A timing result from a separate test
An arXiv methods preprint reports that its CIPS scheduler had a median evaluation time of 2 microseconds in an embedded timing microbenchmark. The comparable figure for the latency-aware event-triggered controller LA-ETC was 121 microseconds. The paper reports a 60.5-fold speedup in that comparison.
The timing result came from a microbenchmark, not directly from the paper's dynamic car-following benchmark. The work combines the CIPS architecture with a dynamic leader-follower adaptive cruise control benchmark and an embedded comparison of five scheduler policies.
Turning an offline certificate into a runtime check
The paper asks whether an offline spatial safety certificate can be transformed into a temporal persistence contract for a plant-model-independent runtime scheduler. The certificate describes a safe region, while the contract tracks whether that certificate can remain valid between sampled checks.
The proposed design links that compilation step to contract-based scheduling and a theorem about composing safe hybrid behavior. The compilation theorem starts with a continuously differentiable spatial certificate and defines a continuous persistence functional that is stated to satisfy the contract until the trajectory first exits the certified domain.
Along valid trajectories, the derived persistence contract was reported to satisfy a rate lower bound of minus 1. The paper says this permits deterministic constant-time evaluation without propagating the plant's ordinary differential equations online.
What was compared
The benchmark comparison covered Periodic, Boolean (Reactive), Spatial ETC, LA-ETC and CIPS. The policies used different trigger inputs and conditions, with LA-ETC serving as the main latency-aware overhead comparator.
The timing implementations used C++-20 with -O2 on a Pico-W Cortex-M0+ ARM platform running at up to 133 MHz. The setup had 16 KB of shared data and program L1 cache and 256 KB of SRAM, and the reported timing was the median per evaluation over 10,000 iterations.
The two timing workloads did different jobs. LA-ETC integrated the complete plant model at every sample over a prediction horizon of regeneration latency plus twice the sampling interval, using fourth-order RK4 integration with a 1-millisecond step. CIPS used no forward propagation and evaluated only the precompiled scalar persistence functional.
The displayed car-following sweeps
The adaptive cruise control benchmark used bounded kinematics: maximum braking deceleration was 6.0 metres per second squared, maximum forward acceleration was 2.0 metres per second squared, and maximum velocity was 20.0 metres per second. Its collision threshold was 3.0 metres, with a 0.5-metre measurement margin.
The offline certificate derivation set the robust safety threshold at 5.55 metres. The reported figure was formed from the 3.0-metre collision threshold, the 0.5-metre measurement margin and a 2.05-metre kinematic buffer.
Across the displayed sampling-interval sweep, with checks every 5, 20 and 50 milliseconds, CIPS recorded no reported fallbacks or violations. The minimum H value was 0.44 metres, while the paper's latency-efficiency measure, Elat, was 100.0% at 5 and 20 milliseconds and 98.4% at 50 milliseconds.
When regeneration latency was set to 10, 50 and 100 milliseconds, the displayed CIPS results again showed no reported missed or late events, fallbacks or violations. Minimum H remained 0.44 metres, and Elat was 100.0%, 100.0% and 98.8% at those three latency settings.
A formal guarantee with conditions
The paper's formal result is conditional. Under Assumptions 5.1 and 5.2, with the reset threshold greater than the sampling interval and the required initial persistence in place, Theorem 5.2 states that the hybrid state remains in the controller-indexed safe set for all future time when the specified trigger and fallback rules are followed.
The comparison also showed different operating trade-offs. Periodic scheduling was reported to preserve safety but to use many unnecessary regenerations, with Elat falling to 4.8% when regeneration latency reached 100 milliseconds. Boolean (Reactive) and Spatial ETC were reported to have systemic safety violations in the benchmark.
The paper says regeneration liveness is not guaranteed: delayed or rejected candidates can let the active object deplete its persistence until fallback.
What the results do not establish
The timing comparison was reported as medians without variability estimates or confidence intervals, and the displayed sweep results were not accompanied by statistical uncertainty.
The reported work combines formal CIPS analysis with a dynamic adaptive cruise control benchmark and an embedded timing microbenchmark. Its strongest safety statement is tied to the stated certificate, contract and runtime assumptions, and the manuscript is an arXiv version 1 preprint dated 25 August 2026.
Paper data and sources
Original title: Compiling Spatial Certificates into Temporal Contracts for Latency-Aware Control
Authors: Avinash malik
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text