π Lesson 6
D4
Underground SLAM Calibration Workflow
SLAM calibration for underground mining is the process of teaching a robot or autonomous vehicle how to accurately map and locate itself in dark, GPS-denied tunnels using sensors like lidar and inertial measurement units.
π― Learning Objectives
- β Explain the impact of IMU bias drift on underground SLAM trajectory divergence
- β Design a calibration sequence for a lidar-IMU-wheel odometry fusion system using observability analysis
- β Analyze SLAM output residuals to diagnose misalignment between sensor coordinate frames
- β Apply Allan variance analysis to quantify IMU noise parameters for calibration initialization
- β Validate calibration performance using ground-truth survey control points in a real mine drift
π Why This Matters
In underground mines, GPS is unavailable, and tunnels are often feature-poor, dusty, and dynamically changing β making localization one of the highest-risk failure modes for autonomous haul trucks. A 10 cm uncalibrated lidar-IMU misalignment can cause >2 m cumulative pose error over 500 m of travel, leading to collisions with rib supports or misaligned loading at drawpoints. This lesson equips you to prevent such failures by mastering the calibration workflow that underpins safe, certified AHS deployment.
π Core Principles
SLAM calibration begins with sensor characterization: understanding how each modality (lidar, IMU, encoder, camera) contributes to state estimation and where uncertainty arises. Unlike outdoor SLAM, underground environments demand rigorous treatment of IMU bias stability, lidar multipath from wet rock surfaces, and wheel slip due to muck accumulation. Calibration is not a one-time setup but a staged process: (1) per-sensor intrinsic calibration (e.g., lidar beam divergence, IMU scale factor), (2) inter-sensor extrinsic calibration (e.g., rotation/translation between lidar and IMU frame), and (3) temporal synchronization (e.g., hardware timestamp alignment). Crucially, observability-aware calibration ensures that unobservable degrees of freedom (e.g., absolute yaw in pure forward motion) are constrained via motion diversity β requiring deliberate calibration trajectories like figure-eights in drifts with known geometry.
π Allan Variance for IMU Bias Stability Estimation
Allan variance quantifies time-correlated IMU noise (bias instability, random walk) essential for tuning Kalman filter process noise matrices during SLAM initialization. It is computed from overlapping time-series segments of stationary IMU data and reveals dominant noise sources across integration times.
Allan Variance (ΟΒ²(Ο))
ΟΒ²(Ο) = (1/(2(Nβ1))) Ξ£_{k=1}^{Nβ1} (ΟΜ_{k+1} β ΟΜ_k)Β²Measures IMU angular/acceleration rate instability as function of cluster time Ο; used to identify bias instability, angular random walk, and rate random walk.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| ΟΒ²(Ο) | Allan variance | (Β°/s)Β² | Variance of averaged angular rate differences over time interval Ο |
| ΟΜ_k | Mean angular rate | Β°/s | Average gyro output over k-th Ο-second window |
| N | Number of clusters | dimensionless | Total number of overlapping Ο-second intervals in dataset |
Typical Ranges:
Tactical-grade IMU (e.g., Xsens MTi-630): 1eβ4 β 1eβ3 (Β°/s)Β² at Ο = 10 s
Navigation-grade IMU (e.g., Honeywell HG1930): 1eβ6 β 1eβ5 (Β°/s)Β² at Ο = 10 s
π‘ Worked Example
Problem: Given 1-hour static IMU gyroscope data sampled at 200 Hz, compute Allan variance at Ο = 10 s to estimate angular random walk (ARW) and bias instability.
1.
Step 1: Segment raw angular rate data (Ο_i) into overlapping windows of length Ο = 10 s (2000 samples); compute mean rate ΟΜ_k for each window k.
2.
Step 2: Compute pairwise differences ΞΟ_k = ΟΜ_{k+1} β ΟΜ_k, then square and average over all k: ΟΒ²(Ο) = (1/(2(Nβ1))) Ξ£(ΞΟ_k)Β².
3.
Step 3: Fit log-log plot of Ο(Ο) vs Ο: slope β β0.5 indicates ARW (Ο_ARW = Ο(Ο) Γ βΟ); plateau region gives bias instability (B = Ο_min Γ β3).
Answer:
For a typical tactical-grade IMU (e.g., ADIS16470), Ο(10 s) β 0.0025 Β°/s β ARW β 0.008 Β°/βh; bias instability β 0.004 Β°/h. These values inform Q-matrix tuning in the EKF-SLAM backend.
ποΈ Real-World Application
At Newmontβs Boddington Underground Expansion (Western Australia), engineers performed lidar-IMU calibration inside a 4.5 m Γ 4.5 m development drift using a Leica MS60 total station as ground truth. They executed a 3-loop figure-eight trajectory while logging synchronized Ouster OS1 lidar, Xsens MTi-630 IMU, and Volvo A30G wheel encoder data. Using Kalibr and ETH Zurichβs maplab pipeline, they identified a 0.8Β° yaw misalignment and 12 mm z-offset between lidar and IMU centers β correcting which reduced loop-closure residual error from 0.42 m to 0.07 m over 850 m. This enabled sub-10 cm lateral positioning accuracy required for automated ore-pass docking.
π§ Interactive Calculator
π§ Open Autonomous Haulage Systems Integration Calculatorπ Case Connection
π Underground Copper Mine AHS Deployment at Codelco El Teniente
Limited GNSS availability, high dust, and narrow ramps requiring <1.2m lateral accuracy