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# RM75 双臂 J3 参考角仿真标定实施计划
> **For agentic workers:** REQUIRED SUB-SKILL: Use superpowers:subagent-driven-development (recommended) or superpowers:executing-plans to implement this plan task-by-task. Steps use checkbox (`- [ ]`) syntax for tracking.
**Goal:** 使用当前双臂 URDF、Placo QP 和 MuJoCo 运动学模型运行可复现的左右臂 J3 参考角粗扫与细扫,并输出评分、稳定区间和推荐角度。
**Architecture:** 新增一个仅供离线实验使用的脚本,负责生成 18 条严格六维 TCP 轨迹、建立三类 QP 试验配置、运行候选角度扫描、计算硬门槛与并列评分,并生成 CSV/JSON/Markdown 结果。生产控制器、QP 求解器和 YAML 均不修改;测试只覆盖轨迹、评分和一个真实 Placo/MuJoCo 冒烟评估。
**Tech Stack:** Python 3.10、NumPy、Placo 0.9.4、MuJoCo 3.10、pytest、ROS2 Humble 工作空间。
---
## 文件结构
- 新增 `xr_rm_teleop/test/j3_reference_calibration.py`:离线轨迹生成、QP/MuJoCo 评估、评分、结果输出和命令行入口。
- 新增 `xr_rm_teleop/test/test_j3_reference_calibration.py`:轨迹端点、严格姿态插值、百分位评分、平台选择和真实模型冒烟测试。
- 生成 `docs/superpowers/results/2026-08-12-rm75-j3-calibration/summary.csv`:候选角度汇总。
- 生成 `docs/superpowers/results/2026-08-12-rm75-j3-calibration/trajectories.csv`:逐轨迹指标。
- 生成 `docs/superpowers/results/2026-08-12-rm75-j3-calibration/result.json`:机器可读结果。
- 生成 `docs/superpowers/results/2026-08-12-rm75-j3-calibration/report.md`:左右臂推荐角度、平台区间、基线对比和最差轨迹。
### Task 1:用失败测试固定轨迹与评分行为
**Files:**
- Create: `xr_rm_teleop/test/test_j3_reference_calibration.py`
- Create: `xr_rm_teleop/test/j3_reference_calibration.py`
- [ ] **Step 1:写轨迹生成失败测试**
测试使用以下公开接口:
```python
def build_task_trajectories(
initial_world_pose: np.ndarray,
control_rate_hz: float = 90.0,
max_linear_speed: float = 0.15,
max_angular_speed: float = 0.5,
) -> list[Trajectory]:
...
```
断言:
```python
def test_build_task_trajectories_creates_nine_strict_6d_routes() -> None:
initial = np.eye(4)
initial[:3, 3] = [0.35, 0.20, 0.10]
trajectories = build_task_trajectories(initial)
assert len(trajectories) == 9
assert {(route.harvest_y, route.harvest_z) for route in trajectories} == {
(y, z)
for y in (0.30, 0.40, 0.50)
for z in (-0.30, -0.20, -0.10)
}
for route in trajectories:
assert np.allclose(route.poses[0], initial)
assert np.allclose(route.poses[-1], initial)
basket = route.waypoints[5]
assert basket[0, 3] == pytest.approx(initial[0, 3])
assert basket[1, 3] == pytest.approx(initial[1, 3])
assert basket[2, 3] == pytest.approx(initial[2, 3] - 0.40)
assert basket[:3, 2] == pytest.approx([0.0, 0.0, -1.0], abs=1e-6)
```
- [ ] **Step 2:写评分和平台选择失败测试**
公开接口:
```python
def rank_candidates(rows: list[CandidateMetrics]) -> list[CandidateMetrics]:
...
def choose_stable_platform(
ranked: list[CandidateMetrics],
scan_step_deg: float,
) -> tuple[float, tuple[float, float]]:
...
```
测试构造三个硬门槛相同的候选,断言评分严格等于:
```python
score = (
0.45 * r_sigma
+ 0.20 * r_q4
+ 0.20 * r_elbow
+ 0.10 * r_smooth
+ 0.05 * r_track
)
```
并断言连续候选均达到最高分的 98% 时返回平台中点,而不是孤立端点。
- [ ] **Step 3:运行测试并确认按预期失败**
Run:
```bash
source /opt/ros/humble/setup.bash
/home/robot/miniconda3/envs/xr/bin/python -m pytest \
src/xr_rm_teleop/test/test_j3_reference_calibration.py -q
```
Expected: FAIL,原因是 `j3_reference_calibration` 或公开函数尚不存在。
### Task 2:实现最小轨迹与评分模块
**Files:**
- Create: `xr_rm_teleop/test/j3_reference_calibration.py`
- Test: `xr_rm_teleop/test/test_j3_reference_calibration.py`
- [ ] **Step 1:实现旋转和 SE(3) 插值**
只使用 NumPy 和标准库:
```python
def rotation_angle(rotation: np.ndarray) -> float:
cosine = np.clip((np.trace(rotation) - 1.0) * 0.5, -1.0, 1.0)
return float(math.acos(cosine))
def rotation_vector(rotation: np.ndarray) -> np.ndarray:
angle = rotation_angle(rotation)
if angle <= 1e-12:
return np.zeros(3)
axis = np.array([
rotation[2, 1] - rotation[1, 2],
rotation[0, 2] - rotation[2, 0],
rotation[1, 0] - rotation[0, 1],
]) / (2.0 * math.sin(angle))
return axis * angle
def interpolate_pose(start: np.ndarray, end: np.ndarray, count: int) -> list[np.ndarray]:
relative = end[:3, :3] @ start[:3, :3].T
vector = rotation_vector(relative)
return [
make_pose(
start[:3, 3] + alpha * (end[:3, 3] - start[:3, 3]),
so3_exp(alpha * vector) @ start[:3, :3],
)
for alpha in np.linspace(0.0, 1.0, count + 1)[1:]
]
```
`rotation_vector` 对接近 180° 的情况使用特征向量兜底,避免工具朝下转换产生除零。
- [ ] **Step 2:实现九条本侧完整轨迹**
定义不可变数据类:
```python
@dataclass(frozen=True)
class Trajectory:
name: str
harvest_y: float
harvest_z: float
waypoints: tuple[np.ndarray, ...]
poses: tuple[np.ndarray, ...]
```
航点固定为:初始、预接近、采摘、预接近、筐上方、筐内、筐上方、初始。每段点数为:
```python
duration = max(
translation_distance / max_linear_speed,
rotation_distance / max_angular_speed,
)
steps = max(1, math.ceil(duration * control_rate_hz))
```
- [ ] **Step 3:实现百分位排名和并列评分**
同值获得同一百分位,单一取值获得 1.0。平滑性和跟踪排名分别定义为:
```python
r_smooth = 0.5 * rank_low(motion_cost) + 0.5 * rank_low(max_joint_speed)
r_track = 0.5 * rank_low(max_position_error) + 0.5 * rank_low(max_orientation_error)
```
硬门槛按 `(N_fail, -N_complete)` 字典序先筛选;只有满足位置误差、姿态误差、J4、
关节限位、速度和跳变条件的候选进入综合评分。
- [ ] **Step 4:运行测试确认通过**
Run:
```bash
source /opt/ros/humble/setup.bash
/home/robot/miniconda3/envs/xr/bin/python -m pytest \
src/xr_rm_teleop/test/test_j3_reference_calibration.py -q
```
Expected: 轨迹与评分测试 PASS。
### Task 3:用失败测试固定真实 Placo/MuJoCo 单轨迹评估
**Files:**
- Modify: `xr_rm_teleop/test/test_j3_reference_calibration.py`
- Modify: `xr_rm_teleop/test/j3_reference_calibration.py`
- [ ] **Step 1:写真实模型冒烟失败测试**
接口:
```python
def evaluate_trajectory(
arm: str,
trajectory: Trajectory,
variant: Variant,
urdf_path: Path,
initial_joint_degrees: tuple[float, ...],
) -> TrajectoryMetrics:
...
```
使用左臂从初始 TCP 沿公共 `+Y` 移动 1 mm 的两点轨迹,断言:
```python
assert metrics.cycles == 2
assert metrics.failures == 0
assert math.isfinite(metrics.min_sigma)
assert metrics.min_q4_margin_deg > 0.0
assert metrics.max_position_error_m <= 2e-3
assert metrics.max_orientation_error_rad <= 5e-3
```
测试还将求得的七关节状态写入 `DualArmKinematicModel` 并断言按名称读回一致。
- [ ] **Step 2:运行冒烟测试并确认按预期失败**
Run:
```bash
source /opt/ros/humble/setup.bash
PYTHONPATH=src/xr_rm_teleop:src/xr_rm_mujoco \
/home/robot/miniconda3/envs/xr/bin/python -m pytest \
src/xr_rm_teleop/test/test_j3_reference_calibration.py::test_evaluate_trajectory_uses_real_placo_and_mujoco -q
```
Expected: FAIL,原因是评估器尚未实现。
- [ ] **Step 3:实现三类 QP 变体**
```python
@dataclass(frozen=True)
class Variant:
name: str
q3_reference_deg: float | None
enable_manipulability: bool
q4_min_deg: float | None
```
- `original`:三个可选项均关闭;
- `manip_j4`:位置可操作度权重 `1e-4`J4 硬下限 10°;
- `q3_<angle>`:在 `manip_j4` 基础上加入 J3 软任务,权重 `1e-5`
J4 约束使用 Placo 0.9.4 的 `add_joint_space_half_spaces_constraint(A, b)`,构造
`-q4 <= -q4_min`。J3 使用 `add_joints_task()`;位置可操作度使用
`add_manipulability_task(tcp_frame, "position", 1.0)`
- [ ] **Step 4:实现逐周期评估与失败保持**
每个目标点前将上一有效关节状态同步给 Placo。求解失败时:
```python
failures += 1
solver.update_joint_state(last_valid_joints)
current_joints = last_valid_joints.copy()
```
不把失败后的 Placo 内部迭代状态带到下一周期。成功状态写入 MuJoCo,并记录六维
雅可比最小奇异值、J4 余量、肘部外展量、TCP 误差、关节速度和运动代价。
- [ ] **Step 5:运行全部标定脚本测试**
Run:
```bash
source /opt/ros/humble/setup.bash
PYTHONPATH=src/xr_rm_teleop:src/xr_rm_mujoco \
/home/robot/miniconda3/envs/xr/bin/python -m pytest \
src/xr_rm_teleop/test/test_j3_reference_calibration.py -q
```
Expected: 全部 PASS。
### Task 4:运行粗扫、细扫并生成结果
**Files:**
- Modify: `xr_rm_teleop/test/j3_reference_calibration.py`
- Generate: `docs/superpowers/results/2026-08-12-rm75-j3-calibration/*`
- [ ] **Step 1:实现命令行和结果输出**
命令行:
```bash
python j3_reference_calibration.py \
--urdf <path> \
--config <dual_arm_rm75.yaml> \
--output-dir <directory> \
--phase coarse|fine|all
```
粗扫结束后对每侧选择最高分候选,在其 ±10°、原扫描边界内以 2° 细扫。CSV 使用
`csv.DictWriter`JSON 使用 `json.dump`,Markdown 报告由同一汇总对象生成,不新增依赖。
- [ ] **Step 2:运行完整仿真标定**
Run:
```bash
cd /home/robot/WS_xr
source /opt/ros/humble/setup.bash
PYTHONPATH=src/xr_rm_teleop:src/xr_rm_mujoco \
/home/robot/miniconda3/envs/xr/bin/python \
src/xr_rm_teleop/test/j3_reference_calibration.py \
--urdf src/xr_rm_teleop/models/dual_rm75/Dual_arm.urdf \
--config src/xr_rm_bringup/config/dual_arm_rm75.yaml \
--output-dir src/docs/superpowers/results/2026-08-12-rm75-j3-calibration \
--phase all
```
Expected: 左右臂粗扫和细扫完成;输出两个基线、全部候选、推荐角度和平台区间。
- [ ] **Step 3:检查结果完整性**
Run:
```bash
/home/robot/miniconda3/envs/xr/bin/python - <<'PY'
import json
from pathlib import Path
path = Path('src/docs/superpowers/results/2026-08-12-rm75-j3-calibration/result.json')
data = json.loads(path.read_text(encoding='utf-8'))
assert set(data['arms']) == {'left', 'right'}
for arm in data['arms'].values():
assert arm['coarse_candidates']
assert arm['fine_candidates']
assert arm['recommended_reference_deg'] is not None
assert len(arm['stable_interval_deg']) == 2
print('result integrity: OK')
PY
```
Expected: `result integrity: OK`
### Task 5:工作空间验证与结果复核
**Files:**
- Verify only.
- [ ] **Step 1:运行新增测试和相关现有测试**
Run:
```bash
cd /home/robot/WS_xr
source /opt/ros/humble/setup.bash
PYTHONPATH=src/xr_rm_teleop:src/xr_rm_mujoco \
/home/robot/miniconda3/envs/xr/bin/python -m pytest \
src/xr_rm_teleop/test/test_j3_reference_calibration.py \
src/xr_rm_teleop/test/test_placo_transforms.py \
src/xr_rm_mujoco/test/test_dual_arm_simulator.py -q
```
Expected: 全部 PASS。
- [ ] **Step 2:按项目规则构建工作空间**
Run:
```bash
cd /home/robot/WS_xr
source /opt/ros/humble/setup.bash
colcon build --symlink-install
```
Expected: 相关 ROS2 包构建成功。
- [ ] **Step 3:运行姿态控制回归测试**
Run:
```bash
cd /home/robot/WS_xr
source /opt/ros/humble/setup.bash
pytest src/xr_rm_teleop/test/test_orientation_control.py -q
```
Expected: 全部 PASS。
- [ ] **Step 4:人工复核结果报告**
确认:
- 每侧确有 9 条完整轨迹;
- `original``manip_j4` 和 J3 候选均存在;
- 推荐角来自硬门槛通过集合;
- 平台选择符合 98% 规则;
- 报告明确列出失败轨迹,且没有把失败更多的候选排到前面;
- 没有修改生产控制器和 YAML。