Refine the action.
Optimize an action chunk using the learned energy gradient. Execute a short prefix, then replan from the next observation.
xk+1 = xk + ηk ∇xEθ(xk, z)
Equilibrium Energy Controlfor Introspective Lifelong Robot Learning
A robot should know how to act, when to ask for help, and how to learn from it.
Equilibrium Energy Control · Research preprint, 2026
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23* Equal contribution, random order† Project lead‡ Corresponding author
Abstract
Long-term robot autonomy depends on more than effective action generation: a policy must recognize when its behavior is no longer sufficiently supported and use assistance to improve. We introduce Equilibrium Energy Control (EqC), a framework for introspective lifelong robot learning built around an explicit conditional energy landscape. EqC casts generative action refinement as equilibrium-seeking optimization, while the geometry of the refinement process reveals whether the generated behavior remains consistent with the learned landscape. This competence signal enables Energy-Gated DAgger, where persistent energy-consistency violations trigger expert takeover and the resulting recovery trajectories are aggregated for subsequent policy updates. EqC integrates naturally into both Diffusion Transformer policies and flow-matching-based vision-language-action (VLA) policies. Across simulation and real-world bimanual manipulation, EqC matches or improves control performance and robustness while enabling timely intervention near the policy's competence boundary. A real-world study further shows how these interventions progressively expand the range of situations handled autonomously, providing a practical path from static generative controllers toward self-improving robot systems.
01 / THE IDEAOne landscape.
One landscape.
Three capabilities.
EqC uses an explicit conditional energy landscape to generate actions, inspect their reliability, and turn timely assistance into new autonomous capabilities.
Read the refinement path.
Measure whether energy progress agrees with the relation learned from demonstrations. Persistent violations signal a need for help.
energy-consistency signal
Make recovery count.
Energy-Gated DAgger collects expert recoveries where the policy needs them, then trains on the accumulated experience.
Dr+1 = Dr ∪ Qr
02 / CONTROL PERFORMANCEBetter control,
Better control,
in the real world and simulation.
02.1 / REAL-WORLD EVALUATION
Three real-world tasks
We evaluate EqC on three bimanual manipulation tasks using an EqC-adapted Galaxea G0.5 policy, with the original G0.5 policy as the baseline. Each policy is evaluated in 20 independent trials per task with randomized object placements.
EqC rollout4× speed
REPORTED SUCCESS RATE
65%
→G0.5
100%
EqC (ours)
Coordinate a brush and dustpan to collect scattered debris, then deposit it into a bin.
One illustrative EqC rollout is shown.
REAL-WORLD AVERAGE SUCCESS
Explore the full evaluation and details. 63.3%G0.5
91.7%EqC (ours)
Across three bimanual tasks · 20 trials per task and method
02.2 / SIMULATION BENCHMARKSAcross tasks
Across tasks
and environments.
We evaluate EqC with Diffusion Transformer and vision-language-action policies across four simulation benchmarks. Each chart reports the benchmark’s average success rate under its evaluation protocol.
Comparison methodsEqC (ours)All charts use a 0–100% scale.
LIBERO
Four task suites
- Diffusion Policy86.5%
- Rectified Flow90.0%
- GeCO93.5%
- EqC (ours)94.0%
EqC: multi-seed mean. Baselines: published results.
VLABench
Five evaluation tracks
- π₀.₅24.5%
- π₀.₅ + EqC (ours)27.1%
- π₀29.4%
- π₀ + GeCO36.0%
- π₀ + EqC (ours)36.7%
Results grouped by π₀.₅ and π₀ backbones.
RoboTwin 2.0
Five tasks · two difficulty settings
- π₀Easy: 49%Hard: 18%
- π₀ + GeCOEasy: 50%Hard: 28%
- π₀ + EqC (ours)Easy: 63%Hard: 33%
Average success over five tasks, shown separately for each difficulty.
LIBERO-Plus
Seven perturbation families
- OpenVLA15.6%
- π₀53.6%
- π₀ + EqC (ours)65.8%
Overall robustness aggregate, as reported in the paper.
Task-level scores, evaluation protocols, and supplementary LIBERO results are available in the full paper.
03 / KNOWING WHEN TO STOPA useful alarm
A useful alarm
comes before failure.
Reliable failure detection is the prerequisite for timely takeover. EqC reads inconsistency along the action-refinement trajectory, rather than relying on the final action alone.
In real-world block-stacking experiments, EqC's energy-consistency signal distinguishes successful from failed rollouts more clearly than Diff-DAgger's loss-based signal. While the Diff-DAgger traces overlap through much of the rollout, EqC shows a clearer separation between outcomes, supporting timely intervention.
Hierarchical block stacking
25 successful + 25 failed rolloutsEqC (ours)
Successful n = 25Failed n = 25
Diff-DAgger (baseline)
Successful n = 25Failed n = 25
Mean traces with ±1 standard deviation. Each signal is shown on its original scale. Source: paper, real-world competence-awareness evaluation.
04 / ENERGY-GATED DAGGERToday's intervention.
Today's intervention.
Tomorrow's autonomy.
When persistent energy-consistency violations trigger an alarm, EqC pauses autonomous execution so that an expert can complete the task, and the resulting recovery trajectory becomes training data for the next policy update.
3× speed · synchronized footage
ROBOT EXECUTIONENERGY-CONSISTENCY SIGNAL
Jump to a moment
AUTONOMOUS SUCCESS AFTER LEARNING
0%→96.7%
30 recoveries. Five learning rounds.
Starting from 18 seed demonstrations, targeted recovery expands the dataset to 48 episodes and improves autonomous block stacking.
Means over 3 independent runs.
20 autonomous evaluation trials per checkpoint, per run.
Matched data and training budgets across methods.
EqC (ours)G0.5 + Diff-DAggerHuman Intervention
05 / ROBOT AGENT AS EXPERTWhat if the expert
What if the expert
is a robot agent?
After initialization and expert preparation, EqC and an Astra-powered robot agent form a fully automated intervention-and-learning pipeline.
The prepared agent adapts its script to the intervention state. Execution shown at 4× speed.
18 + 6seed demos + agent recoveries
20 / 20autonomous evaluation successes
Proof-of-concept garment-folding experiment; separate from the three-run lifelong learning evaluation.
gpt-6-astra × EqCLarge-model capabilities.
Large-model capabilities.
Compact-policy execution.
Astra is prepared using the same 18 demonstrations that train the initial garment-folding policy. Through full-task and takeover practice, it consolidates spatial reasoning and manipulation experience into reusable skills and control code.
Once preparation is complete, the framework provides a fully automated loop of failure detection, expert recovery, and policy learning. When EqC signals that assistance is needed and pauses execution, Astra adapts its prepared code to the current scene and executes a recovery script to complete the task. The resulting demonstrations are then used to update the compact EqC policy, enabling it to learn from the larger model's recovery experience and improve its autonomous execution.
01 / PREPARE
→Demonstrations → skills
Fit a script, practice on the robot, reflect, and consolidate reusable skills.
02 / RECOVER
→Alarm → adapted script
Observe the intermediate state and execute a recovery using the prepared skills.
03 / LEARN
Experience → policy
Train EqC on the recovery data, bringing the large model's capabilities into autonomous control.
06 / CONTINUED LEARNINGNew tasks.
New tasks.
Growing capabilities.
Moving from blocks to cups reveals new competence gaps and interference with a previously learned skill. Targeted recovery on both tasks restores block-stacking performance while enabling autonomous cup stacking.
STARTING FROM A LEARNED SKILL
The policy has already learned hierarchical block stacking: Run 1, Round 5, trained on 48 block demonstrations.
From one task to two.
Hierarchical block stacking → Hierarchical cup stacking
- TRANSFER START
Before adaptation
A trained block-stacking policy meets the cup task.
Block stacking100%Cup stacking0%Blocks already mastered; no cup demonstrations yet.
48cumulative demonstrations - UPDATE 01
Learn the new task
Add 6 cup-stacking recovery demonstrations.
Block stacking60%Cup stacking50%Cup stacking improves, but the prior block skill regresses.
54cumulative demonstrations - UPDATE 02
Recover both tasks
Add 6 cup recoveries and 6 block recoveries.
Block stacking100%Cup stacking100%The same policy now performs both tasks autonomously.
66cumulative demonstrations
A sequential task-shift study, separate from the three-run lifelong learning evaluation.
KEEP EXPLORING
A promising path towardlifelong robot learning.
From static policies to growing competence.
Citation
@misc{yang2026eqc,
title={{EqC}: Equilibrium Energy Control for Introspective Lifelong Robot Learning},
author={Haodong Yang and Runhan Huang and Bowen Zhang and Iofai Lei and
Zunzhe Zhang and Xiangcheng Zhang and Shaoting Zhu and Linzhan Mou and
Yicheng Liu and Hang Zhao},
year={2026},
eprint={2610.18790},
archivePrefix={arXiv},
primaryClass={cs.RO},
url={https://arxiv.org/abs/2610.18790}
}