Technical Summary: APEX – Adaptive Policy Execution for Precise Manipulation

1. Problem Definition: The Test-Time Execution Gap

Modern imitation learning systems, including visuomotor and Vision-Language-Action (VLA) policies, typically output high-level action references (e.g., joint targets or end-effector poses) that are executed by low-level controllers, such as Proportional-Derivative (PD) schemes. However, a critical discrepancy exists between the policy's commanded reference and the robot's actual realized motion, termed the test-time execution gap.

This gap arises from two primary sources:

1. Inadequate High-Level Outputs: Policy outputs often lack higher-order reference signals (velocity, acceleration) and may contain discontinuities, which are insufficient for precise low-level tracking.
2. Imperfect Low-Level Dynamics: Commercial controllers often operate with unmodeled dynamics, parameter uncertainties, and inaccessible gain parameters ($K_p, K_d$).

Existing solutions generally require intrusive modifications, such as altering the policy architecture, retraining with residual learning, or changing the controller itself. These approaches are often impractical for large, pretrained models or proprietary commercial platforms where the policy and controller are treated as inaccessible "black boxes." The central question addressed is: Can the execution gap be bridged without modifying either the policy or the controller?

2. Methodology: The APEX Framework

The authors propose Adaptive Policy EXecution (APEX), a plug-and-play framework inserted between the high-level policy and the low-level controller. Inspired by biological motor control—where fast sensorimotor loops correct deviations on the fly without regenerating high-level plans—APEX operates as an online correction layer that leaves both the policy and controller untouched.

APEX functions in two stages:

A. Adaptive Passive Filtering (Signal Reconstruction)

Since policy outputs ($a_\pi$) often lack the velocity ($\dot{a}$) and acceleration ($\ddot{a}$) signals required for dynamic feasibility, APEX first reconstructs a smooth, dynamically feasible reference ($\bar{a}$) using an adaptive passive filter.

• The filter is driven by the tracking error $e_a = a_\pi - a$.
• It generates well-defined $\dot{\bar{a}}$ and $\ddot{\bar{a}}$ signals internally, ensuring the reference supplied to the controller is smooth and bandwidth-limited.

B. Test-Time Adaptive Correction

To compensate for unknown system dynamics (inertia $J$) and inaccessible controller gains ($K_p, K_d$), APEX augments the filtered reference with adaptive terms. The command $a_r$ sent to the controller is formulated as:
$$a_r = \bar{a} + \hat{w}[\hat{J}\ddot{\bar{a}} + \alpha e_a] + \hat{w}_d \dot{\bar{a}}$$
Where:

• $\hat{w}$, $\hat{w}_d$, and $\hat{J}$ are time-varying estimates of the unknown parameters ($1/K_p$, $K_d/K_p$, and $J$).
• These coefficients are updated online via an adaptive law driven by the real-time tracking error and the filtered reference velocity, without differentiating the raw policy output.

Theoretical Guarantees

The paper provides a stability analysis (Theorem 1) proving that for a system with unknown parameters and bounded disturbances, the closed-loop system signals remain bounded, and the tracking error converges to a residual set. This guarantees asymptotic tracking performance even without exact knowledge of the robot's dynamics.

3. Key Contributions

1. Black-Box Compatibility: APEX is the first framework to bridge the execution gap without requiring modifications to the policy architecture, retraining, or access to the low-level controller's internal parameters.
2. Dual-Stage Correction: It uniquely combines a passive filter for reconstructing higher-order signals with an adaptive law for compensating unknown dynamics, addressing both policy-side artifacts and controller-side limitations.
3. Provable Convergence: The framework offers theoretical convergence guarantees under standard adaptive control assumptions.
4. Generalizability: The method is agnostic to the specific policy class (deterministic or generative) and action representation (joint-space or task-space).

4. Experimental Results

The authors evaluated APEX across simulation and real-world (UR5) settings, testing four policy classes: ACT, Diffusion Policy, Flow Matching, and the VLA $\pi_{0.5}$.

• Isolating the Execution Gap: In a "demonstration replay" experiment (where expert trajectories are replayed directly to the controller, removing policy error), APEX reduced tracking error by 41.2% (from 30.84 mrad to 18.15 mrad) and increased success rates from 62.5% to 81.3%. This confirms that low-level controller imperfections alone cause significant failures.
• Policy-Controller Bridging: When paired with learned policies, APEX improved success rates by 4.8 to 25.8 percentage points across all tested policy classes.
  • Notable gains were observed on the PegInsertion task (3mm radial clearance), where Flow Matching success improved from 20% to 35% on a real UR5.
  • APEX demonstrated robustness across varying PD controller gains ($K_p, K_d$), outperforming fixed-parameter corrections.
• Cross-Platform Validation: The framework successfully generalized across different simulators (ManiSkill, LIBERO), action representations (joint vs. end-effector), and real-world hardware.

5. Significance and Claims

The paper claims that the test-time execution gap is a fundamental bottleneck in precision-sensitive manipulation, often overlooked in favor of improving policy training. The significance of APEX lies in its ability to recover lost performance from well-trained policies simply by correcting the execution stream.

The authors emphasize that:

• Even expert-level action references fail to execute accurately on commercial hardware due to controller limitations.
• A lightweight, non-intrusive correction layer at the policy-controller interface is sufficient to bridge this gap.
• The adaptive nature of APEX allows it to function effectively even when system dynamics are unknown or when the controller is a "black box," making it highly practical for real-world deployment of large-scale imitation learning models.

Limitations Acknowledged: The current implementation requires manual tuning of adaptation gains, and the disturbance term is treated as bounded rather than explicitly estimated, leading to bounded rather than zero-error convergence. Future work aims to integrate self-tuning mechanisms and disturbance observers.