Vela replaces fixed-rate action chunks with continuous spline trajectories, reaching 45.3% average success on LIBERO-X, 49.7% overall on EBench, and 67.5% mean subtask success on a real dual-arm egg-cake task

Representing future motion as a continuous trajectory rather than action chunks on a fixed temporal grid lets one output budget cover both long horizons and locally precise motion. Prior spline-based policies mainly target task-specific policies, single platforms, or downstream action tokenization and execution; this work makes trajectory-space action modeling the pretraining output space of a foundation model with a shared cross-embodiment action interface. On LIBERO-X the average success rate is 45.3% versus 39.3% for the point-wise baseline; on EBench the overall success rate is 49.7% with a progress score of 66, versus 41.4% and 54 for the baseline; ablations show post-hoc spline fitting alone (38.9% and 40.0%) does not recover the gains.

Motion-dependent horizon adaptation lets a fixed control-point budget allocate temporal resolution by motion complexity: longer spans for smooth motion, shorter spans for rapid local variation. Existing spline policies typically predict over a globally fixed temporal span, imposing one compromise between temporal coherence and local expressivity on all motions; here each demonstrated motion is assigned the longest span that still adequately represents it under a noise-aware criterion. With the same spline representation and control-point budget, the fixed-horizon variant averages 43.2% success versus 45.3% with adaptive horizons, improving at every one of the five perturbation levels.

Decoded-trajectory flow matching (DT-FM) weights control-point errors by their effect on the decoded trajectory, aligning supervision with trajectory geometry better than isotropic control-point supervision. CP-FM supervises the same flow residual with Euclidean distance in parameter space, whereas DT-FM measures it after spline decoding, equivalently replacing isotropic weighting with the decoder-induced quadratic form. CP-FM averages 44.0% success, an equal-weight CP-FM plus DT-FM combination 44.9%, and DT-FM alone 45.3%; the authors note the differences are modest, indicating effective trajectory-space learning does not hinge on a particular loss composition.

Trajectory-space modeling transfers to physical manipulation, remaining effective on multi-stage bimanual coordination, tool use, and sustained contact tasks. Most spline-policy studies stay in simulation or on a single platform; this work provides physical-robot evidence on a wheeled dual-arm robot for egg-cake cooking and potato shredding. Each of the four egg-cake subtasks is evaluated over 10 trials, with Vela at 67.5% mean subtask success versus 37.5% for the point-wise baseline and 40.0% for OpenWAM; on potato shredding Vela matches or exceeds both baselines at every stage.

The results target imitation-learning-based robot manipulation with multi-embodiment demonstration data: pretraining uses roughly 20,000 hours of public data (60 datasets, 11 embodiment classes) plus roughly 20,000 hours of private data, at a scale of a 3B PaliGemma vision-language backbone with a 300M flow-matching action expert and no additional trainable parameters. The method suits tasks needing long-horizon coverage and contact-rich fine manipulation, such as tabletop precision assembly, mobile pick-and-place, and multi-stage bimanual cooking; at deployment the policy predicts control points and horizon directly from context without fitting or horizon search, so inference cost is comparable to the point-wise baseline. Teams wanting to reuse the representation can adopt its shared action interface and noise-calibrated target construction to convert existing action-chunk data into spline supervision targets.

Several points remain worth watching: first, the horizon-adaptation gain appears at all five perturbation levels but is modest in size (43.2% fixed versus 45.3% adaptive), and its stability across data scales and embodiments is not yet established; second, the three geometry objectives differ only slightly in average success (44.0%, 44.9%, 45.3%), so loss design reads as a refinement rather than a prerequisite; third, the real-world conclusions rest on two tasks with 10 trials per subtask, a limited statistical grain; fourth, the current policy adapts only the temporal horizon while keeping the control-point count fixed, and varying both would require variable-length prediction and matching training objectives, which the authors flag as an open direction; fifth, the model scale matches the point-wise baseline, so how trajectory-space modeling behaves with larger backbones and more data remains to be characterized.