Observability Analysis and Online Calibration of Visual-Inertial-Wheel Odometry for 4WIS4WID Mobile Robots

Visual-Inertial Odometry(VIO), which is critical to mobile robot navigation, uses cameras with a large number of pixels. Capturing and processing camera images requires significant resources. This work presents a minimalist approach to planar odometry, demonstrating that just four visual measurements and an IMU can provide robust motion estimation for differential-drive robots. Our key insight is that four downward-facing photodiodes that sense the world through optical Gabor masks produce signals that encode speed. Based on this, we jointly optimize the mask parameters alongside a Temporal Convolutional Network (TCN) using a physically-grounded simulator. The resulting model decodes speed from just the four measurements produced by the photodiodes. Pairing these estimates with the angular speed from an IMU yields a continuous planar trajectory. We validate our approach with a prototype sensor mounted on a differential drive robot. Across diverse indoor and outdoor terrains, our system closely tracks the reference ground truth without any real-world fine-tuning. Our work shows that minimalist sensing enables efficient and accurate planar odometry.

Monocular visual-inertial odometry (VIO) cannot recover metric scale from vision alone; scale must be resolved through inertial measurements. We present a trajectory-dependent observability analysis showing that translational acceleration, produced by curvature, not constant-speed straight-line travel, is the fundamental source that couples scale to the inertial state. This relationship is formalized through the gravity-acceleration asymmetry in the IMU model, from which we derive rank conditions on the observability matrix and propose a lightweight excitation metric computable from raw IMU data. Controlled experiments on a differential-drive robot with a monocular camera and consumer-grade IMU validate the theory, with straight-line motion yielding 9.2% scale error, circular motion 6.4%, and figure-eight motion 4.8%, with excitation spanning four orders of magnitude. These results establish trajectory design as a practical mechanism for improving metric scale recovery.

Deformable scenes violate the rigidity assumptions underpinning classical visual--inertial odometry (VIO), often leading to over-fitting to local non-rigid motion or to severe camera pose drift when deformation dominates visual parallax. In this paper, we introduce DefVINS, the first visual-inertial odometry pipeline designed to operate in deformable environments. Our approach models the odometry state by decomposing it into a rigid, IMU-anchored component and a non-rigid scene warp represented by an embedded deformation graph. As a second contribution, we present VIMandala, the first benchmark containing real images and ground-truth camera poses for visual-inertial odometry in deformable scenes. In addition, we augment the synthetic Drunkard's benchmark with simulated inertial measurements to further evaluate our pipeline under controlled conditions. We also provide an observability analysis of the visual-inertial deformable odometry problem, characterizing how inertial measurements constrain camera motion and render otherwise unobservable modes identifiable in the presence of deformation. This analysis motivates the use of IMU anchoring and leads to a conditioning-based activation strategy that avoids ill-posed updates under poor excitation. Experimental results on both the synthetic Drunkard's and our real VIMandala benchmarks show that DefVINS outperforms rigid visual--inertial and non-rigid visual odometry baselines. Our source code and data will be released upon acceptance.