Organizations: Chair of Robotics and Systems Intelligence (RSI), Munich Institute of Robotics and Machine Intelligence (MIRMI), Technical University of Munich (TUM), 80992 Munich, Germany · Chair of Information-oriented Control (ITR), School of Computation, Information and Technology (CIT), Technical University of Munich (TUM), 80333 Munich, Germany · Chair of AI Planning in Dynamic Environments, Munich Institute of Robotics and Machine Intelligence (MIRMI), Technical University of Munich (TUM), 80992 Munich, Germany · School of Mechanical Engineering, Translational Research Center, Tongji University, Shanghai 201804, China, affiliated with Shanghai Yangzhi Rehabilitation Hospital and also with Shanghai Key Laboratory of Wearable Robotics and Human-Machine Interaction · Mohamed Bin Zayed University of Artificial Intelligence, Abu Dhabi 23201, United Arab Emirates
Generative models have become increasingly powerful tools for robot motion generation, enabling flexible and multimodal trajectory generation across various tasks. Yet, most existing approaches remain limited in handling multiple types of constraints, such as collision avoidance, actuation limits, and dynamic consistency, which are typically addressed individually or heuristically. In this work, we propose UniConFlow, a unified constrained flow matching-based framework for trajectory generation that systematically incorporates both equality and inequality constraints. Moreover, UniConFlow introduces a novel prescribed-time zeroing function that shapes a time-varying guidance field during inference, allowing the generation process to adapt to varying system models and task requirements. Furthermore, to further address the computational challenges of long-horizon and high-dimensional trajectory generation, we propose two practical strategies for the terminal constraint enforcement and inference process: a violation-segment extraction protocol that precisely localizes and refines only the constraint-violating portions of trajectories, and a trajectory compression method that accelerates optimization in a reduced-dimensional space while preserving high-fidelity reconstruction after decoding. Empirical validation across three experiments, including a double inverted pendulum, a real-to-sim car racing task, and a sim-to-real manipulation task, demonstrates that UniConFlow outperforms state-of-the-art generative planners and conventional optimization baselines, achieving superior performance on certified motion planning metrics such as safety, kinodynamic consistency, and action feasibility. Project page is available at: https://uniconflow.github.io.
Figures & tables
Method
Obstacle Avoidance
Safety Guarantee
Dynamics Consistency
Admissible Action
Long-Horizon Planning
Dataset Creation
Real-world Experiments
Diffuser [ 7 ]
✗
✗
✗
✗
✗
✓
✗
Decision Diffuser [ 24 ]
✓
✗
✓
✗
✗
✓
✗
Diffusion-based Policy [ 8 , 12 , 13 ]
✗
✗
⚫
✗
✗
✓
✓
ChainedDiffuser [ 11 ]
✗
✗
⚫
⚫
✓
✓
✓
DPCA [ 34 ]
✓
✗
✗
✗
✗
✗
✗
DPCC [ 35 ]
✓
✗
✓
✓
✗
✓
✗
TABLE I : Comparison of representative diffusion- and flow-based motion planners across key properties. Long-Horizon Planning: the method generates a complete task-level trajectory rather than a single short-horizon action chunk. Dataset Creation: the method provides an explicit data generation pipeline or a publicly released dataset. Real-World Experiments: the method is validated on a physical robotic platform. ✓ denotes that the property is explicitly addressed in the respective work, ✗ that it is not, and ⚫ that it is not applicable.
Fig. 1 : Function r(t) over time with cr=0 and γr(t,r)=γr=r in Definition 5 .
Fig. 2 : Function g(t) over time with cr=0 , γr(t,r)=γr=r in Definition 5 and g(0)=1 , gˉ(0)=2 in Theorem 1 with PTZF (a) and with PT function (b). Green area denotes the free generation process.
Fig. 3 : Visualization of the motion of the double inverted pendulum. State sequences (top row) and action rollouts (bottom row) for the stabilization task across different methods: Diffuser-D, TVS, SafeFlow, PCFM, and UniConFlow.
Fig. 4 : Performance comparison across normalized metrics for the double inverted pendulum scenario. SR-S, SR-A, AR, and TSR represent percentage-based success metrics, while KC-F, KC-I, Cost, and Time are inverted min-max normalized metrics (higher is better).
Fig. 5 : Dataset creation pipeline for generative models in car racing scenarios. Geometric raw data including centerline, track boundaries, and raceline for the Nürburgring Nordschleife (left); extracted and rasterized track segment (middle); training data is generated through optimal control problems with random initial conditions for both forward and reverse driving (right).
Fig. 6 : Terminal refinement process for the car racing scenario. The window-based segmentation strategy preserves the global trajectory shape (left). Refine the safe segment where kinodynamic consistency may be violated, due to numerical errors (middle). The final refined trajectory achieves safety, admissibility, and kinodynamic consistency (right).
Fig. 7 : Performance heatmap for car racing scenarios in forward and reverse driving cases. All values are normalized to [0,1] with inversion applied to KC, Cost, and Time such that higher scores uniformly represent better performance.
Fig. 8 : Visualization of state and action rollout trajectories generated by UniConFlow versus optimization-based methods.
Fig. 9 : The experimental setup for the manipulator. The obstacle is modeled as an ellipsoid for collision avoidance purposes, with its geometric center defined by the attached marker. Marker positions are measured via an NDI Polaris Vega XT optical tracker visualized in Cigna-6D, while the robot state is visualized in RViz.
Fig. 10 : The datasets (left) are obtained either by expert demonstration with Franka arm or optimal control in a simulation environment. In the sampling process (middle), the rectangle filled with diagonal lines signifies the obstacles. The green path represents the collision-free trajectory navigating between red obstacles within the bounded workspace after PTZF-based guided sampling, while the blue path before PTZF-based guided sampling. The terminal refinement (right) is the same process in the car racing case in Fig. 6 .
Fig. 11 : Success rate in 3D spatial motion scenario.
Fig. 12 : Values of the RMSE of kinodynamic consistency, cost, and inference time (ms) in 3D spatial motion scenario.
Pipeline Component
Pendulum
Raceline
Pseudo-2D Manip.
3D Manip.
Time(ms)
(%)
Time(ms)
(%)
Time(ms)
(%)
Time(ms)
(%)
Generative Model ODE
1.95
78.0
2.00
76.9
22.50
71.0
81.50
77.6
PTZF Constraints & QP
0.35
14.0
0.22
8.5
3.20
10.1
15.50
14.8
Terminal Refinement
0.20
8.0
0.38
14.6
6.00
18.9
8.00
7.6
Total Inference
2.50
100
2.60
100
31.70
100
105.00
100
TABLE II : Computational Cost Ablation of Inference Components
Task
Stage 1 (PTZF Output)
Stage 2 (Terminal Refinement)
Certified Rate
State RMSE
State Corr. ℓ2 Dist.
State Fréchet Distance
Action Corr. ℓ2 Dist.
Action Fréchet Distance
Pendulum
88.4%
0.03
0.07
0.38
0.31
1.13
Raceline
98.1%
0.07
0.06
0.52
0.31
0.003
0.59
0.009
Pseudo-2D Manip.
89.2%
29.84
7.12
13.49
4.18
9.21
3D Manipulator
86.1%
17.18
12.01
15.79
6.73
11.17
TABLE III : Inference Components Impact Ablation of Terminal Enforcement on Generative Output
In recent years Flow Matching has become a prominent method for generative modeling robot motion generation. In its generic form Flow Matching is an ODE-based neural sampler that is trained by regressing empirical flow fields associated with motion samples as data. However, in robot motion generation we often have additional constraints that might not be present in the collected data. The majority of current approaches train the flow on the available data and use inference-time guidance to enforce task-specific constraints. To address this mismatch, we propose ConFlow, a constraint-guided flow matching framework that incorporates constraint information directly into the training objective via differentiable barrier or cost functions. To address design specifications such as smoothness and boundary conditions, we propose replacing the standard Gaussian source distribution used in flow matching training with a conditional Gaussian Process. Our approach also uses infeasible demonstrations as negative supervision, improving constraint satisfaction without requiring additional expert data. Experiments on a two-robot navigation task demonstrate that ConFlow achieves lower collision rates and higher trajectory quality than standard flow matching baselines, with or without inference-time guidance. These results validate training-time constraint integration as an effective approach to closing the training--inference gap in generative motion models.
Nutan Chen, Jianxiang Feng, Marvin Alles +1
LS Wiiri Robot Innovation Center · Independent Researcher · Technical University of Munich +1
While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.
Jianming Ma, Qiyue Yang, Yang Zhang +4
Shanghai Jiao Tong University, Shanghai, China · Shanghai Innovation Institute, Shanghai, China
Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce Hierarchical Diffusion-Flow (HDFlow), a novel hierarchical planning framework that optimally leverages the strengths of diffusion and rectified flow models to overcome the limitations of single-paradigm generative planners. HDFlow employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate HDFlow on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/
Nandiraju Gireesh, Yuanliang Ju, Chaoyi Xu +3
1Peking University · University of Toronto. · 2Galbot