Trajectory Planning without Trajectory Data: A Manifold-Guided Approach

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 constructing trajectories on the learned manifold of the state space. Experiments on classical planning problems in maze demonstrate the effectiveness of our work. We further show that the method can be used in higher dimension space where table-top robot arms are considered. Our method is able to find feasible path given only infeasible straight line reference, and be comparable to State-of-the-Art trajectory-based model without actually learning on trajectory data.