Trajectory Planning without Trajectory Data: A Manifold-Guided Approach

Silong Yong, Anji Liu, Cunxi Dai, Carl Busart, Guanya Shi, Yilun Du, Katia Sycara, Yaqi Xie · N/A · 2026

Summary

Abstract Summary

A common way for trajectory planning is to leverage generative models trained on large collections of expert trajectories. At inference time, the model generates executable trajectories by conditioning on task goal constraints. However, trajectory-based methods rely on costly supervision, scale poorly with sequence length, and often generalize poorly to unseen constraints such as novel start-goal pairs. We propose an alternative to learn the underlying state-space manifold and use the geometry of the manifold for trajectory planning. This approach requires only state observations and enables generalization to unseen constraints by con- structing trajectories on the learned manifold of the state space. Experiments on Maze2D and robotic motion-planning benchmarks show that Ariadne constructs feasible paths from state-only supervision and generalizes to unseen start-goal combinations. On high-dimensional dual-arm planning, it remains competitive with trajectory-supervised and classical planners, while requiring no trajectory data for training.

Key Points

A common way for trajectory planning is to leverage generative models trained on large collections of expert trajectories.
At inference time, the model generates executable trajectories by conditioning on task goal constraints.
However, trajectory-based methods rely on costly supervision, scale poorly with sequence length, and often generalize poorly to unseen constraints such as novel start-goal pairs.
We propose an alternative to learn the underlying state-space manifold and use the geometry of the manifold for trajectory planning.
This approach requires only state observations and enables generalization to unseen constraints by con- structing trajectories on the learned manifold of the state space.

Trajectory Construction on the Learned Manifold

Before proceeding, we briefly clarify the notion of the data manifold. Let $\mathcal{X}\subset\mathbb{R}^{d}$ denote the ambient state space. Given state-only training data sampled from valid system behaviors, we assume that feasible states concentrate around a lower-dimensional subset $\mathcal{M}\subset\mathcal{X}$, which we refer to as the data manifold .

Intuitively, $\mathcal{M}$ represents the set of dynamically feasible and physically valid states of the system.

Trajectory Construction on the Learned Manifold — Trajectory Planning without Trajectory Data: A Manifold-Guided Approach — Figure 3 : While the score function provided by the diffusion model points toward the data manifold and can be viewed as an approximation of the normal direction of a (D-1)-dim manifold embedded in D-dimensional space, it no longer holds when we’re facing a more general and realistic case where the manifold might be even lower dimensional. We therefore propose to use the Jacobian of the score function for normal estimation as shown on the right.

Incorporating Endpoint Constraints

The original move-then-project procedure uses endpoint information through the direction vector pointing toward the target. However, once this direction is projected onto the tangent space, its magnitude and orientation are altered. In particular, the projection removes the normal component of motion, but this removal is not controlled with respect to the remaining progress toward the goal.

Experiments

In practice, we use a straight-line reference path between endpoints, which we find sufficient for stable performance. We further adopt arc-length-based step sizes to ensure consistent progression along the trajectory, and adapt the implementation for different generative models (e.g., diffusion and flow matching) accordingly. Detailed discussions are provided in Appendix E .

We evaluate Ariadne on three planning benchmarks: Maze2D Janner et al. (2022) ; Fu et al. (2020) , YAM 6D tabletop manipulation, and DualKuka Luo et al. (2024) .

Experiments — Trajectory Planning without Trajectory Data: A Manifold-Guided Approach — Figure 5 : Dualkuka planned trajectory. Dark colors represent start and light colors represent end.

Sources and Demonstrations

Figures are reproduced from Yong et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.