fix: FK/IK geometry, build/consume path and simulator physics; correct docs and roadmap specs

.github/agents/algo-implementer.agent.md

@@ -8,6 +8,8 @@ handoffs:
     prompt: "Review the deployed algorithm against AGENTS.md: float-only, no heap, tests, doc, CMake wiring."
 ---
 
+# Algorithm Implementer
+
 You deploy ONE algorithm at a time from its `roadmap/<domain>/<Name>/` spec into the codebase.
 Authoritative rules: `AGENTS.md`. Recipe: `roadmap/DEPLOYMENT.md`. Follow both exactly.
 

.github/agents/executor.agent.md

@@ -8,6 +8,8 @@ handoffs:
     prompt: "Review the implementation changes made above against robotics-toolbox project standards."
 ---
 
+# Executor
+
 Canonical rules: `AGENTS.md`. Implement exactly what's asked — nothing more.
 
 ## Workflow

.github/agents/modernizer.agent.md

@@ -8,6 +8,8 @@ handoffs:
     prompt: "Review the refactoring changes made above against robotics-toolbox project standards."
 ---
 
+# Modernizer
+
 Canonical rules: `AGENTS.md`. You modernize ONE pre-roadmap algorithm at a time so it matches
 current roadmap conventions. Refactor is **behavior-preserving** — no new features, no public-API
 change unless required to remove duplication.
@@ -39,15 +41,12 @@ The `test/Test*.cpp` is a first-class deliverable of every modernization. Audit
 - [ ] `EXPECT_NEAR` + `math::Tolerance<float>()` for float comparisons.
 - [ ] Anonymous-namespace fixture; macros outside; no heap; no comments.
 
-Keep `TYPED_TEST` where the algorithm is multi-type; behavior and assertions stay identical.
+Behavior and assertions stay identical when restructuring a test.
 
 ## Preserve types — hard rule
 
-Keep existing `Q15`/`Q31` support and its `TYPED_TEST` where the algorithm already has it — do
-**NOT** strip multi-type. The multi-type guard
-(`static_assert(math::is_qnumber<T>::value || std::is_floating_point_v<T>, ...)`) stays for those.
-Float-only migration applies ONLY to algorithms that are already float-only; those follow
-`static_assert(std::is_floating_point_v<T>)` + `TEST_F` on `float`.
+Every algorithm in this repository is float-only: `static_assert(std::is_floating_point_v<T>)` +
+`TEST_F` on `float`. Do not introduce `Q15`/`Q31` or `TYPED_TEST` while modernizing.
 
 ## Memory — quick reference
 

.github/agents/orchestrator.agent.md

@@ -18,6 +18,8 @@ handoffs:
     prompt: "Refactor the pre-roadmap algorithm described above to reuse shared utilities and simplify tests, following robotics-toolbox conventions."
 ---
 
+# Orchestrator
+
 Triage requests and route to the right specialist. Do NOT implement or plan yourself.
 
 ## Workflow

.github/agents/planner.agent.md

@@ -8,6 +8,8 @@ handoffs:
     prompt: "Implement the plan outlined above, following all project conventions strictly."
 ---
 
+# Planner
+
 Canonical rules: `AGENTS.md`. Produce plans only — no code edits.
 
 ## Workflow

.github/agents/reviewer.agent.md

@@ -11,6 +11,8 @@ handoffs:
     prompt: "Revise the implementation plan based on the review feedback above."
 ---
 
+# Reviewer
+
 Canonical rules: `AGENTS.md`. Review only — no file modifications.
 
 ## Workflow

.github/agents/unit-tester.agent.md

@@ -8,6 +8,8 @@ handoffs:
     prompt: "Review the authored unit tests against AGENTS.md, testing.instructions.md, and TESTING.md: TEST_F on float, StrictMock only, no heap, one behaviour per test, independent reference values, no redundant cases, CMake wiring, tests green."
 ---
 
+# Unit Tester
+
 You add or extend the unit tests for ONE algorithm at a time in
 `robotics/<domain>/test/Test<Name>.cpp`. Authoritative rules: `AGENTS.md`. Testing rules:
 `.github/instructions/testing.instructions.md`. Metric families per algorithm:

.github/instructions/robotics-cpp.instructions.md

@@ -67,6 +67,8 @@ Apply `OPTIMIZE_FOR_SPEED` (from `numerical/math/CompilerOptimizations.hpp`) on
 
 ## Documentation — MANDATORY
 
-For every algorithm added or modified, update the corresponding `doc/{domain}/{AlgorithmName}.md` file. Follow `doc/TEMPLATE.md` exactly. Documentation is **design-first**: cover mathematical background, algorithm behaviour, complexity, pitfalls, and connections. Do **not** include implementation details, class names, template parameters, or usage code examples — docs describe the algorithm design; code follows from it.
+For every algorithm added or modified, update the corresponding `doc/{domain}/{AlgorithmName}.md` file. Follow `doc/TEMPLATE.md` exactly.
+Documentation is **design-first**: cover mathematical background, algorithm behaviour, complexity, pitfalls, and connections.
+Do **not** include implementation details, class names, template parameters, or usage code examples — docs describe the algorithm design; code follows from it.
 
 Canonical rules: [AGENTS.md](../../AGENTS.md).

.github/instructions/testing.instructions.md

@@ -20,21 +20,23 @@ applyTo: "**/test/**"
 ## Fixture Test Pattern (float)
 
 ```cpp
-#include "numerical/solvers/DiscreteAlgebraicRiccatiEquation.hpp"
+#include "robotics/kinematics/ForwardKinematics.hpp"
+#include "numerical/math/Tolerance.hpp"
 #include <gtest/gtest.h>
 
 namespace
 {
-    class TestDare : public ::testing::Test
+    class TestForwardKinematics
+        : public ::testing::Test
     {
     protected:
-        solvers::DiscreteAlgebraicRiccatiEquation<float, 2, 1> solver;
+        kinematics::ForwardKinematics<float, 2> fk{ math::Vector<float, 3>{ 0.8f, 0.0f, 0.0f } };
     };
 }
 
-TEST_F(TestDare, solves_simple_system)
+TEST_F(TestForwardKinematics, elbow_at_ninety_degrees_places_tool_above_elbow)
 {
-    // Arrange, Act, Assert
+    // Arrange, Act, Assert — EXPECT_NEAR(actual, expected, math::Tolerance<float>())
 }
 ```
 

.github/prompts/orchestrate.prompt.md

@@ -5,7 +5,11 @@ argument-hint: "Describe the algorithm, feature, bug fix, or change you want to
 model: "Claude Sonnet 4.6"
 ---
 
-Analyze the following task for the **robotics-toolbox** project — a robot-manipulator algorithms library (kinematics, dynamics, trajectories, and manipulator control) targeting resource-constrained embedded systems, consuming shared numerical primitives from numerical-toolbox-cpp via FetchContent. Gather relevant context from the codebase — identify affected modules, existing patterns, the float-only numeric policy, and documentation requirements. Then provide a brief scope summary and use the handoff buttons to route to the appropriate specialist:
+# Orchestrate
+
+Analyze the following task for the **robotics-toolbox** project — a robot-manipulator algorithms library (kinematics, dynamics, trajectories, and manipulator control) targeting resource-constrained embedded systems, consuming shared numerical primitives from numerical-toolbox-cpp via FetchContent.
+Gather relevant context from the codebase — identify affected modules, existing patterns, the float-only numeric policy, and documentation requirements.
+Then provide a brief scope summary and use the handoff buttons to route to the appropriate specialist:
 
 - **Plan Implementation**: For complex tasks needing detailed upfront design (new algorithms, architectural changes, multi-file modifications)
 - **Execute Directly**: For straightforward changes with a clear path (bug fixes, small improvements)

.github/prompts/unit-test.prompt.md

@@ -5,6 +5,8 @@ argument-hint: "Name the robotics/ algorithm to author unit tests for (e.g. Biqu
 model: "Claude Sonnet 5"
 ---
 
+# Unit Test
+
 Author (or extend) the unit tests for the named **robotics-toolbox** algorithm in
 `robotics/<domain>/test/Test<Name>.cpp`. Follow the `unit-tester` workflow: read the algorithm's
 public interface and doc; look up its family in `TESTING.md` and select the metric

.github/workflows/ci.yml

@@ -59,34 +59,57 @@ jobs:
           name: test-logs
           path: build/host/Testing/Temporary/
   host_build_test:
-    name: Host Build & Test
+    name: Host Build & Test (${{ matrix.os }})
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        os: [macos-latest, windows-latest]
+        include:
+          - os: macos-latest
+            cache-variant: ccache
+            cmake-args: "['-DCMAKE_C_COMPILER_LAUNCHER=ccache', '-DCMAKE_CXX_COMPILER_LAUNCHER=ccache']"
+          # The Visual Studio generator ignores compiler launchers; sccache cannot cache /Zi, so debug info is embedded (/Z7).
+          # CC/CXX make run-cmake skip its vcpkg-based MSVC setup; msvc-dev-cmd already did it.
+          - os: windows-latest
+            cache-variant: sccache
+            cmake-args: "['-GNinja', '-DCMAKE_C_COMPILER_LAUNCHER=sccache', '-DCMAKE_CXX_COMPILER_LAUNCHER=sccache', '-DCMAKE_POLICY_DEFAULT_CMP0141=NEW', '-DCMAKE_MSVC_DEBUG_INFORMATION_FORMAT=Embedded']"
+            cc: cl
+      fail-fast: false
     steps:
       - name: Configure Git
+        shell: bash
         run: |
           git config --global url."https://${{ secrets.PRIVATE_REPO_TOKEN }}@github.com/".insteadOf "https://github.com/"
           git config --global url."https://github.com/".insteadOf "git@github.com:"
           git config --global --add safe.directory '*'
       - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7.0.1
         with:
           persist-credentials: false
+      - if: ${{ runner.os == 'Windows' }}
+        uses: ilammy/msvc-dev-cmd@0b201ec74fa43914dc39ae48a89fd1d8cb592756 # v1.13.0
+      - if: ${{ runner.os == 'Windows' }}
+        uses: seanmiddleditch/gha-setup-ninja@3b1f8f94a2f8254bd26914c4ab9474d4f0015f67 # v6
       - uses: hendrikmuhs/ccache-action@f09c25b45002a07be2955cbe52e8cee55643f89d # v1.2.24
         with:
+          variant: ${{ matrix.cache-variant }}
           key: ${{ github.job }}-${{ matrix.os }}
           max-size: 2G
           save: ${{ github.ref == 'refs/heads/main' }}
       - uses: lukka/run-cmake@5d55ea7949e25f69f0ecb516d8d572297e03a956 # v10.9
+        env:
+          CC: ${{ matrix.cc }}
+          CXX: ${{ matrix.cc }}
         with:
           configurePreset: "host-single-Debug"
           buildPreset: "host-single-Debug"
           testPreset: "host-single-Debug"
-          configurePresetAdditionalArgs: "['-DCMAKE_C_COMPILER_LAUNCHER=ccache', '-DCMAKE_CXX_COMPILER_LAUNCHER=ccache']"
+          configurePresetAdditionalArgs: ${{ matrix.cmake-args }}
+      - name: Re-run failed tests
+        if: ${{ failure() }}
+        run: ctest --preset host-single-Debug --rerun-failed --output-on-failure
+        continue-on-error: true
       - name: Upload test logs
         if: ${{ failure() }}
         uses: actions/upload-artifact@043fb46d1a93c77aae656e7c1c64a875d1fc6a0a # v7.0.1
         with:
-          name: test-logs
-          path: build/host/Testing/Temporary/
+          name: test-logs-${{ matrix.os }}
+          path: build/host-single-Debug/Testing/Temporary/