fix(mobile): DistanceTransform, PRM, QuinticPoly and CurvaturePoly planners

[petercorke]

What

Entries 26-30 of the typing-pass problem list, and what a full review of the four planner files turned up. Stacked on #778 (the PRMPlanner.plot override has to match the new PlannerBase.plot); until #778 merges this PR also shows its commits.

Bugs fixed (each test failed first)

DistanceTransformPlanner

• next() wrapped around at the left and top borders: for a goal on the opposite edge it stepped off the map, and query() never terminated.
• An unknown metric raised UnboundLocalError; it is a ValueError (also from the constructor).
• plot_3d always called a blocking plt.show(). It has block (default True, as before) and path_style (ls is deprecated).
• The class docstring example passed distance="manhattan"; the argument is metric. It only ran because unknown arguments were swallowed (fixed on fix(mobile): PlannerBase argument checks, plot without side effects, and <thing>_style arguments #778 itself).

PRMPlanner

• plot printed "plotted background" and "plotted roadmap" (entry 27) and returned None; it now returns the axes. vertex=/edge= become vertex_style=/edge_style=, defaults VERTEX_STYLE/EDGE_STYLE, old names deprecated (the book's fig5_19.py and fig5_20.py use them).
• plan(animate=...) was accepted and did nothing (deprecated).
• query required start and goal, and inserted the arguments as given rather than the validated start and goal; both are now optional and default to the constructor's.
• Unused attributes removed; the class docstring described a distance transform planner.

QuinticPolyPlanner

• goal_vel and goal_acc were ignored: the start values were passed as the goal (entry 28). The book does not use this planner.
• When no path time met the acceleration and jerk limits it silently returned the last candidate, which violates them; it is now a RuntimeError.
• It printed "find path!!", and start/goal were kept as given (a tuple), not as arrays (entry 29).

CurvaturePolyPlanner

• It printed the optimizer result on every query, its example imported DubinsPlanner and then used CurvaturePolyPlanner (a NameError in the docs build), and solvepath had a mutable default argument.

Test changes

tests/test_prm_constructor.py asserted the private call _create_roadmap(npoints, thresh, None), including the dead animate argument; it now asserts (npoints, thresh).

Each roadmap connection is one edge, not two

_create_roadmap visited every ordered pair of vertices, so each connection was added from both of its ends. pgraph's UGraph is a multigraph and does not de-duplicate, so the roadmap held two parallel edges per connection:

• the edge count was doubled (the book's 10,000 edges is 5,000 connections);
• current pgraph draws parallel edges as two arcs (curvature +/-0.175), where older pgraph overlaid them, so a regenerated roadmap looked like lenses rather than straight lines.

Each unordered pair is now considered once. Measured on the house floorplan, seed=0:

	before	after
50 points	222 edges, 12 components	111 edges, 12 components
300 points	10,000 edges, 13 components	5,000 edges, 13 components
query br3 -> kitchen, br2 -> kitchen		identical path arrays
drawn with current pgraph	arcs	straight lines, as in the book

The two printed edge counts in the book's notebook change (erratum, petercorke/RVC3-python#55).

Not changed, noted

• PRMPlanner._test_path samples round(length) points along an edge, so an edge shorter than half a cell is not tested at all. A denser test is not "more correct": three plausible tests (the current one, both ends plus a point per cell, and the grid cells along the segment) disagree on at most 16 of 13,640 candidate connections, and none is exact. Left as it is.
• CurvaturePolyPlanner does not check whether the optimizer succeeded. On the book's cases it does (end error 1e-4 to 4e-3). A warning is proposed separately.

Full suite 1106 passed (both compiled extensions, pinned SMTB), mypy clean.

🤖 Generated with Claude Code

[codacy-production]

Not up to standards ⛔

🔴 Issues 3 high

Alerts:
⚠ 3 issues (≤ 0 issues of at least minor severity)

Results:
3 new issues

Category	Results
ErrorProne	2 high
Security	1 high

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🟢 Metrics 58 complexity · 0 duplication

Metric	Results
Complexity	58
Duplication	0

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[codecov]

Codecov Report

❌ Patch coverage is 0% with 75 lines in your changes missing coverage. Please review.
✅ Project coverage is 0.00%. Comparing base (44ce707) to head (9a97583).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/roboticstoolbox/mobile/PRMPlanner.py	0.00%	37 Missing ⚠️
...roboticstoolbox/mobile/DistanceTransformPlanner.py	0.00%	25 Missing ⚠️
src/roboticstoolbox/mobile/QuinticPolyPlanner.py	0.00%	9 Missing ⚠️
src/roboticstoolbox/mobile/CurvaturePolyPlanner.py	0.00%	4 Missing ⚠️

Additional details and impacted files

@@          Coverage Diff          @@
##            main    #781   +/-   ##
=====================================
  Coverage   0.00%   0.00%           
=====================================
  Files        144     144           
  Lines      14733   14746   +13     
=====================================
- Misses     14733   14746   +13     

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