Becoming a Fruit Ninja: Real-Time Probabilistic Kinodynamic Planning for Manipulator Projectile Interception

Lucas Chen; Austin Garrett; Andrew Niu; Zachary Kingston

cs.ROSep 18, 2026

Becoming a Fruit Ninja: Real-Time Probabilistic Kinodynamic Planning for Manipulator Projectile Interception

Authors: Lucas Chen, Austin Garrett, Andrew Niu, Zachary Kingston

Organizations: Department of Computer Science, Purdue University, West Lafayette, IN, USA

Abstract

Projectile interception is a challenging dynamic manipulation problem. Intercepting a thrown object with a robot arm requires reaching a point on the object's path as the object passes through it. Slicing also fixes the blade's velocity and orientation at contact. The goal is therefore a subset of the states of the robot and arrival times that moves as the object falls, and the arm must reach it within its actuator limits in milliseconds. We present FRUITNINJA, an anytime sampling-based planner that grows a tree on the GPU in batches toward the interception manifold. Each edge is an exact cubic whose travel time is found by a parallel search against the arm's dynamics, so every edge satisfies the actuator limits. Plans are ranked by a risk-aware objective over the uncertainty in the object's position and the arm's arrival time. We evaluate on a Franka Research 3 against six baselines in a calibrated real-time simulator, where FRUITNINJA cuts 96.7% of tosses in the open and 68.3% among five obstacles, versus the best baseline's 68.3% and 35.0% respectively.

Figures & tables

Figure 1: System architecture. The planner observes the object state and produces a commanded reference $(q_{g},\dot{q}_{g},T)$ at $50\text{\,}\mathrm{Hz}$ ; the controller refits a cubic from measured state and commands torques at $1\text{\,}\mathrm{kHz}$ . The planner’s latency compensation shifts the target forward by $\Delta t_{\text{plan}}\approx$20\text{\,}\mathrm{ms}$$ . — Figure 1: System architecture. The planner observes the object state and produces a commanded reference $(q_{g},\dot{q}_{g},T)$ at $50\text{\,}\mathrm{Hz}$ ; the controller refits a cubic from measured state and commands torques at $1\text{\,}\mathrm{kHz}$ . The planner’s latency compensation shifts the target forward by $\Delta t_{\text{plan}}\approx$ 20\text{,}\mathrm{ms}$$ .

Figure 2: Cut rate, catch rate, and cut speed vs. median solve time. Each point is one planner configuration (varying batch size, iterations, or population). FRUITNINJA reaches $96.7\text{\,}\mathrm{\%}$ cut rate at $12\text{\,}\mathrm{ms}$ ; baselines plateau below $70\text{\,}\mathrm{\%}$ .

	$N=0$ (no obstacle)				$N=3$ (3 capsules)				$N=5$ (5 capsules)
planner	cut $\uparrow$	catch $\uparrow$	thru $\downarrow$	$\lx@six@unitobject v\uparrow$	cut $\uparrow$	catch $\uparrow$	thru $\downarrow$	$\lx@six@unitobject v\uparrow$	cut $\uparrow$	catch $\uparrow$	thru $\downarrow$	$\lx@six@unitobject v\uparrow$
FRUITNINJA (ours)	96.7	98.3	$\times$	5.35	81.7	85.0	$7.3$	$5.36$	68.3	81.7	$11.5$	5.06
RRTC (CPU)	$73.3$	98.3	$\times$	$4.76$	$58.3$	$78.3$	$24.1$	$4.75$	$21.7$	$36.7$	$27.0$	$4.27$
CEM	$68.3$	$76.7$	$\times$	$5.30$	$53.3$	$65.0$	$4.7$	5.37	$38.3$	$53.3$	5.3	$5.03$
CMA-ES	$68.3$	$86.7$	$\times$	$4.96$	$65.0$	$80.0$	5.0	$5.11$	$35.0$	$68.3$	$5.4$	$5.00$
TrajOpt	$41.7$	$73.3$	$\times$	$3.81$	$31.7$	$51.7$	$8.1$	$3.80$	$43.3$	$63.3$	$14.5$	$3.79$

Table I : Obstacle avoidance (60 tosses per clutter level). Cut/catch:

\mathrm{\%}

;

\bar{v}

: contact-conditional speed (

\mathrm{m}\text{/}\mathrm{s}

); thru: fraction of plans whose executed motion passes through a capsule. Gold : best cut rate per level. Averages are calculated only on successful trials. FRUITNINJA maintains the best cut and catch rate even as obstacle density increases.

Figure 3: An example of a simulated intercept sequence with obstacles. We insert up to five 750mm long capsule shaped obstacles into the workspace of the FR3 and benchmark planning for each planner. The results for 0, 3, and 5 capsules are reported in Table I .

variant	cut (%) $\uparrow$	$\bar{v}$ (m/s) $\uparrow$	solve (ms) $\downarrow$
cubic (control)	$96.1\pm 1.0$	$5.41\pm 0.06$	$9.65\pm 0.07$
order 1	$78.9\pm 7.5$	$6.13\pm 0.09$	$8.26\pm 0.12$
order 2, no $\dot{q}_{1}$	$41.7\pm 2.9$	$4.74\pm 0.11$	$8.40\pm 0.07$
order 2, no $\dot{q}_{0}$	$76.7\pm 4.4$	$5.25\pm 0.02$	$9.02\pm 0.15$
order 4	$94.3\pm 0.9$	$5.47\pm 0.07$	$9.10\pm 0.30$
order 5 (min $\dddot{q}$ )	$95.6\pm 1.0$	$5.41\pm 0.07$	$9.25\pm 0.18$

Table II: Trajectory parameterization. Each variant is three seeds

\times

60

throws.

ablation	cut (%) $\uparrow$	catch (%) $\uparrow$	$\bar{v}$ (m/s) $\uparrow$
full objective (control)	$96.7\pm 1.7$	$97.2\pm 2.0$	$5.45\pm 0.07$
$-\log P_{\text{object}}$	$90.0\pm 2.3$	$94.2\pm 1.2$	$5.33\pm 0.00$
$-\log P_{\text{inrange}}$	$28.3\pm 10.3$	$47.8\pm 9.7$	$4.96\pm 0.28$
$-\log P_{\text{arm}}$	$85.0\pm 0.0$	$96.7\pm 0.0$	$4.38\pm 0.01$
flat covariance	$85.0\pm 2.3$	$93.3\pm 2.3$	$5.45\pm 0.00$

Table III: Probability model ablation. Each row removes one or two terms from the objective ( 2 ); the pairwise rows remove both named terms. “Flat covariance” freezes

\sigma(t)

at its initial value. Mean

\pm

std. dev. across seeds.

variant	cut (%) $\uparrow$	catch (%) $\uparrow$	$\bar{v}$ (m/s) $\uparrow$
control	$97.2\pm 1.0$	$98.3\pm 0.0$	$5.37\pm 0.06$
leave one out
$-$ torque	$\bm{96.7\pm 1.7}$	$97.8\pm 1.0$	$\bm{5.37\pm 0.06}$
$-$ velocity	$84.4\pm 5.1$	$94.4\pm 2.5$	$5.33\pm 0.09$
$-$ friction, armature	$\bm{96.7\pm 1.7}$	$\bm{98.3\pm 0.0}$	$5.31\pm 0.06$
leave one in

Table IV: Arm dynamics model ablation (three seeds

\times

60 throws per variant). Velocity removes the joint-velocity ratio and position-dependent taper; friction and armature are Eq. 4 .

	cut $\uparrow$	catch $\uparrow$	$\bar{v}\uparrow$
real control	86.7 $\pm$ 6.2	86.7 $\pm$ 6.2	4.29 $\pm$ 0.20
simulation
FRUITNINJA (ours)	86.7 $\pm$ 6.2	86.7 $\pm$ 6.2	4.93 $\pm$ 0.13
RRTC (CPU)	50.0 $\pm$ 9.1	73.3 $\pm$ 8.1	4.63 $\pm$ 0.37
CEM	70.0 $\pm$ 8.4	76.7 $\pm$ 7.7	5.42 $\pm$ 0.18
CMA-ES	33.3 $\pm$ 8.6	46.7 $\pm$ 9.1	4.56 $\pm$ 0.32

Table V: Real object trajectories with simulated FR3. The “real control” row is a trial done fully in the real world.

Dynamic Robotic Manipulation

Dynamic robotic manipulation studies how robots act on moving or deformable objects and respond to fast-changing physical interactions.

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Dept. of Aerospace Engineering Sciences, University of Colorado Boulder, USA · Dept. of Computer Science, University of Colorado Boulder, USA

Robot Navigation Safe Motion Planning Partially Observable Markov Decision Processes

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Target interception in crowded environments requires reaching a moving objective while navigating among multiple uncertain human agents. Since human navigation intent is not directly observable, the robot must reason over multiple possible future interaction outcomes. We formulate interception in crowds as a partially observable Markov decision process and solve it online using tree search under a fixed computational budget. In this setting, the action-space structure directly shapes the search tree and how computational effort is allocated. We perform a controlled comparison between a sequential path-speed planner, which first plans a spatial path and then modulates speed along it, and a unified planner that jointly branches over steering and speed within tree search. Across simulations with up to 200 humans, both approaches perform similarly at low crowd density but diverge sharply as density increases. At the highest crowd density, the sequential planner has a safe-interception rate 31 percentage points lower and requires 44% more time than the unified steering-speed planner, revealing a structural limitation of spatial restriction. Project webpage: https://tic-planning.github.io/

Abstract

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