arXiv subjects

Aleš Kučera

Publications and source records attributed to Aleš Kučera.

3 recordsLinked to original sources

arXiv2026

Propagating Elevation-Map Uncertainty Through the Contact Maximum in Closed Form

Risk-aware planners score paths on uncertain elevation maps using the path cost's mean and standard deviation. Modeling rigid contact, however, requires computing a maximum over several uncertain cells. First-order propagation loses accuracy here by differentiating at only a single cell, while Monte Carlo sampling requires a full path evaluation per draw. We compute the moments of that contact maximum in closed form using Clark's pairwise recursion. By tracking each contact's covariance against the shared map cells, we propagate the smooth remainder using exact Gaussian quadratic-form identities. A contest-depth calibration, fitted once on two design traverses, closes the aggregate standard-deviation shortfall that remains. On 317 held-out rover path segments, scored against a Monte Carlo reference from the same belief, every pre-registered criterion was met. The corrected Clark fold cuts the median error of the mean from linearization's 2.3% to 0.19% and attains the lowest error in the conditional value at risk (CVaR) at the 90% level of every method tested. A benchmark plan costs just 5.5 microseconds on a GPU. These accuracy gains concentrate at contested contacts. While they seldom change which path is chosen on this terrain, the fold still selects the reference-best path in 98% of decisions against linearization's 93 to 96%. On a second dataset the mean transfers, though the risk number does not.

cs.RO↗

arXiv2026

Ostrich: Taking Large Strides Through Stiff Contact in Differentiable Dynamics

Three properties determine whether a differentiable simulator can drive gradient-based optimization through contact: simulation accuracy, gradient reliability, and per-iteration cost. Tape-based engines such as MJX and Newton Semi-Implicit require timesteps small enough to keep contacts numerically tractable, and their backpropagation memory grows linearly with the number of timesteps T. Surrogate models bound memory by approximating contact away, but the resulting gradients lose the geometry the optimization depends on. We present Ostrich, a GPU-accelerated rigid-body simulator that resolves hard contacts and friction with non-smooth Newton iteration at large timesteps (h ~ 0.1 s), and differentiates the converged residual via the implicit function theorem, reusing the forward Schur complement to compute the adjoint at O(1) memory per timestep. On real-robot trajectories over a pallet obstacle, Ostrich holds MuJoCo's sim-to-real accuracy up to a 50x larger timestep. Its gradients converge from random initializations where MJX descends slowly and Newton Semi-Implicit stalls; a warm iteration runs 211x faster than MJX's and 4.7x faster than Semi-Implicit's. On the same scene Ostrich differentiates 8,192 parallel worlds on a single 24 GB GPU, sustaining 29x checkpointed MJX's optimization throughput; without checkpointing both baselines exhaust memory at far fewer worlds. We close with a gradient-based trajectory optimization demonstration over triangle-mesh terrain across a 10 s horizon, a setting where prior engines either restrict to primitive geometry or face the convergence and memory limits shown above.

cs.RO↗

arXiv2017

Flare-induced changes of the photospheric magnetic field in a $δ$-spot deduced from ground-based observations

Aims: Changes of the magnetic field and the line-of-sight velocities in the photosphere are being reported for an M-class flare that originated at a $δ$-spot belonging to active region NOAA 11865. Methods: High-resolution ground-based near-infrared spectropolarimetric observations were acquired simultaneously in two photospheric spectral lines, Fe I 10783 Å and Si I 10786 Å, with the Tenerife Infrared Polarimeter at the Vacuum Tower Telescope (VTT) in Tenerife on 2013 October 15. The observations covered several stages of the M-class flare. Inversions of the full-Stokes vector of both lines were carried out and the results were put into context using (extreme)-ultraviolet filtergrams from the Solar Dynamics Observatory (SDO). Results: The active region showed high flaring activity during the whole observing period. After the M-class flare, the longitudinal magnetic field did not show significant changes along the polarity inversion line (PIL). However, an enhancement of the transverse magnetic field of approximately 550 G was found that bridges the PIL and connects umbrae of opposite polarities in the $δ$-spot. At the same time, a newly formed system of loops appeared co-spatially in the corona as seen in 171 Å filtergrams of the Atmospheric Imaging Assembly (AIA) on board SDO. However, we cannot exclude that the magnetic connection between the umbrae already existed in the upper atmosphere before the M-class flare and became visible only later when it was filled with hot plasma. The photospheric Doppler velocities show a persistent upflow pattern along the PIL without significant changes due to the flare. Conclusions: The increase of the transverse component of the magnetic field after the flare together with the newly formed loop system in the corona support recent predictions of flare models and flare observations.

astro-ph.SR↗