v3.3.0

Root collection now follows CBiRRT, and it is much cheaper. Over 100 seeds
of the pick demo, every run succeeds (it was 97%), and the median solve drops
from 0.68 to 0.07 s (p90 from 1.69 to 0.18 s). Two changes, each measured
against the one before it with tools/planning_benchmark.py:

• The start and goal sets keep growing during the search (#196).
• IK windings of one physical configuration share a collision verdict
  (#200). This gives the same paths, faster.

Migrating from 3.2.0:

• The same seed gives a different path.
• goal_bias and start_bias are deprecated, and their meaning changed.
  Prefer goal_sample_probability and start_sample_probability; the old
  names map to them, with a warning, until 4.0.
• C++ consumers: the PlannerConfig fields are renamed the same way.

The start and goal sets keep growing during the search, as in CBiRRT (#196).
On each tree's turn a weighted coin, the paper's P_sample, either draws new
members of that tree's own start or goal set and adds them as roots, or takes
an ordinary turn toward a random configuration. Until now, roots were
collected once, before the search, and frozen. Measured over 100 seeds per
problem, with both versions interleaved on one machine
(tools/planning_benchmark.py):

• every run that used to time out now succeeds: pick goes from 97% to 100%
  of seeds, and the TSR-chain crank from 93% to 100%;
• the slow tail shrinks: pick's p90 goes from 1.69 to 0.84 s (worst case
  from a 30 s timeout to 1.75 s); the crank's p90 from 11.0 to 5.4 s (worst
  case from a 120 s timeout to 12.6 s); transport's p90 from 0.45 to 0.32 s;
• medians hold or improve, for example pick from 0.68 to 0.54 s, measured
  as root collection plus search;
• the door, whose up-front roots already connect it in one iteration, is
  unchanged.

Changed

• Behaviour. The same seed now gives a different path, in both backends.
  Every reference-artifact case keeps its outcome and passes validation;
  native parity holds.

• Parameters. New start_sample_probability and goal_sample_probability
  (default 0.1) replace start_bias and goal_bias. The meaning changed: the
  old biases steered a turn's extension toward a member of the other tree's
  set. The new probabilities add roots to the tree's own set. A finite set
  never tosses the coin, because its members are all roots already. The old
  names still work until 4.0, mapped to the new ones, with a
  DeprecationWarning that says the meaning changed.

• Faster root collection, same result (#200). SSIK returns every winding
  of every IK branch: 320 solutions per pick pose, but only about 12
  physically distinct arm poses. Root collection now collision-checks each
  physical configuration once per draw instead of every winding. Pick's root
  collection goes from 0.41 s to 0.03 s, so its median solve drops from 0.53
  to 0.07 s (p90 from 0.80 to 0.18 s). Transport's median drops from 0.14 to
  0.05 s. All 700 benchmark runs give identical paths. This needs two
  declarations, never inferred:

  • the IK solver's revolute_joints (SSIK: every joint);
  • the collision checker's full_turn_invariant (the MuJoCo checkers, when
    every planned joint is a hinge).

  stats["reused_verdicts"] counts the shared verdicts. C++: Sample::key,
  IKSolver::revolute_joints(), StateValidator::full_turn_invariant() and
  SolveStats::reused_verdicts are new.

• New stat. PlanResult.stats["search_roots"] counts the roots added
  during the search, on both backends.

• New tool. tools/planning_benchmark.py measures planning time and work
  on realistic problems. benchmarks/ holds the v3.2.0 baseline and this
  change's measurement.

• C++ consumers. PlannerConfig::goal_bias and start_bias are renamed
  to goal_sample_probability and start_sample_probability, with the new
  meaning. Tree::add_root is new. SolveStats::search_roots is new.