Observability Analysis and Online Calibration of Visual-Inertial-Wheel Odometry for 4WIS4WID Mobile Robots
Authors: Branimir Ćaran, Vladimir Milić, Bojan Šekoranja, Bojan Jerbić
Organizations: Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, 10000, Croatia · Croatian Academy of Sciences and Arts, Zagreb, 10000, Croatia
In this paper, we present a visual-inertial-wheel odometry (VIWO) framework with online calibration for four-wheel independently steered and driven (4WIS4WID) mobile robots. We derive a 2D odometry model directly from the four driving velocities and steering angles, using both the longitudinal rolling constraints and the lateral no-slip constraints of all wheels. A preintegration model and analytical Jacobians are developed for efficient filtering and calibration. An observability analysis of the linearized VIWO system shows that a drive-only model makes all steering offsets unobservable, whereas the proposed redundant model restores their observability. The analysis also identifies four standard VINS unobservable directions and three additional directions associated with the arbitrary placement of the odometry reference frame. Furthermore, we characterize several degenerate motions, including zero yaw rate, constant steering, and a non-rolling wheel, and derive the corresponding excitation conditions for the thirteen wheel intrinsics that remain after fixing the odometry frame reference. The performance of the proposed system has been demonstrated in both simulation and real-world experiments on a 4WIS4WID mobile robot.
Figures & tables
Fig. 1: 4WIS4WID mobile robot where each wheel i is independently steered by δi and driven at ωdi , so the ICR may be placed anywhere in the plane.
Motion
Unobservable
General motion
4 inertial + 3 gauge
Zero yaw rate ( ω≡0 )
xw , yw
Constant steering configuration
2 per wheel (8 total)
Wheel j not rolling
rj , δoj
Pure translation
OpI
One axis rotation
OpI along axis
TABLE I: Degenerate motions and the corresponding unobservable calibration parameters.
Fig. 2: Estimation error (solid) and 3σ bound (dotted) for six Monte-Carlo runs along the ICR-sweep trajectory. Shown are the IMU-odometry extrinsics and representative wheel intrinsics ( r1 , δo2 , xw2 ).
Configuration
RPE 10 [deg]
RPE 10 [m]
RPE 25 [deg]
RPE 25 [m]
NEES
True init., calib. ON
0.014
0.0045
0.021
0.0055
3.56
True init., calib. OFF
0.050
0.0071
0.081
0.0111
10.39
Bad init., calib. ON
0.014
0.0046
0.018
0.0060
3.72
Bad init., calib. OFF
0.602
20.9823
1.465
47.4002
170.75
TABLE II: Relative pose error (RPE) and mean NEES over 20 Monte-Carlo runs.
Fig. 3: Experimental results
Parameter
Before
After
wheel radii r [mm]
[25.6, 25.6, 25.6, 25.6]
[26.3, 26.3, 28.1, 26.8]
wheel positions xw [m]
[-0.1125, -0.1125, 0.1125]
[-0.1029, -0.1029, 0.1454]
wheel positions yw [m]
[0.1125, -0.1125, -0.1125]
[0.1267, -0.1216, -0.1216]
steering offsets δo [rad]
[0.0, 0.0, 0.0]
[0.0168, -0.0098, -0.0633]
Ext. Pos [m]
[0.1457, 0.0279, 0.0576]
[0.1696, 0.0192, 0.0244]
Ext. Ori [rad]
[1.2085, 1.2093, 1.2091]
[1.2498, 1.2060, 1.2206]
TABLE III: Values of the calibration parameters before and after online calibration for real world experiment
Computer Science, Maharishi International University, Iowa, USA · Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia · Computer Science, Iowa State University, Iowa, USA +1