The Curse of Precision: A Data Scaling Law for High-Precision Robotic Manipulation
Cuijie Xu, Yuanfan Xu, Min Xue, Jianjie Lin, Xudong Zhang, Jian Wang, Yu Wang, Jincheng Yu
AI summary
Problem
While scaling laws for robotic generalization are well-studied, the quantitative relationship between data volume and task precision in closed-world manipulation remains unexplored.
Approach
The authors conduct a large-scale simulation study across multiple manipulation tasks, training diffusion policies with varying data sizes and precision levels to empirically derive and validate a new precision scaling law.
Key results
- Data requirements grow super-exponentially as target precision approaches a limit c, modeled by log(N) ∝ 1/(P − c)
- The limit precision c is an emergent system property rather than a fixed physical constant
- Enhancing sensors (e.g., adding a wrist camera) or expert policy quality measurably lowers c and expands achievable precision
- The scaling law holds consistently across diverse tasks and observation modalities
Why it matters
Provides a quantitative framework and practical roadmap for engineering data-efficient, high-reliability robotic manipulation systems.
Abstract
While scaling laws for imitation learning have primarily focused on generalization in open-world settings, the relationship between data and precision in closed-world tasks like robotic assembly remains largely unexplored. This paper systematically investigates this relationship and introduces a novel scaling law. We find that to achieve a fixed success rate, the required number of demonstrations N, grows super- exponentially as the target precision P, approaches a limit c. This relationship is accurately captured by the model log(N) ∝ 1/(P −c). Crucially, we reveal that the limit precision c is not a static physical constant of the task but an emergent property of the entire agent system, including its sensors and expert policy. Through experiments on canonical manipulation tasks, we validate this law and demonstrate that improving system components—such as adding a wrist camera or using a more effective expert—measurably lowers c, thus expanding the sys- tem’s achievable precision. Our work provides a new theoretical framework for precision in robotics and a quantitative metric to evaluate system capabilities. Furthermore, these findings provide a practical methodology for guiding the development and debugging of high-precision manipulation systems.