granular op• Data kinds: scalar × scalar → table
• Call: import fullseye as fs; fs.ledger.heap_scene_mjcf(n_spheres: 'int' = 1200, radius: 'float' = 0.004, *, mu_slide: 'float' = 0.16, mu_roll: 'float' = 0.09, density: 'float' = 2500.0, orifice_d: 'float' = 0.048, orifice_height: 'float' = 0.06, bin_radius: 'float' = 0.05, timestep: 'float' = 0.0015, base_roll: 'float' = 0.01, base_slide: 'float' = 1.0, solver_iterations: 'int' = 50, solver: 'str' = 'CG', cone: 'str' = 'elliptic', condim: 'int' = 6, contact_tc: 'float' = 0.006, seed: 'int' = 0) -> 'dict' (to call the implementation directly, import granular; granular.heap_scene_mjcf(n_spheres: 'int' = 1200, radius: 'float' = 0.004, *, mu_slide: 'float' = 0.16, mu_roll: 'float' = 0.09, density: 'float' = 2500.0, orifice_d: 'float' = 0.048, orifice_height: 'float' = 0.06, bin_radius: 'float' = 0.05, timestep: 'float' = 0.0015, base_roll: 'float' = 0.01, base_slide: 'float' = 1.0, solver_iterations: 'int' = 50, solver: 'str' = 'CG', cone: 'str' = 'elliptic', condim: 'int' = 6, contact_tc: 'float' = 0.006, seed: 'int' = 0) -> 'dict'; from the registry, opsdrive.get("heap_scene_mjcf"))
MJCF string of a scene with rigid spheres stacked in a flat-bottomed hopper (square orifice, side orifice_d) (no mujoco needed, listed in the ledger).
Spheres are stacked in layers inside a cylindrical bin (radius bin_radius, bottom plate at height orifice_height). They flow out through the hole in the bottom plate and form a heap on a plane (it stops once the heap reaches the hole —— the same as a real heap below a hopper). The hole is a square enclosed by 4 plates (Beverloo's formula uses the circular-hole D₀; a square is compared via its equivalent diameter). Friction is (mu_slide, 0.005, mu_roll·R): MuJoCo's rolling friction coefficient has units of length (torque / normal force), so the dimensionless DEM μ_r (0.09 from Sunday et al. 2020) is multiplied by the radius. The base is a rough table (sliding friction of the plane base_slide default 1.0, rolling base_roll [m] default 0.01; the same role as sandpaper glued to the bottom in angle-of-repose experiments). With a smooth table (μ 0.16) the first spheres to fall rolled away and no heap formed (measured: 1,200 spheres spread into a single layer of radius 0.15 m). Rolling resistance saturates at the sliding-friction limit μ_s g (single-sphere measurement: with a rolling coefficient of 0.01 as well as 0.1, from 1 m/s it travels 0.32 m = deceleration 1.6 m/s²), so it is sliding friction that holds the base in place. contact_tc = time constant of the soft contact [s] (solref).
Set it to at least 2·timestep: with 0.004 s at timestep 2 ms (= the limit), 2,000 spheres of radius 3.5 mm diverged (maximum speed 12.6 m/s, measured). The default solver is CG + elliptic cone (Newton took over 280 s for 700 spheres in a dense heap → aborted, measured).
Returns: xml (string), positions (initial centres (n, 3)), info (n, radius, mu_slide, mu_roll, orifice_d, bin_radius, orifice_height, timestep, mass_each, mass_total, column_top, bulk_density_bin). Raises ValueError: contact_tc < 2 timestep / the hole does not fit in the bin / the spheres do not fit in the bin / misspelled solver or cone.
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_granular_heap_repose — py -3.11 examples/poc_granular_heap_repose.py
table as input)course_layout · course_occupancy · course_contains · world_build · world_camera · world_move · lidar_scan · rss_longitudinal_same
granular)heap_volume_cone · heap_mass · heap_volume_heightmap · beverloo_rate · beverloo_fit · discharge_synth · dispense_mass_from_video · hopper_discharge_rate
*Provenance: granular.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.