114 lines
3.7 KiB
Python
114 lines
3.7 KiB
Python
"""SO(3) rotation hand-eye solver for ``R_A R_X = R_X R_B``."""
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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 MotionPair
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from .geometry import orthonormalize_rotation, rotation_angle_deg, skew, so3_exp, so3_log
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@dataclass(frozen=True)
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class RotationHandeyeResult:
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R_IMU_lidar: np.ndarray
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residual_rms_deg: float
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residual_median_deg: float
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pair_count: int
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ok: bool
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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 _tsai_rotation_initial(pairs: list[MotionPair]) -> np.ndarray:
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"""Closed-form rotation hand-eye initial guess (Tsai-style linear solve)."""
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rows: list[np.ndarray] = []
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rhs: list[np.ndarray] = []
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for pair in pairs:
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alpha = so3_log(pair.R_A)
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beta = so3_log(pair.R_B)
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if np.linalg.norm(alpha) < 1e-6 or np.linalg.norm(beta) < 1e-6:
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continue
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w = np.sqrt(_pair_weight(pair))
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rows.append(w * skew(alpha + beta))
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rhs.append(w * (beta - alpha))
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if len(rows) < 2:
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return np.eye(3)
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a = np.vstack(rows)
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b = np.concatenate(rhs)
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try:
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rotvec, *_ = np.linalg.lstsq(a, b, rcond=None)
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except np.linalg.LinAlgError:
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return np.eye(3)
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return orthonormalize_rotation(so3_exp(rotvec))
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def _pair_residual_deg(r_x: np.ndarray, pair: MotionPair) -> float:
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err = so3_log(r_x.T @ pair.R_A @ r_x @ pair.R_B.T)
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return float(np.degrees(np.linalg.norm(err)))
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def solve_rotation_handeye(pairs: list[MotionPair] | tuple[MotionPair, ...]) -> RotationHandeyeResult:
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"""Solve ``R_A R_X = R_X R_B`` with weighted robust nonlinear refinement."""
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usable = [pair for pair in pairs if rotation_angle_deg(pair.R_A) > 1.0 and rotation_angle_deg(pair.R_B) > 1.0]
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notes: list[str] = []
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if len(usable) < 3:
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return RotationHandeyeResult(
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R_IMU_lidar=np.eye(3),
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residual_rms_deg=1e9,
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residual_median_deg=1e9,
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pair_count=len(usable),
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ok=False,
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notes=("need at least 3 motion pairs with meaningful rotation",),
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)
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r0 = _tsai_rotation_initial(usable)
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weights = np.asarray([_pair_weight(pair) for pair in usable], dtype=float)
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notes.append(
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f"weighted hand-eye: weight median={float(np.median(weights)):.3g}, "
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f"min={float(np.min(weights)):.3g}, max={float(np.max(weights)):.3g}"
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)
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def pack(r: np.ndarray) -> np.ndarray:
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return so3_log(r)
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def unpack(vec: np.ndarray) -> np.ndarray:
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return orthonormalize_rotation(so3_exp(vec))
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def residual(vec: np.ndarray) -> np.ndarray:
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r_x = unpack(vec)
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residuals = []
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for pair, weight in zip(usable, weights):
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err = so3_log(r_x.T @ pair.R_A @ r_x @ pair.R_B.T)
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residuals.append(np.sqrt(weight) * err)
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return np.concatenate(residuals)
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opt = least_squares(residual, pack(r0), loss="huber", f_scale=np.deg2rad(1.0), max_nfev=200)
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r_x = unpack(opt.x)
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errs = np.asarray([_pair_residual_deg(r_x, pair) for pair in usable], dtype=float)
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# Report unweighted RMS/median for interpretability.
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rms = float(np.sqrt(np.mean(errs**2)))
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med = float(np.median(errs))
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notes.append(f"optimized over {len(usable)} pairs")
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ok = rms < 5.0 and len(usable) >= 3
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if not ok:
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notes.append("rotation residual RMS too high or too few pairs")
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return RotationHandeyeResult(
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R_IMU_lidar=r_x,
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residual_rms_deg=rms,
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residual_median_deg=med,
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pair_count=len(usable),
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ok=ok,
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notes=tuple(notes),
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)
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