Can an input shaper make a liquid-carrying cart’s move robust to a stale slosh-frequency calibration, and how fast can it be?

What it found

Follow-up to slosh-twin. Convolving the twin’s bang-bang acceleration with a ZV or ZVD shaper multiplies the undamped residual exactly by V(ε) = |sin(πε/2)| or sin²(πε/2), ε the frequency error (verified against exact propagation to 10 digits), while distance and the acceleration cap are preserved. Designed at a full tank, both shapers keep the 1 cm tolerance at every fill from 100% to 10% (ε down to −9.5%; worst residual 4.8 mm ZV, 0.6 mm ZVD) in 5.90 s and 6.90 s, where the null-tuned move needs 8 s at half fill and 28 s at 25% and below. Closed forms give the largest tolerated |ε| (e.g. 10.7% for ZV at half fill). Searching the design frequency for a fill band [0.1, 1] yields a 5.85 s ZV move, but only by detuning to spend the whole tolerance (worst residual 9.88 mm, no margin). Stylised: one linear slosh mode, ideal actuator, no nonlinear slosh.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

• What is a digital twin worth for training a controller?What a digital twin is worth for training a controller: exact LQ sim-to-real regret with a stability cliff, a validation blind spot (zero score gap yet mistrained control without probing), and a twin worth exactly σ²/(vδ²) real samples at any accuracy.
• How wide should domain randomization be, and what does it buy?Domain randomization over a twin, exactly: cliff-limited width, quartic price when the twin was right, cliff pushed out ~15%, but uniform-average training is not minimax and the best width tracks the prior.
• What does it cost to keep a digital twin in sync with a drifting plant, and is probing worth it?Keeping a digital twin in sync with a drifting plant: closed-form Kalman tracking variance and control regret (matched to simulation), a frozen twin loses half its edge in ln 2/(2(1−ρ)) steps, probing never pays for one drifting parameter, and a two-parameter closed-loop blind direction gives a mean-field dither law ν* ∝ q^{1/6} that self-exciting certainty-equivalent control mostly makes unnecessary.
• How often, and how long, should a digital twin be re-identified as the plant drifts?Re-identifying a drifting twin by dedicated experiments: closed-form interval T*∝q_d^{−2/3} with downtime, noise and drift regret exactly equal at the optimum, excess ∝q_d^{1/3}, a 4× drift misjudgement costs ≤26%, but the second-order optimum destabilises 0.7–15% of cycles and a safe schedule is 37–200× worse than an always-on Kalman twin.
• What should you pay a digital-twin provider for?What to pay a digital-twin provider for: cost-paid twins differ from Brier-paid ones, certainty-equivalence loss is quartic in spread, payment caps make the elicited twin jump at a closed-form threshold, and Brier mispays probing by 15×.
• How long can a digital twin be wrong before you can prove it, and what does waiting cost?Anytime-valid e-process audit of a digital twin in closed loop: peeking-safe (2.4% vs 58% false alarms), delay set by the controller's own excitation, regret before detection nearly independent of the gap, dither pays only for gross errors.

All 164 Digital twins & sim-to-real projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.