## Summary
Creatures (pets following, monsters chasing, NPCs approaching) would **oscillate — "pace back and forth really fast"** at concave obstacles (reported at the Britain Inn L-desk: a pet at `(1493,1614,20)` never reaching its master at `(1494,1605,21)`) instead of routing around them.
**Root cause** (the A* pathfinder itself was correct): all goal-seeking funnels through `MoveTo` and `WalkMobileRange` → `MoveTowardsOrAwayFrom`, which step greedily via `DoMove(dir, badStateOk:true)`. `DoMove` returns `true` even when the direct step was blocked and the creature merely **auto-turned and sidestepped** (`MoveResult.SuccessAutoTurn`), and the caller then set `Path = null`, discarding the `PathFollower`. So at a concave obstacle a non-progressing sidestep was mistaken for progress and the creature never committed to a route. (AOS pet-follow runs at `CurrentSpeed = 0.1`, hence the "really fast" shuffle.)
## What changed
- **New centralized `BaseAI.ApproachTarget(target, run, range)` primitive.** A greedy step is committed only when it **fully succeeds (`MoveResult.Success`) and actually gets closer**; otherwise the creature commits to a **persistent `PathFollower`** that routes around the obstacle and is never discarded by a greedy step. The open-terrain fast path (one greedy step, no pathfinding) is preserved. `MoveTo`, `MoveTowardsOrAwayFrom`, and `MoveToWithCollisionAvoidance` all delegate to it — public signatures unchanged, so no AI-class call site changes.
- **Best-distance give-up + idle.** A creature that cannot reach a **stationary** in-range goal stops shuffling and idles after `ApproachGiveUpTicks` (40) ticks without lowering its closest-ever distance; a **moving** goal (active chase) never gives up. It resumes the moment the goal moves.
- **Pathfinder fix (required):** `BitmapAStarAlgorithm.IsBlockedByDynamic` now skips the dynamic mobile-block check **at the goal cell only** (`MoveImpl.Goal`). Previously A* returned `null` whenever the target mobile stood on the goal cell, so creatures could never pathfind *toward* another mobile — only toward empty ground. The follower stops within `range` short of it. Static/item blocking and all non-goal mobile blocking are unchanged.
## Tests
New AI-loop integration tests in `ApproachTargetTests.cs` drive the real `BaseAI` primitives against live Britain Inn map statics: exact-repro pet follow, open-terrain (asserts zero pathfinding), `MoveTo` chase (static + walking-away target), route-around-a-dynamic-wall, and walled-off give-up-and-idle.
- Pathfinding + AI subset: **52/52** pass.
- Full `UOContent.Tests`: **301/301** pass. (Note: the test host lingers on shutdown — a pre-existing infra quirk unrelated to this change; all tests complete and pass.)
- Full solution build: clean (0 warnings / 0 errors).
## Notes
- Branched off `main`; independent of the in-flight step-cache work.
- Out of scope (future work): proactive "SmartAI" look-ahead pathfinding so clever creatures plan a route before walking into the obstacle, rather than reacting after they hit it.
## Test Plan
- [X] In-game: order a pet to `follow`/`come` across the Britain Inn L-desk; confirm it routes around and reaches you instead of pacing.
- [X] Aggro a monster and kite it around a building/treeline; confirm it chases around obstacles.
- [X] Confirm open-terrain following/chasing feels unchanged (no extra latency).
- [X] Confirm a creature with a genuinely unreachable target idles rather than shuffling forever.
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