DRIFT: Diffusion-based Rule-Inferred For Trajectories

Motion planning often admits multiple feasible solutions, making multimodal generation valuable, particularly for flexible multi-robot coordination. Diffusion models naturally learn such trajectory distributions, yet incorporating coarse and partial trajectory priors without restricting generation remains challenging. Such priors indicate a desirable region of the solution space rather than a single solution, motivating conditioned generation that preserves multimodality. In this paper, we guide trajectory generation in the clean trajectory space and progressively incorporate trajectory priors with a timestep-dependent guidance strength. At each reverse diffusion step, the reconstructed clean trajectory provides a unified space for integrating planning costs and partial trajectory priors. Planning costs are incorporated through gradient-based refinement, while the partial prior is progressively injected at the corresponding noise levels with decreasing guidance strength. This guides generation toward the prior in early stages while gradually releasing the constraint to preserve the inherent multimodality of the diffusion model. The framework naturally extends to multi-robot planning by incorporating inter-robot collision costs. Experiments on single- and multi-robot planning tasks demonstrate controllable trajectory synthesis, diverse feasible solutions, and safe multi-agent coordination.

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.

We present a learning-enhanced motion planner for differential drive mobile manipulators to improve efficiency, success rate, and optimality. For task representation encoder, we propose a keypoint sequence extraction module that maps boundary states to 3D space via differentiable forward kinematics. Point clouds and keypoints are encoded separately and fused with attention, enabling effective integration of environment and boundary states information. We also propose a primitive-based truncated diffusion model that samples from a biased distribution. Compared with vanilla diffusion model, this framework improves the efficiency and diversity of the solution. Denoised paths are refined by trajectory optimization to ensure dynamic feasibility and task-specific optimality. In cluttered 3D simulations, our method achieves higher success rate, improved trajectory diversity, and competitive runtime compared to vanilla diffusion and classical baselines. The source code is released at https://github.com/nmoma/nmoma .