ELMP: Efficient Learning for Motion Planning via Analytical Policy Gradients

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.

Embodied robots have achieved strong performance in many real-world manipulation tasks, yet agile dynamic manipulation remains challenging due to high sensitivity to motion parameters and sparse outcome-level feedback. Tasks such as shooting a basketball into a hoop require precise control of fast open-loop motions, where small trajectory variations can lead to large outcome deviations, making data-efficient adaptation difficult for existing methods that rely on large-scale interaction, reward engineering, or accurate dynamic modeling. We propose Prior Reinforce (P.R.), a simple and practical framework for goal-conditioned dynamic manipulation. The method first learns a structured motion manifold from a small set of demonstrations using a conditional diffusion model, and then adapts motions toward new goals through feedback-driven optimization in a low-dimensional condition space. By separating motion generation from outcome-driven adaptation, the framework enables efficient refinement using only a small number of real-world trials under noisy perception. Experiments on multiple real-world dynamic manipulation tasks demonstrate that P.R. reliably achieves new goals within as few as ten total trials while remaining robust to perception noise and hardware uncertainty, suggesting a practical approach for low-trial real-world robot adaptation. Project website: https://adap-robotics.github.io/.

Different stages of manipulation tasks exhibit varying levels of difficulty, suggesting stage-dependent motion speeds and temporal prediction horizons. However, existing IL-based visuomotor policies typically imitate the execution speed of expert demonstrations and operate with a fixed temporal prediction horizon, limiting flexibility and overall task throughput. In this paper, we introduce AutoSpeed, a model-agnostic learning framework that enables existing visuomotor policies to predict trajectories with stage-adaptive motion speeds, without requiring speed or stage annotations. We treat future trajectories at different speeds as candidate optimization targets, evaluate each candidate using a composite cost that trades off prediction error against prediction horizon, and optimize the policy toward the minimum-cost candidate. With a fixed-length action sequence, speed modulation adjusts the effective temporal prediction horizon: simple stages are executed faster with a longer prediction horizon, whereas complex stages are executed more slowly with a shorter prediction horizon. Specifically, we implement speed modulation in the frequency domain via the discrete cosine transform (DCT), which enables smooth, non-integer speed scaling and thus preserves motion continuity. Extensive evaluations show that AutoSpeed substantially reduces task execution time while also improving success rates. Under the AutoSpeed framework, the inferred motion speeds exhibit a strong correspondence with task stages.