World Models and Simulation

A short reproducible cubic example shows why equal parameter steps bunch up waypoints and what finite-polyline resampling actually equalizes.

Four vertical reactions can satisfy the same three balance equations in different ways. A finite reference model explains why equal sharing needs an additional assumption.

A stationary finite-post experiment separates line of sight from angular sampling. Four actual ray-query cases give 1, 0, 1 and 2 target samples while keeping visibility probes outside the scan counts.

A finite-wheel experiment compares 100 ms count windows with completed edge periods. Sparse crossings explain zero and 37.5 rpm estimates at steady 15 rpm, plus a stale period after an ideal stop.

Matching an IMU’s axes to the robot frame does not change its measurement point. A controlled rotating assembly compares radial and axial offsets, ideal specific force and finite-difference error.

Correct ranges can form a distorted point cloud when every beam uses one sensor pose. A finite-wall experiment compares first-pose and beam-time reconstruction, with separate wall and chord errors.

Unit length does not make a transformed mesh normal perpendicular to its surface. A finite triangle comparison separates forward scaling, inverse transpose, reflection orientation and singular geometry.

Moving a point load beyond two shaft supports can make one reaction exceed the applied force and reverse the other. Preserve both force and moment balance, then check whether the supports permit those directions.

A prescribed backlash model pairs one input angle with two output positions. Retain the approach state, define which shaft owns the width and check the zero-width control.

Two ideal 20-degree moves with different velocity ceilings take the same time. Compare the analytic peak, finite mesh samples and the travel needed for a cruise segment.