Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models

Davood Soleymanzadeh; Xiao Liang; Minghui Zheng

cs.ROApr 8, 2026

Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models

Authors: Davood Soleymanzadeh, Xiao Liang, Minghui Zheng

Organizations: J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA · Zachry Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843 USA

Abstract

Open-loop end-to-end neural motion planners have recently been proposed to improve motion planning for robotic manipulators. These methods enable planning directly from sensor observations without relying on a privileged collision checker during motion planning. However, existing planners produce a single path for a given planning problem and cannot exploit their open-loop nature to propose multiple motion plans. To address this limitation, we introduce Flow Motion Policy, an open-loop neural motion planner that uses flow matching to generate a batch of motion plan proposals by learning a distribution over motion plans conditioned on the planning observation. At inference time, it samples multiple candidate motion plans to enable efficient best-of- $N$ inference while avoiding iterative collision checking during planning. We benchmark the Flow Motion Policy against representative sampling-based, optimization-based and neural motion planning methods. Evaluation results demonstrate that Flow Motion Policy improves planning success and efficiency, highlighting the effectiveness of stochastic generative policies for end-to-end motion planning and best-of- $N$ sampling. Project website: https://davoodsz.github.io/FlowMotionPolicy.github.io/

Figures & tables

Fig. 2: Flow Motion Policy architecture. This framework leverages current time-step $t$ planning information (i.e., planning scene ( $\mathcal{P}_{w}$ ) point cloud, robot ( $\mathcal{P}_{r}$ ) point cloud, robotic manipulator configuration ( $\mathbf{q}_{t}$ )) together with robotic manipulator goal configuration ( $\mathbf{q}_{\text{goal}}$ ) for end-to-end open-loop motion planning in complex environments. $\mathbf{h}_{t}$ , $\mathbf{h}_{r}$ , and $\mathbf{h}_{w}$ are the current time-step $t$ planning information corresponding embeddings, respectively, and $\mathbf{h}_{\text{goal}}$ is the goal configuration embeddings. “PointNet++” are set abstraction layers from PointNet++ [ 28 ] . $\epsilon\sim\mathcal{N}(0,I)$ is Gaussian noise, $t$ is flow time, and $x^{0}$ is denoised increment action sequence. Best-of- $N$ Sampling operates on a batch of planned motions and utilizes a lightweight inference-time optimization process to output the first collision-free path.

	RRTC [ 1 ]	BIT* [ 15 ]	cuRobo [ 2 ]	cuRobo-Vox [ 2 ]	MPNets [ 3 ]	SIMPNet [ 17 ]	GAIDE [ 19 ]	PerFACT [ 4 ]	FMP-1 (ours)	FMP-100 (ours)
T $(s)\downarrow$
TableTop	$2.85{\pm}0.97$	$3.19{\pm}2.67$	$1.97{\pm}1.98$	$1.62{\pm}1.37$	$2.66{\pm}1.26$	$5.68{\pm}10.20$	$3.00{\pm}2.58$	$0.22{\pm}0.01$	$\mathbf{0.16}{\pm}0.01$	$0.58{\pm}0.44$
Box	$0.73{\pm}0.54$	$1.40{\pm}1.47$	$0.45{\pm}0.92$	$0.46{\pm}0.68$	$2.41{\pm}1.01$	$2.68{\pm}1.66$	$2.17{\pm}2.02$	$0.23{\pm}0.05$	$\mathbf{0.16}{\pm}0.03$	$0.38{\pm}0.07$
Bins	$1.10{\pm}0.67$	$1.84{\pm}1.81$	$0.17{\pm}0.20$	$\mathbf{0.16}{\pm}0.19$	$3.45{\pm}1.62$	$3.97{\pm}2.52$	$3.72{\pm}3.56$	$0.24{\pm}0.04$	$\mathbf{0.16}{\pm}0.02$	$0.43{\pm}0.27$
Shelf1	$2.71{\pm}0.73$	$4.35{\pm}2.38$	$0.89{\pm}1.36$	$0.48{\pm}1.13$	$2.29{\pm}0.01$	$3.28{\pm}0.10$	$2.99{\pm}1.58$	$0.24{\pm}0.03$	$\mathbf{0.16}{\pm}0.03$	$0.58{\pm}0.49$
Shelf2	$3.91{\pm}1.12$	$5.95{\pm}2.09$	$0.48{\pm}1.22$	$0.37{\pm}0.63$	$2.57{\pm}0.89$	$2.96{\pm}1.43$	$5.56{\pm}2.57$	$0.22{\pm}0.01$	$\mathbf{0.15}{\pm}0.03$	$0.67{\pm}0.71$

TABLE I: Comparison with Bechmark Planners. Planning performance of Flow Motion Policy with 20 inference flow steps and benchmark planners across evaluation planning tasks. “ FMP-1 ” denotes Flow Motion Policy without inference-time optimization (

N=1

), while “ FMP-100 ” refers to the variant with inference-time optimization using 100 planned paths (

N=100

). “T” represents planning time, “SR” denotes success rate, “C” denotes path length, “S” denotes path smoothness, and “J” denotes path jerk.“

\downarrow

” indicates lower values are preferable, and “

\uparrow

” indicates higher values are preferable.

Fig. 3: Best-of-

\mathbf{N}

Sampling. Planning success rate and planning time of Flow Motion Policy and Neural MP [ 25 ] adaptation across the held-out planning tasks. “GMM-1” and “GMM-100” are Neural MP [ 25 ] adaptation with Gaussian Mixture Model (GMM) without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively. “FMP-1” and “FMP-100” are Flow Motion Policy without inference-time optimization and inference-time optimization (

N=100

), respectively.

Flow Motion Policy ( $N=1$ )
	TableTop		Box		Bins		Shelf
							Task I		Task II		Task III
	T $(s)\downarrow$	SR $(\%)\uparrow$	T $(s)\downarrow$	SR $(\%)\uparrow$	T $(s)\downarrow$	SR $(\%)\uparrow$	T $(s)\downarrow$	SR $(\%)\uparrow$	T $(s)\downarrow$	SR $(\%)\uparrow$	T $(s)\downarrow$	SR $(\%)\uparrow$
MLP	$\mathbf{0.16{\pm}0.01}$	$\mathbf{48.0}$ %	$\mathbf{0.16{\pm}0.02}$	$60.7$ %	$\mathbf{0.16{\pm}0.03}$	$75.5$ %	$\mathbf{0.16{\pm}0.03}$	$45.0$ %	$\mathbf{0.15{\pm}0.03}$	$34.4$ %	$\mathbf{0.16{\pm}0.01}$	$33.4$ %
U-Net [ 35 ]	$0.75{\pm}0.01$	$\mathbf{48.0}$ %	$0.75{\pm}0.03$	$59.4$ %	$0.77{\pm}0.03$	$72.3$ %	$0.77{\pm}0.02$	$44.0$ %	$0.76{\pm}0.03$	$31.4$ %	$0.77{\pm}0.01$	$32.4$ %
Transformer [ 35 ]	$0.55{\pm}0.01$	$43.0$ %	$0.57{\pm}0.01$	$60.0$ %	$0.54{\pm}0.03$	$77.3$ %	$0.55{\pm}0.01$	$53.0$ %	$0.56{\pm}0.03$	$\mathbf{36.0}$ %	$0.55{\pm}0.02$	$\mathbf{35.0}$ %

TABLE II: Policy Head Architecture Ablation. Planning success rate and planning time of Flow Motion Policy with 20 inference flow steps and Diffusion Motion Policy with 100 denoising steps during inference with various head architectures. “DMP-1” and “DMP-100” are Diffusion Motion Policy without inference-time optimization and inference-time optimization (

N=100

), respectively. “FMP-1” and “FMP-100” are Flow Motion Policy without inference-time optimization and inference-time optimization (

N=100

), respectively. “DiT” denotes DiT-Block Policy [ 36 ] . “T” represents planning time, “SR” denotes success rate, “C” denotes path length, “S” denotes path smoothness, and “J” denotes path jerk.“

\downarrow

” indicates lower values are preferable, and “

\uparrow

” indicates higher values are preferable.

Fig. 4: Policy Head Architecture Ablation. Average planning success rate and planning time of Flow Motion Policy and Diffusion Motion Policy with various head architectures across all held-out evaluation tasks. “DMP-1” and “DMP-100” are Diffusion Motion Policy without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively. “FMP-1” and “FMP-100” are Flow Motion Policy without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively. “DiT” denotes DiT-Block Policy [ 36 ] .

Policy Head	MLP	U-Net [ 35 ]	Transformer [ 35 ]	DiT [ 36 ]	Neural MP [ 25 ]
Network Size $\downarrow$	1.40M	2.29M	2.97M	3.20M	20.00M

TABLE III: Policy Network Size. Policy parameter size of Flow Motion Policy and ablative structures. “DiT” denotes DiT-Block Policy [ 36 ] , and “

\downarrow

” indicates lower is better.

Fig. 5: Best-of- $N$ Sampling. Qualitative path diversity of Flow Motion Policy for a fixed start-goal-scene query. Flow Motion Policy generates diverse path proposals which enables best-of- $N$ sampling to select collision-free candidates after collision checking.

$N$	Joint Diversity (rad)	EE Diversity (m)	Goal-Reaching	Collision-Free
100	$0.092{\pm}0.024$	$0.041{\pm}0.012$	100/100	45/100

TABLE IV: Best-of-

\mathbf{N}

Sampling. path-level diversity of Flow Motion Policy for a fixed start-goal-scene query. Diversity is measured as the mean pairwise per-waypoint distance across

N

sampled paths.

Fig. 6: Number of Function Evaluation (NFE). Average planning success rate and planning time of Diffusion Motion Policy with various head architectures and denoising steps (NFE) across all held-out evaluation tasks. “DMP-1” and “DMP-100” are Diffusion Motion Policy without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively. “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 7: Time-to-Solution for FMP across different policy head architectures with various numbers of sampled paths ( $N\in[10,200]$ ) at inference. “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 8: Number of Function Evaluation (NFE). Average planning success and planning time for Diffusion Motion Policy and Flow Motion Policy a range of inference steps (NFE) across all held-out planning tasks. “DMP-1” and “DMP-100” are Diffusion Motion Policy without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively. “FMP-1” and “FMP-100” are Flow Motion Policy without inference-time optimization (

N=1

) and inference-time optimization (

N=100

), respectively.

Fig. 9: Diffusion Motion Policy inference Time Optimization . Success rate and planning time of Diffusion Motion Policy with various head architectures across a range of trajectories (

N\in[10,200]

) in inference time optimization. “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 10: Flow Motion Policy inference Time Optimization . Success rate and planning time of Flow Motion Policy with various head architectures across a range of trajectories (

N\in[10,200]

) in inference time optimization. “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 11: Inference Flow Steps. Success rate and average planning time of Flow Motion Policy with various head architectures across a range of inference flow steps (

\text{step}\in[5,90]

) without inference time optimization (

N=1

). “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 12: Real-World Deployment Setup: Illustration of the deployment of Flow Motion Policy in a real-world environment. A calibrated camera (Intel RealSense D435i RGB-D) is used to capture the workspace point cloud.

Fig. 13: Inference Flow Steps. Success rate and average planning time of Flow Motion Policy with various head architectures across a range of inference flow steps (

\text{step}\in[5,90]

) with inference time optimization (

N=100

). “DiT” denotes DiT-Block Policy [ 36 ] .

Fig. 14: Flow Motion Policy Deployment in Real-world. The path for the given motion planning problem is visualized for each environment, illustrating the planned motion execution across subsequent frames.

	Bins	Articulated	Shelves	Total #	Total [%]
FMP-1	5/10	3/10	2/10	10/30	33.4%
FMP-100	10/10	10/10	6/10	26/30	86.7 %

TABLE V: Flow Motion Policy Deployment in Real-world. Planning success rate of Flow Motion Policy performance in real-world evaluation tasks. “ FMP-1 ” and “ FMP-100 ” are Flow Motion Policy without inference-time optimization (

N=1

) and with inference-time optimization (

N=100

), respectively.

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Abstract

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