Traj-LO
Traj-LO 把 LiDAR 量測視為高頻串流點,以由多段線性插值組成的連續時間軌跡描述感測器運動,並在滑動視窗內同時最小化點到平面幾何誤差與軌跡平滑(運動學)約束。由於每個點都用其時間戳查詢對應位姿,因此不需另外做運動補償。作者主張僅靠 LiDAR 也能在快速運動與 IMU 飽和情境下運作,並支援多 LiDAR。
本頁內容
LiDAR-only odometry with a piecewise-linear continuous-time trajectory optimized in a sliding window, coupling point-to-plane geometry with smoothness constraints so no separate deskewing is needed.
技術屬性
欄位內容為文獻擷取紀錄的原文用語(英文),以原文為據;「未查證」表示本研究尚未讀到該資訊,不代表該方法不具備此能力。
| 感測輸入 | 3D LiDAR only (single or multiple, spinning and non-repetitive) |
|---|---|
| 原文測試平台 | vehicle、UAV、handheld |
| 狀態估計 | Sliding-window nonlinear least squares (Gauss-Newton with analytic SE(3) Jacobians) over K+1 control poses of a piecewise-linear continuous-time trajectory (K = 4 segments of 0.03 s in experiments), with point-to-plane terms, a smoothness term penalizing velocity change between consecutive segments, and a Schur-complement marginalization prior with first-estimate Jacobians; marginalization lowered ATE in all four ablation settings (Table IV) |
| 資料關聯 | point-to-plane to map neighbours, normals from PCA of five closest points; no feature selection |
| 時間表示 | continuous-time piecewise-linear segments in SE(3) (e.g., 0.01 s segments for an indoor aggressive sequence) |
| 去畸變 | not required: each point is registered with the pose queried at its own timestamp |
| 迴圈閉合 | none |
| 全域最佳化 | none |
| 地圖表示 | Spatial hashing voxel map (following CT-ICP and KISS-ICP) storing up to 20 points per voxel, 7 nearest voxels searched, new points dropped when a voxel is full, points farther than 100 m removed; voxel size 0.4 m indoor, 0.8 m outdoor and 0.2 m for the Point-LIO indoor sequence |
| 先驗資訊 | none |
| 可輸出幾何 | odometry and voxel point map; export format 原文未報告 |
| 計算需求 | AMD Ryzen 9 5900X CPU; on NTU VIRAL nya01 (395 s) total processing 116.2 s with four segments and marginalization (173.2 s without) and 49.7 s with one segment, versus KISS-ICP 47.7 s, CT-ICP 152.8 s and FLOAM 25.6 s; memory capped at 208 MB because the map keeps points within a fixed radius |
使用設備
原文使用的感測器、運算硬體與載具(equipment)。型號保留原文寫法,連結到設備頁中同一型號的歸併名稱;角色依原文用途分為方法輸入、資料集感測器、執行運算平台、參考或真值量測(reference or ground truth)與比較對象設備。
| 類別 | 型號(原文寫法) | 角色 | 資料集 | 原文規格 | 出處 |
|---|---|---|---|---|---|
| LiDAR | Velodyne HDL-64E S2歸入:Velodyne HDL-64E | 資料集感測器 | KITTI odometry | KITTI points are motion-corrected, per-point time discarded | (Zheng & Zhu, 2024, Sec. IV-A) |
| LiDAR | two 16-channel Ouster LiDARs (horizontal and vertical OS1-16) | 資料集感測器 | NTU VIRAL | 10 Hz with per-point relative timestamps | (Zheng & Zhu, 2024, Sec. IV-A; Table II footnote) |
| LiDAR | Ouster OS0-64 | 資料集感測器 | Hilti 2021 | 360 deg FoV at 10 Hz, handheld | (Zheng & Zhu, 2024, Sec. IV-A; Table III footnote) |
| LiDAR | Livox MID70 | 資料集感測器 | Hilti 2021 | 70 deg circular FoV, non-repetitive Risley-prism scan, 10 Hz | (Zheng & Zhu, 2024, Sec. IV-A; Sec. IV-D) |
| LiDAR | Livox Avia | 資料集感測器 | Point-LIO dataset | rotating-platform and swinging-rope sequences beyond the IMU range | (Zheng & Zhu, 2024, Sec. IV-A; Sec. IV-E) |
| 慣性量測單元(IMU) | 9-axis IMU (external IMU) | 資料集感測器 | NTU VIRAL | 385 Hz; used only by the LIO baselines | (Zheng & Zhu, 2024, Sec. IV-A; Table II footnote) |
| 慣性量測單元(IMU) | IMU embedded in the OS0-64 | 資料集感測器 | Hilti 2021 | used only by LIO baselines | (Zheng & Zhu, 2024, Table III footnote) |
| 全測站 | Leica Nova MS60 | 參考或真值量測 | NTU VIRAL | ground truth trajectory | (Zheng & Zhu, 2024, Sec. IV-A) |
| 全測站 | Hilti PLT 300 automated total station | 參考或真值量測 | Hilti 2021 | millimeter-accurate ground truth (or MoCap) | (Zheng & Zhu, 2024, Sec. IV-A) |
| 運算硬體 | AMD Ryzen 9 5900X CPU | 執行運算平台 | 未標示 | all experiments; runtime and memory in Table V | (Zheng & Zhu, 2024, VoR Sec. IV) |
| 其他 | motion capture (MoCap) system | 參考或真值量測 | Hilti 2021 | alternative ground truth source | (Zheng & Zhu, 2024, Sec. IV-A) |
作者報告的優勢與限制
優勢
- On Hilti 2021 handheld sequences continuous-time methods outperform discrete-time LO with the non-repetitive Livox MID70 even without IMU, but MID70 accuracy is lower than with the Ouster OS0-64 and Traj-LO with MID70 alone diverged on the Lab sequence (Sec. IV-D; Table III)
- Adding the vertical LiDAR (L1+L2) removes the large z-direction errors on the tnp sequences (ATE 0.049, 0.040, 0.049 m versus 0.505, 0.607, 0.101 m with L1 only) and on spms lowers ATE and avoids the spms_02 divergence (Sec. IV-C; Fig. 4; Table II)
- KITTI online benchmark 0.58% translation and 0.0014 deg/m rotation error (Sec. IV-B)
- Maps aggressive motion beyond the IMU range on the Point-LIO rotating platform where FAST-LIO fails (Sec. IV-E; Fig. 5)
限制
- Single horizontal LiDAR shows larger ATE during jerky take-off and landing phases (arXiv v1 Sec. IV-C and Fig. 4 on spms_03; this paragraph is not retained in the version of record)
- Constant velocity within segments may not hold for fast motion, requiring short segments (Sec. III-B) (author-stated assumption)
- Assumes the odometry starts from a stationary state and uses the first 0.3 s of points to initialize the map (Sec. III-E)
- Single-LiDAR Traj-LO diverged on NTU VIRAL spms_02 and has ATE of 0.505 m and 0.607 m on tnp_01 and tnp_02 (Table II)
- Odometry only; a complete LiDAR-only SLAM is left for future work (Sec. V)
營建工程相關證據
作者描述其使用的 Hilti 2021 資料集包含辦公室、實驗室與施工環境之室內序列及施工現場之室外序列,地面真值來自 Hilti PLT 300 全測站或動作擷取系統。表 III 的 Cons2 依 Hilti 2021 官方序列名稱推定為 Construction Site Outdoor 2(推論),該序列官方地面真值為全測站量測的 3 自由度稀疏點位;Traj-LO 在 Cons2 的 ATE 為 0.065 m(OS0-64)、0.135 m(MID70)與 0.063 m(兩者併用)。僅有軌跡層級評估,未評估點雲幾何。
原文驗證環境:公開基準、施工中工地、獨立參考量測
報告的性能數據
以下是原文作者報告的性能數值(author-reported results),不是本研究重新量測的結果。每張圖只並列同一個比較組(comparison group,同一張表、同一組實驗設定)內的方法;不同比較組之間的數值不可直接比較,也不構成排名。
本方法共出現在 8 個比較組,合計 73 筆紀錄。以下列出本方法紀錄最多的 4 組,其餘 4 組列在最後,並連到性能比較頁。
Cao et al., 2025 · Table II (NTU VIRAL) 本方法 18 筆
指標APE (RMSE, meters)
表格設定(擷取紀錄原文):NTU VIRAL drone sequences, horizontal OS1-16 for RESPLE; APE RMSE with the official NTU VIRAL evaluation script; T-LO, C-MLO (two LiDARs) and F-LIO2 values are copied from refs. [13] (Traj-LO), [16] (CTE-MLO) and [18] (Nguyen et al. 2024, not the FAST-LIO2 paper), respectively, per the Table II footnote; x marks failure (Cao et al., 2025, Table II (NTU VIRAL))
APE (RMSE, meters),NTU VIRAL · eee_01
只並列這張表在相同設定下報告的方法;以「本方法:」開頭者為本頁方法。失敗、未執行與未報告以標記呈現,不是 0。
按 Tab 進入圖表後,用上下方向鍵逐一瀏覽各類別,Esc 關閉提示框;也可開啟表格檢視閱讀全部數值。
這些是 Cao et al., 2025 在此表設定下報告的數值(author-reported results),只能在同一個比較組內對照,不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Cao et al., 2025, Table II (NTU VIRAL))
| 方法(原文寫法) | 報告值 | 出處 |
|---|---|---|
| T-LO (Traj-LO)本方法 | 0.055 m | (Cao et al., 2025, Table II) |
| C-MLO (CTE-MLO, 2 LiDARs) | 0.08 m | (Cao et al., 2025, Table II) |
| F-LIO2 (FAST-LIO2) | 0.069 m | (Cao et al., 2025, Table II) |
| R-LO (RESPLE LiDAR-only)原文提出 | 0.044 m | (Cao et al., 2025, Table II) |
| R-LIO (RESPLE LiDAR-inertial)原文提出 | 0.036 m | (Cao et al., 2025, Table II) |
Zheng & Zhu, 2024 · Table III 本方法 18 筆
指標ATE (m)
表格設定(擷取紀錄原文):Hilti 2021 handheld sequences; L1 Ouster OS0-64, L2 Livox MID70, I IMU embedded in L1; ground truth from Hilti PLT 300 total station or MoCap; x divergence, dash invalid result (Zheng & Zhu, 2024, Table III)
ATE (m),Hilti 2021 SLAM challenge · RPG
只並列這張表在相同設定下報告的方法;以「本方法:」開頭者為本頁方法。失敗、未執行與未報告以標記呈現,不是 0。
- 失敗
按 Tab 進入圖表後,用上下方向鍵逐一瀏覽各類別,Esc 關閉提示框;也可開啟表格檢視閱讀全部數值。
這些是 Zheng & Zhu, 2024 在此表設定下報告的數值(author-reported results),只能在同一個比較組內對照,不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Zheng & Zhu, 2024, Table III)
| 方法(原文寫法) | 報告值 | 出處 |
|---|---|---|
| FLOAM (L1) | 2.775 m | (Zheng & Zhu, 2024, Table III) |
| FLOAM (L2) | 無數值失敗註記(擷取紀錄):invalid result (dash) | (Zheng & Zhu, 2024, Table III) |
| KISS-ICP (L1) | 0.187 m | (Zheng & Zhu, 2024, Table III) |
| KISS-ICP (L2) | 3.726 m | (Zheng & Zhu, 2024, Table III) |
| CT-ICP (L1) | 0.188 m | (Zheng & Zhu, 2024, Table III) |
| CT-ICP (L2) | 0.197 m | (Zheng & Zhu, 2024, Table III) |
| Ours (Traj-LO, L1)本方法原文提出 | 0.172 m | (Zheng & Zhu, 2024, Table III) |
| Ours (Traj-LO, L2)本方法原文提出 | 0.218 m | (Zheng & Zhu, 2024, Table III) |
| Ours (Traj-LO, L1+L2)本方法原文提出 | 0.17 m | (Zheng & Zhu, 2024, Table III) |
| LIO-SAM | 無數值失敗註記(擷取紀錄):invalid result (dash) | (Zheng & Zhu, 2024, Table III) |
| FAST-LIO [7] (L1+I) | 0.182 m | (Zheng & Zhu, 2024, Table III) |
| FAST-LIO [7] (L2+I) | 0.282 m | (Zheng & Zhu, 2024, Table III) |
| CLIC (L1+I) | 0.394 m | (Zheng & Zhu, 2024, Table III) |
| CLIC (L2+I) | 無數值失敗註記(擷取紀錄):invalid result (dash) | (Zheng & Zhu, 2024, Table III) |
Zheng & Zhu, 2024 · Table I 本方法 12 筆
指標RTE (%)
表格設定(擷取紀錄原文):KITTI odometry RTE (%); points are motion-corrected in KITTI so continuous registration is disabled and motion constraints span 4 scans; 0.205 deg vertical correction; Online is the KITTI leaderboard score on test sequences 11 to 21 (version of record table has no AVG column) (Zheng & Zhu, 2024, Table I)
RTE (%),KITTI odometry · 00
只並列這張表在相同設定下報告的方法;以「本方法:」開頭者為本頁方法。失敗、未執行與未報告以標記呈現,不是 0。
按 Tab 進入圖表後,用上下方向鍵逐一瀏覽各類別,Esc 關閉提示框;也可開啟表格檢視閱讀全部數值。
這些是 Zheng & Zhu, 2024 在此表設定下報告的數值(author-reported results),只能在同一個比較組內對照,不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Zheng & Zhu, 2024, Table I)
| 方法(原文寫法) | 報告值 | 出處 |
|---|---|---|
| FLOAM | 0.71% | (Zheng & Zhu, 2024, Table I) |
| KISS-ICP | 0.52% | (Zheng & Zhu, 2024, Table I) |
| CT-ICP | 0.49% | (Zheng & Zhu, 2024, Table I) |
| Ours (Traj-LO)本方法原文提出 | 0.5% | (Zheng & Zhu, 2024, Table I) |
Cao et al., 2025 · Table III (GrandTour) 本方法 8 筆
指標APE (RMSE, meters)
表格設定(擷取紀錄原文):GrandTour ANYmal D quadruped with Boxi rig: L1 Hesai XT32, L2 Livox Mid360, I built-in IMU of L2; APE RMSE via evo after interpolating estimates at ground-truth timestamps; x marks failure; sequences marked * are not in the public release (Cao et al., 2025, Table III (GrandTour))
APE (RMSE, meters),GrandTour · JTL
只並列這張表在相同設定下報告的方法;以「本方法:」開頭者為本頁方法。失敗、未執行與未報告以標記呈現,不是 0。
- 失敗
按 Tab 進入圖表後,用上下方向鍵逐一瀏覽各類別,Esc 關閉提示框;也可開啟表格檢視閱讀全部數值。
這些是 Cao et al., 2025 在此表設定下報告的數值(author-reported results),只能在同一個比較組內對照,不代表方法在其他資料或設定下的表現。
資料來源作者報告值(Cao et al., 2025, Table III (GrandTour))
| 方法(原文寫法) | 報告值 | 出處 |
|---|---|---|
| T-LO (L1)本方法 | 0.046 m | (Cao et al., 2025, Table III) |
| C-MLO (L1+L2) | 無數值失敗註記(擷取紀錄):failed | (Cao et al., 2025, Table III) |
| F-LIO2 (L1+I) | 無數值失敗註記(擷取紀錄):failed | (Cao et al., 2025, Table III) |
| R-LO (L1)原文提出 | 0.035 m | (Cao et al., 2025, Table III) |
| R-MLO (L1+L2)原文提出 | 0.026 m | (Cao et al., 2025, Table III) |
| R-LIO (L1+I)原文提出 | 0.028 m | (Cao et al., 2025, Table III) |
| R-MLIO (L1+L2+I)原文提出 | 0.028 m | (Cao et al., 2025, Table III) |
其他比較組
來源
Zheng & Zhu, 2024
(2024)Traj-LO: In Defense of LiDAR-Only Odometry Using an Effective Continuous-Time TrajectoryIEEE Robotics and Automation Letters, 9(2):1961-1968
DOI 10.1109/lra.2024.3352360arXiv 2309.13842程式碼
同儕審查已出版已讀全文近十年查證後修正
相關版本
- 預印本:Traj-LO (arXiv v1) https://arxiv.org/abs/2309.13842
- 程式碼釋出:kevin2431/Traj-LO https://github.com/kevin2431/Traj-LO
程式碼:https://github.com/kevin2431/Traj-LO(授權:MIT (LICENSE file checked))。有公開程式碼不等於已被重現,也不代表目前版本與論文版本相同。