474 lines
18 KiB
Python
474 lines
18 KiB
Python
"""Joint extrinsic refinement: Phase-A rotation factors + Phase-C SE(3) IMU factors."""
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from __future__ import annotations
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from dataclasses import dataclass
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import numpy as np
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from scipy.optimize import least_squares
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from .contracts import ImuSeries, MotionPair
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from .geometry import make_transform, orthonormalize_rotation, so3_exp, so3_log
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from .imu_preintegration import (
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apply_bias_jacobian_correction,
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apply_constant_bias_correction,
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preintegrate_gyro,
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preintegration_rotation_residual,
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residual_whiten_matrix,
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)
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from .observability import ObservabilityReport, analyze_observability
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G_NORM = 9.80665
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@dataclass(frozen=True)
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class JointExtrinsicResult:
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T_IMU_lidar: np.ndarray
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translation_accepted: bool
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residual_rms_rot_deg: float
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residual_rms_trans_m: float
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observability: ObservabilityReport
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gyro_bias_rad_s: np.ndarray | None = None
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accel_bias_m_s2: np.ndarray | None = None
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gravity_m_s2: np.ndarray | None = None
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notes: tuple[str, ...] = ()
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def _pair_weight(pair: MotionPair) -> float:
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weight = float(pair.metadata.get("weight", 1.0))
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if not np.isfinite(weight) or weight <= 0:
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return 1.0
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return weight
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def _pair_j_bg(pair: MotionPair) -> np.ndarray | None:
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raw = pair.metadata.get("J_bg")
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if raw is None:
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return None
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return np.asarray(raw, dtype=float).reshape(3, 3)
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def _pair_cov(pair: MotionPair) -> np.ndarray:
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raw = pair.metadata.get("cov")
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if raw is None:
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sigma = float(pair.metadata.get("preint_sigma_rad", 1e-2))
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return np.eye(3) * max(sigma, 1e-4) ** 2
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return np.asarray(raw, dtype=float).reshape(3, 3)
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def _corrected_delta_r(
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pair: MotionPair,
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delta_bias: np.ndarray,
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*,
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imu: ImuSeries | None,
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bias0: np.ndarray,
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) -> np.ndarray:
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j_bg = _pair_j_bg(pair)
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if j_bg is not None:
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return apply_bias_jacobian_correction(pair.R_A, j_bg, delta_bias)
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if imu is not None and "t_i_imu_s" in pair.metadata and "t_j_imu_s" in pair.metadata:
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preint = preintegrate_gyro(
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imu.t_s,
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imu.gyro_rad_s,
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float(pair.metadata["t_i_imu_s"]),
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float(pair.metadata["t_j_imu_s"]),
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bias0 + delta_bias,
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)
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return preint.delta_R
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duration = float(pair.metadata.get("duration_s", max(pair.t_j_s - pair.t_i_s, 1e-3)))
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return apply_constant_bias_correction(pair.R_A, duration, delta_bias)
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def _gravity_basis(g0: np.ndarray) -> np.ndarray:
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"""Return 3×2 orthonormal basis spanning the plane orthogonal to ``g0``."""
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g = np.asarray(g0, dtype=float).reshape(3)
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n = np.linalg.norm(g)
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if n < 1e-9:
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g = np.array([0.0, 0.0, -G_NORM])
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n = G_NORM
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g = g / n
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axis = np.array([1.0, 0.0, 0.0]) if abs(g[0]) < 0.9 else np.array([0.0, 1.0, 0.0])
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e1 = np.cross(g, axis)
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e1 /= max(np.linalg.norm(e1), 1e-12)
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e2 = np.cross(g, e1)
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return np.column_stack([e1, e2])
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def _gravity_from_params(xy: np.ndarray, g0: np.ndarray, basis: np.ndarray) -> np.ndarray:
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raw = np.asarray(g0, dtype=float).reshape(3) + basis @ np.asarray(xy, dtype=float).reshape(2)
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n = float(np.linalg.norm(raw))
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if n < 1e-9:
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return np.asarray(g0, dtype=float).reshape(3)
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return raw * (G_NORM / n)
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def _lidar_to_imu_relative(r_x: np.ndarray, t_x: np.ndarray, r_b: np.ndarray, t_b: np.ndarray):
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"""Map LiDAR relative pose to IMU: ``T_A = T_X T_B T_X^{-1}``."""
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r_a = orthonormalize_rotation(r_x @ r_b @ r_x.T)
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t_a = (np.eye(3) - r_a) @ t_x + r_x @ t_b
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return r_a, t_a
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def _corrected_preint_quantities(
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pair: MotionPair,
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bg_i: np.ndarray,
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ba_i: np.ndarray,
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bg0: np.ndarray,
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ba0: np.ndarray,
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) -> tuple[np.ndarray, np.ndarray, np.ndarray]:
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"""First-order correct ΔR/Δv/Δp for keyframe biases vs preintegration biases."""
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dbg = np.asarray(bg_i, dtype=float).reshape(3) - np.asarray(bg0, dtype=float).reshape(3)
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dba = np.asarray(ba_i, dtype=float).reshape(3) - np.asarray(ba0, dtype=float).reshape(3)
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j_bg = pair.metadata.get("J_bg9")
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j_ba = pair.metadata.get("J_ba")
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delta_v0 = np.asarray(pair.metadata.get("delta_v", [0.0, 0.0, 0.0]), dtype=float).reshape(3)
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delta_p0 = (
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np.asarray(pair.t_A_m, dtype=float).reshape(3)
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if pair.t_A_m is not None
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else np.asarray(pair.metadata.get("delta_p", [0.0, 0.0, 0.0]), dtype=float).reshape(3)
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)
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if j_bg is None or j_ba is None:
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delta_r = apply_bias_jacobian_correction(
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pair.R_A,
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_pair_j_bg(pair) if _pair_j_bg(pair) is not None else np.zeros((3, 3)),
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dbg,
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)
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return delta_r, delta_v0, delta_p0
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j_bg_m = np.asarray(j_bg, dtype=float).reshape(9, 3)
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j_ba_m = np.asarray(j_ba, dtype=float).reshape(9, 3)
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delta_r = orthonormalize_rotation(pair.R_A @ so3_exp(j_bg_m[0:3] @ dbg))
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delta_v = delta_v0 + j_bg_m[3:6] @ dbg + j_ba_m[3:6] @ dba
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delta_p = delta_p0 + j_bg_m[6:9] @ dbg + j_ba_m[6:9] @ dba
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return delta_r, delta_v, delta_p
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def _build_nav_rotations(
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keyframe_ids: list[int],
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id_to_idx: dict[int, int],
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consecutive_pairs: dict[tuple[int, int], MotionPair],
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r_x: np.ndarray,
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t_x: np.ndarray,
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) -> list[np.ndarray]:
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"""Chain IMU orientations in the first-keyframe nav frame using LiDAR+extrinsic."""
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rotations = [np.eye(3) for _ in keyframe_ids]
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for k in range(len(keyframe_ids) - 1):
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a = keyframe_ids[k]
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b = keyframe_ids[k + 1]
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pair = consecutive_pairs.get((a, b))
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if pair is None:
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rotations[k + 1] = rotations[k]
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continue
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t_b = np.zeros(3) if pair.t_B_m is None else np.asarray(pair.t_B_m, dtype=float)
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r_meas, _ = _lidar_to_imu_relative(r_x, t_x, pair.R_B, t_b)
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rotations[k + 1] = orthonormalize_rotation(rotations[k] @ r_meas)
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# Ensure list indexed by id_to_idx
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del id_to_idx
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return rotations
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def _solve_phase_c_se3(
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pairs: list[MotionPair],
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r_x: np.ndarray,
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*,
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gyro_bias0: np.ndarray,
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gravity_init: np.ndarray,
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sigma_bg_rw: float = 1.0e-5,
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sigma_ba_rw: float = 1.0e-3,
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) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray, np.ndarray, float, float, list[str]]:
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"""Keyframe IMU factor optimization for full SE(3)."""
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notes: list[str] = []
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usable = [pair for pair in pairs if pair.t_B_m is not None and "delta_v" in pair.metadata]
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if len(usable) < 3:
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notes.append("phase-C skipped: need pairs with full preintegration metadata")
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return r_x, np.zeros(3), gravity_init, gyro_bias0, np.zeros(3), 1e9, 1e9, notes
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# Unique keyframes sorted by IMU time.
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stamp: dict[int, float] = {}
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for pair in usable:
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stamp[pair.i] = float(pair.metadata.get("t_i_imu_s", pair.t_i_s))
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stamp[pair.j] = float(pair.metadata.get("t_j_imu_s", pair.t_j_s))
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keyframe_ids = sorted(stamp.keys(), key=lambda kid: stamp[kid])
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k_count = len(keyframe_ids)
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id_to_idx = {kid: idx for idx, kid in enumerate(keyframe_ids)}
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consecutive_pairs: dict[tuple[int, int], MotionPair] = {}
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for pair in usable:
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if id_to_idx[pair.j] == id_to_idx[pair.i] + 1:
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consecutive_pairs[(pair.i, pair.j)] = pair
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g0 = np.asarray(gravity_init, dtype=float).reshape(3)
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if np.linalg.norm(g0) < 1e-6:
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g0 = np.array([0.0, 0.0, -G_NORM])
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g0 = g0 * (G_NORM / max(np.linalg.norm(g0), 1e-9))
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basis = _gravity_basis(g0)
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ba0 = np.zeros(3)
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bg0 = np.asarray(gyro_bias0, dtype=float).reshape(3)
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# State: dθ(3), t(3), g_xy(2), v(3K), bg(3K), ba(3K)
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n_v = 3 * k_count
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n_b = 3 * k_count
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dim = 3 + 3 + 2 + n_v + n_b + n_b
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x0 = np.zeros(dim)
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# velocities start at 0; biases at prior
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for idx in range(k_count):
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x0[8 + n_v + 3 * idx : 8 + n_v + 3 * idx + 3] = bg0
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whitened = []
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for pair in usable:
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cov9 = pair.metadata.get("cov9")
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if cov9 is None:
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cov = _pair_cov(pair)
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cov9_m = np.eye(9)
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cov9_m[0:3, 0:3] = cov
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cov9_m[3:6, 3:6] = np.eye(3) * 0.25
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cov9_m[6:9, 6:9] = np.eye(3) * 1.0
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else:
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cov9_m = np.asarray(cov9, dtype=float).reshape(9, 9)
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whitened.append(residual_whiten_matrix(cov9_m))
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def unpack(vec: np.ndarray):
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r_opt = orthonormalize_rotation(so3_exp(vec[0:3]) @ r_x)
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t_opt = vec[3:6]
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g_opt = _gravity_from_params(vec[6:8], g0, basis)
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base = 8
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vels = vec[base : base + n_v].reshape(k_count, 3)
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base += n_v
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bgs = vec[base : base + n_b].reshape(k_count, 3)
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base += n_b
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bas = vec[base : base + n_b].reshape(k_count, 3)
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return r_opt, t_opt, g_opt, vels, bgs, bas
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def residuals(vec: np.ndarray) -> np.ndarray:
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r_opt, t_opt, g_opt, vels, bgs, bas = unpack(vec)
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nav_r = _build_nav_rotations(keyframe_ids, id_to_idx, consecutive_pairs, r_opt, t_opt)
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out: list[np.ndarray] = []
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for pair, whiten in zip(usable, whitened):
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i_idx = id_to_idx[pair.i]
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j_idx = id_to_idx[pair.j]
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dt = float(pair.metadata.get("duration_s", pair.t_j_s - pair.t_i_s))
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dt = max(dt, 1e-3)
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delta_r, delta_v, delta_p = _corrected_preint_quantities(
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pair, bgs[i_idx], bas[i_idx], bg0, ba0
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)
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t_b = np.asarray(pair.t_B_m, dtype=float).reshape(3)
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r_meas, t_meas = _lidar_to_imu_relative(r_opt, t_opt, pair.R_B, t_b)
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r_i = nav_r[i_idx]
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v_i = vels[i_idx]
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v_j = vels[j_idx]
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err_r = so3_log(delta_r.T @ r_meas)
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err_v = v_j - v_i - g_opt * dt - r_i @ delta_v
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err_p = r_i @ (t_meas - delta_p) - v_i * dt - 0.5 * g_opt * (dt**2)
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err = np.concatenate([err_r, err_v, err_p])
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w = np.sqrt(_pair_weight(pair))
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out.append(w * (whiten @ err))
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# Bias random-walk between consecutive keyframes.
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for k in range(k_count - 1):
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dt = max(stamp[keyframe_ids[k + 1]] - stamp[keyframe_ids[k]], 1e-3)
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scale_g = 1.0 / (max(sigma_bg_rw, 1e-8) * np.sqrt(dt))
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scale_a = 1.0 / (max(sigma_ba_rw, 1e-8) * np.sqrt(dt))
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out.append(scale_g * (bgs[k + 1] - bgs[k]))
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out.append(scale_a * (bas[k + 1] - bas[k]))
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# Weak priors: first-keyframe biases and translation magnitude.
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out.append(50.0 * (bgs[0] - bg0))
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out.append(20.0 * bas[0])
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out.append(0.2 * t_opt) # soft |t| prior ~ meters
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return np.concatenate(out)
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# Cap evaluations: Phase-C is high-dimensional; synthetic ICP already dominates runtime.
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opt = least_squares(residuals, x0, loss="huber", f_scale=0.05, max_nfev=80)
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r_opt, t_opt, g_opt, vels, bgs, bas = unpack(opt.x)
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rot_errs = []
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trans_errs = []
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nav_r = _build_nav_rotations(keyframe_ids, id_to_idx, consecutive_pairs, r_opt, t_opt)
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for pair in usable:
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i_idx = id_to_idx[pair.i]
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j_idx = id_to_idx[pair.j]
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dt = max(float(pair.metadata.get("duration_s", pair.t_j_s - pair.t_i_s)), 1e-3)
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delta_r, delta_v, delta_p = _corrected_preint_quantities(
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pair, bgs[i_idx], bas[i_idx], bg0, ba0
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)
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t_b = np.asarray(pair.t_B_m, dtype=float).reshape(3)
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r_meas, t_meas = _lidar_to_imu_relative(r_opt, t_opt, pair.R_B, t_b)
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r_i = nav_r[i_idx]
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err_r = so3_log(delta_r.T @ r_meas)
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err_p = r_i @ (t_meas - delta_p) - vels[i_idx] * dt - 0.5 * g_opt * (dt**2)
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rot_errs.append(np.degrees(np.linalg.norm(err_r)))
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trans_errs.append(float(np.linalg.norm(err_p)))
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del delta_v, j_idx
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rot_rms = float(np.sqrt(np.mean(np.square(rot_errs)))) if rot_errs else 1e9
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trans_rms = float(np.sqrt(np.mean(np.square(trans_errs)))) if trans_errs else 1e9
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bg_mean = np.mean(bgs, axis=0)
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ba_mean = np.mean(bas, axis=0)
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notes.append(
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"phase-C SE3 (Δv/Δp + g + keyframe v/bias RW): "
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f"keyframes={k_count}, pairs={len(usable)}, "
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f"|t|={float(np.linalg.norm(t_opt)):.3f} m, "
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f"|g|={float(np.linalg.norm(g_opt)):.3f}, "
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f"trans_rms={trans_rms:.3f} m"
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)
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return r_opt, t_opt, g_opt, bg_mean, ba_mean, rot_rms, trans_rms, notes
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def solve_joint_extrinsic(
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pairs: list[MotionPair] | tuple[MotionPair, ...],
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r_x: np.ndarray,
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*,
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force_rotation_only: bool = False,
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imu: ImuSeries | None = None,
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delta_t_s: float = 0.0,
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gyro_bias_rad_s: np.ndarray | None = None,
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gravity_init_m_s2: np.ndarray | None = None,
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bias_prior_sigma_rad_s: float = 0.02,
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enable_phase_c: bool | None = None,
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) -> JointExtrinsicResult:
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"""Refine extrinsic using Phase-A whitened rotation factors, optional Phase-C SE(3)."""
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del delta_t_s # reserved for future SE(3) time coupling
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if enable_phase_c is None:
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enable_phase_c = not force_rotation_only
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usable = [pair for pair in pairs if pair.t_B_m is not None]
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observability = analyze_observability(usable, r_x)
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notes = list(observability.notes)
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r = orthonormalize_rotation(np.asarray(r_x, dtype=float))
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bias0 = np.zeros(3) if gyro_bias_rad_s is None else np.asarray(gyro_bias_rad_s, dtype=float).reshape(3)
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weights = np.asarray([_pair_weight(pair) for pair in usable], dtype=float)
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whitens = [residual_whiten_matrix(_pair_cov(pair)) for pair in usable]
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prior_w = 1.0 / max(bias_prior_sigma_rad_s, 1e-4)
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def rotation_residuals(r_opt: np.ndarray, delta_bias: np.ndarray) -> np.ndarray:
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residuals = []
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for pair, weight, whiten in zip(usable, weights, whitens):
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delta_r = _corrected_delta_r(pair, delta_bias, imu=imu, bias0=bias0)
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err = preintegration_rotation_residual(delta_r, r_opt, pair.R_B)
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residuals.append(np.sqrt(weight) * (whiten @ err))
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residuals.append(prior_w * delta_bias)
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return np.concatenate(residuals) if residuals else np.zeros(0)
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def residual_rot_bias(vec: np.ndarray) -> np.ndarray:
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r_opt = orthonormalize_rotation(so3_exp(vec[:3]) @ r)
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return rotation_residuals(r_opt, vec[3:])
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if usable:
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opt = least_squares(
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residual_rot_bias,
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np.zeros(6),
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loss="huber",
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f_scale=np.deg2rad(1.0),
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max_nfev=200,
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)
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r = orthonormalize_rotation(so3_exp(opt.x[:3]) @ r)
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delta_bias = opt.x[3:]
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bias_out = bias0 + delta_bias
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notes.append(
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"phase-A joint refine (Σ-whitened + J_bg): "
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f"|δb|={float(np.linalg.norm(delta_bias)):.3e} rad/s, "
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f"weighted pairs={len(usable)}"
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)
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else:
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bias_out = bias0
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delta_bias = np.zeros(3)
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notes.append("no pairs for joint refine")
|
||
|
||
rot_errs = []
|
||
for pair in usable:
|
||
delta_r = _corrected_delta_r(pair, delta_bias, imu=imu, bias0=bias0)
|
||
err = preintegration_rotation_residual(delta_r, r, pair.R_B)
|
||
rot_errs.append(np.degrees(np.linalg.norm(err)))
|
||
rot_rms = float(np.sqrt(np.mean(np.square(rot_errs)))) if rot_errs else 1e9
|
||
|
||
t = np.zeros(3)
|
||
translation_accepted = False
|
||
trans_rms = 1e9
|
||
gravity_out: np.ndarray | None = None
|
||
accel_bias_out: np.ndarray | None = None
|
||
|
||
if gravity_init_m_s2 is None:
|
||
gravity_init = np.array([0.0, 0.0, -G_NORM])
|
||
else:
|
||
gravity_init = np.asarray(gravity_init_m_s2, dtype=float).reshape(3)
|
||
|
||
if (
|
||
enable_phase_c
|
||
and not force_rotation_only
|
||
and observability.translation_observable
|
||
and observability.rotation_observable
|
||
and len(usable) >= 5
|
||
):
|
||
r, t, gravity_out, bias_out, accel_bias_out, rot_rms, trans_rms, c_notes = _solve_phase_c_se3(
|
||
usable,
|
||
r,
|
||
gyro_bias0=bias_out,
|
||
gravity_init=gravity_init,
|
||
)
|
||
notes.extend(c_notes)
|
||
translation_accepted = bool(trans_rms < 0.75 and np.linalg.norm(t) > 1e-4)
|
||
if not translation_accepted:
|
||
notes.append("phase-C translation residual/gate failed; keeping translation at zero")
|
||
t = np.zeros(3)
|
||
elif (
|
||
not force_rotation_only
|
||
and observability.translation_observable
|
||
and observability.rotation_observable
|
||
and len(usable) >= 5
|
||
):
|
||
# Legacy hand-eye translation fallback when Phase-C metadata missing.
|
||
def residual_se3(vec: np.ndarray) -> np.ndarray:
|
||
r_opt = orthonormalize_rotation(so3_exp(vec[:3]) @ r)
|
||
t_opt = vec[3:]
|
||
residuals = []
|
||
for pair, weight, whiten in zip(usable, weights, whitens):
|
||
delta_r = _corrected_delta_r(pair, delta_bias, imu=imu, bias0=bias0)
|
||
residuals.append(
|
||
np.sqrt(weight) * (whiten @ preintegration_rotation_residual(delta_r, r_opt, pair.R_B))
|
||
)
|
||
pred = (pair.R_A - np.eye(3)) @ t_opt
|
||
meas = r_opt @ np.asarray(pair.t_B_m, dtype=float)
|
||
residuals.append(np.sqrt(weight) * (pred - meas))
|
||
return np.concatenate(residuals)
|
||
|
||
opt_t = least_squares(residual_se3, np.zeros(6), loss="huber", f_scale=0.05, max_nfev=200)
|
||
r = orthonormalize_rotation(so3_exp(opt_t.x[:3]) @ r)
|
||
t = opt_t.x[3:]
|
||
rot_errs = []
|
||
trans_errs = []
|
||
for pair in usable:
|
||
delta_r = _corrected_delta_r(pair, delta_bias, imu=imu, bias0=bias0)
|
||
rot_errs.append(np.degrees(np.linalg.norm(preintegration_rotation_residual(delta_r, r, pair.R_B))))
|
||
pred = (pair.R_A - np.eye(3)) @ t
|
||
meas = r @ np.asarray(pair.t_B_m, dtype=float)
|
||
trans_errs.append(np.linalg.norm(pred - meas))
|
||
rot_rms = float(np.sqrt(np.mean(np.square(rot_errs))))
|
||
trans_rms = float(np.sqrt(np.mean(np.square(trans_errs))))
|
||
translation_accepted = trans_rms < 0.5
|
||
notes.append(f"legacy translation refine rms={trans_rms:.3f} m")
|
||
if not translation_accepted:
|
||
notes.append("translation residual too large; keeping translation at zero")
|
||
t = np.zeros(3)
|
||
else:
|
||
notes.append("rotation-only extrinsic returned (phase-A; phase-C SE3 gated off)")
|
||
|
||
return JointExtrinsicResult(
|
||
T_IMU_lidar=make_transform(t, r),
|
||
translation_accepted=bool(translation_accepted and np.linalg.norm(t) > 0),
|
||
residual_rms_rot_deg=rot_rms,
|
||
residual_rms_trans_m=0.0 if not translation_accepted else trans_rms,
|
||
observability=observability,
|
||
gyro_bias_rad_s=np.asarray(bias_out, dtype=float),
|
||
accel_bias_m_s2=None if accel_bias_out is None else np.asarray(accel_bias_out, dtype=float),
|
||
gravity_m_s2=None if gravity_out is None else np.asarray(gravity_out, dtype=float),
|
||
notes=tuple(notes),
|
||
)
|