$χ_{0}$: Resource-Aware Robust Manipulation via Taming Distributional Inconsistencies

TL;DR

The paper addresses robustness gaps in real-world, long-horizon robotic manipulation by modeling three distributional pillars—training data ($P_{train}$), model bias ($Q_{model}$), and deployment trajectories ($P_{test}$)—and proposes χ$_0$, a resource-efficient framework. It combines Model Arithmetic (weight-space merging of policies trained on data subsets), Stage Advantage (stage-conditioned, low-variance progress signals for long-horizon tasks), and Train-Deploy Alignment (inference-augmented data and temporal smoothing) to align $P_{train}$, $Q_{model}$, and $P_{test}$. Empirical results on two dual-arm garment manipulation systems show that χ$_0$ surpasses the open-source π$_{0.5}$ baseline by about 250% in success rate with only ~20 hours of demonstrations on 8×A100 GPUs and can operate autonomously for 24 hours; ablations demonstrate the complementary value of MA, SA, and TDA. The work offers a practical, data-efficient path toward production-level robustness in complex manipulation tasks and provides code, data, and models to the community.

Abstract

High-reliability long-horizon robotic manipulation has traditionally relied on large-scale data and compute to understand complex real-world dynamics. However, we identify that the primary bottleneck to real-world robustness is not resource scale alone, but the distributional shift among the human demonstration distribution, the inductive bias learned by the policy, and the test-time execution distribution -- a systematic inconsistency that causes compounding errors in multi-stage tasks. To mitigate these inconsistencies, we propose $χ_{0}$, a resource-efficient framework with effective modules designated to achieve production-level robustness in robotic manipulation. Our approach builds off three technical pillars: (i) Model Arithmetic, a weight-space merging strategy that efficiently soaks up diverse distributions of different demonstrations, varying from object appearance to state variations; (ii) Stage Advantage, a stage-aware advantage estimator that provides stable, dense progress signals, overcoming the numerical instability of prior non-stage approaches; and (iii) Train-Deploy Alignment, which bridges the distribution gap via spatio-temporal augmentation, heuristic DAgger corrections, and temporal chunk-wise smoothing. $χ_{0}$ enables two sets of dual-arm robots to collaboratively orchestrate long-horizon garment manipulation, spanning tasks from flattening, folding, to hanging different clothes. Our method exhibits high-reliability autonomy; we are able to run the system from arbitrary initial state for consecutive 24 hours non-stop. Experiments validate that $χ_{0}$ surpasses the state-of-the-art $π_{0.5}$ in success rate by nearly 250%, with only 20-hour data and 8 A100 GPUs. Code, data and models will be released to facilitate the community.

Figures (19)

• Figure 1: Top: System overview. A robot teamwork system with two dual-arm ALOHA robots performing long-horizon collaborative garment manipulation, including flattening, folding and hanging. Bottom: Technical philosophy and performance. Distributional inconsistencies are inherent to robot learning ($P_\text{train}$: expert demonstrations; $Q_\text{model}$: policy inductive bias; $P_\text{test}$: deployment trajectories). $\chi_0$ systematically resolves these pairwise mismatches: Model Arithmetic aligns $Q_\text{model}$ with $P_\text{train}$; Train-Deploy Alignment bridges $P_\text{train}$ and $P_\text{test}$; and Stage Advantage optimizes $Q_\text{model}$ for $P_\text{test}$. The contributions of these modules collectively enable $\chi_0$ to surpass the baseline $\pi_{0.5}$black2025pi05 in terms of success rate by approximately 250%.
• Figure 2: Pipeline of $\chi_0$. Our framework addresses distributional inconsistencies across three stages. (Left) $P_{\text{train}}$: heuristic DAgger and spatio-temporal augmentation expand training coverage, with Stage Annotation for advantage estimation; (Middle) $Q_{\text{model}}$: Model Arithmetic merges complementary policies in weight space, guided by stage-aware advantage; (Right) $P_{\text{test}}$: temporal chunk-wise smoothing ensures execution accuracy, while on-policy DAgger enables closed-loop refinement.
• Figure 3: Souping strategies in Model Arithmetic. Policies trained on separate subsets are merged via weighted interpolation. (Top) Inverse Loss assigns higher coefficients to models with lower validation loss. (Bottom) Other strategies.
• Figure 4: Cumulative value based on SA. Red/green stands for negative/positive. Top: Task A shows slip fails and recovery; Middle: Task B shows fetching and cloth misplace; Bottom: Task C shows pull-over and visual occlusion.
• Figure 5: Train-Deploy-Alignment strategies and T-SNE visualizations. Left: three complementary strategies for distribution alignment. Right: T-SNE visualizations showing progressive distribution alignment as each strategy is applied.