The Curse of Precision: A Data Scaling Law for High-Precision Robotic Manipulation

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 $\log(N) \propto 1/(P-c)$. 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 system'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.

Mind the Gap: Learning Implicit Impedance in Visuomotor Policies via Intent-Execution Mismatch

Teleoperation inherently relies on the human operator acting as a closed-loop controller to actively compensate for hardware imperfections, including latency, mechanical friction, and lack of explicit force feedback. Standard Behavior Cloning (BC), by mimicking the robot's executed trajectory, fundamentally ignores this compensatory mechanism. In this work, we propose a Dual-State Conditioning framework that shifts the learning objective to "Intent Cloning" (master command). We posit that the Intent-Execution Mismatch, the discrepancy between master command and slave response, is not noise, but a critical signal that physically encodes implicit interaction forces and algorithmically reveals the operator's strategy for overcoming system dynamics. By predicting the master intent, our policy learns to generate a "virtual equilibrium point", effectively realizing implicit impedance control. Furthermore, by explicitly conditioning on the history of this mismatch, the model performs implicit system identification, perceiving tracking errors as external forces to close the control loop. To bridge the temporal gap caused by inference latency, we further formulate the policy as a trajectory inpainter to ensure continuous control. We validate our approach on a sensorless, low-cost bi-manual setup. Empirical results across tasks requiring contact-rich manipulation and dynamic tracking reveal a decisive gap: while standard execution-cloning fails due to the inability to overcome contact stiffness and tracking lag, our mismatch-aware approach achieves robust success. This presents a minimalist behavior cloning framework for low-cost hardware, enabling force perception and dynamic compensation without relying on explicit force sensing. Videos are available on the \href{https://xucj98.github.io/mind-the-gap-page/}{project page}.