 48.02$
Greedy- $K20$	$3.90\pm 0.08$	$8.16\pm 0.41$	$100.74\pm 21.65$
Greedy- $K30$	$18.50\pm 0.22$	$7.73\pm 0.25$	$101.50\pm 27.27$
Greedy- $K50$	$138.45\pm 1.35$	$7.48\pm 0.20$	$87.10\pm 33.74$

TABLE IV : Planning-execution trade-off for four objects (simulation)

Panel of Figure 12 — Fig. 8 : Left: Two objects held by fingertips in the Allegro hand using a manually-tuned configuration that minimizes release interference. Right: Release delay measurement using an ATI nano F/T sensor.

Method	Computation	Execution	Throws Landed
Naive	$0.06\pm 0.02$ s	$5.20\pm 0.98$ s	14/20
Greedy	$69.8\pm 32.3$ s	$3.69\pm 0.37$ s	14/20

TABLE V : Real-world validation (two objects,

n=10

configurations)

Fig. 9 : Reactive multi-object multi-target throwing. When target positions change mid-execution, the system re-plans and adapts in real-time. See the supplementary video for the full demonstration.

Method	Planning	Execution	Arbitrary	Scales to
	time	quality	targets?	$N$ objects?
Naive	$<100$ ms	Baseline	Yes	Yes
Greedy- $K$	0.1–20 s	Improved	Yes	Yes
Greedy (full)	$>60$ s	Best	Yes	Yes
Precomputed	$<5$ ms	Best ∗	No	No †

TABLE VI : Search strategy comparison

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