Estimation of Spacecraft Inertia Tensor Using Attitude-Only Data from Torque-Free Motion
Authors: Daigo Kobayashi, Vakhtang Putkaradze
Organizations: Assistant Professor, Department of Aerospace Engineering and Mechanics, 213 Hardaway Hall, Tuscaloosa, Alabama 35487-0350, USA. · Professor, Department of Mathematics, 345 Gordon Palmer Hall, Tuscaloosa, Alabama 35487-0350, USA.
We present an attitude-only framework for estimating a spacecraft's normalized inertia tensor from torque-free rotational motion. Our method supports both continuous single-arc observations and the joint use of multiple short torque-free arcs, while requiring neither gyroscope measurements nor known control torques. A Karush-Kuhn-Tucker formulation provides a fast linear initialization, which is refined by nonlinear shooting using the exact Jacobi-elliptic solution of Euler's equations and a Magnus-expansion quaternion map. Under controlled attitude noise, tests using a single 500-second arc reduced inertia-tensor error by approximately one order of magnitude relative to an Extended Kalman Filter initialized from the same estimate, while requiring nearly two orders of magnitude less computation. Joint estimation from three 100-second arcs provided a similar improvement in accuracy and remained more than one order of magnitude faster. Photorealistic proximity-operations simulations further evaluated both strategies using monocular image-derived attitudes. The 2000-second single-arc cases achieved sub-thousandth median inertia-tensor error and supported 10-hour attitude predictions with single-digit-degree median error. In three-arc cases using 30-300 seconds per arc, our method consistently outperformed the EKF refinement, with performance governed by rotational excitation and temporal sampling.
This paper proposes a complementary filter on SO(3) for attitude estimation from scalar measurements corresponding to projections of known inertial vectors onto body-frame sensing directions. The observer evolves directly on SO(3) and employs a constant-gain innovation tailored to the scalar-output structure. Under suitable persistence-of-excitation conditions, almost-global asymptotic stability is established when at least three inertial vectors are measured along a common body-frame direction. For configurations involving only two scalar measurements, sufficient conditions for asymptotic convergence are derived together with an explicit characterization of the region of attraction. Numerical simulations illustrate the proposed results.
Alessandro Melis, Soulaimane Berkane, Robert Mahony +1
Spacecraft attitude control is traditionally achieved using momentum exchange devices or propellant-consuming thrusters. Meanwhile, a growing number of missions require robotic manipulators, which are typically treated as disturbance sources to be rejected rather than as actuators for spacecraft reorientation. This work investigates the use of manipulator motions for propellant-free attitude control by formulating a trajectory optimization problem with critical joint and collision avoidance constraints. Using an interior point solver for the resulting nonlinear program, complex slew and detumble trajectories are demonstrated for a range of spacecraft-manipulator systems with varying kinematic complexity and mass properties. The achievable control authority is compared directly with that of reaction wheel arrays via momentum and torque envelopes, demonstrating the potential for manipulators to serve as redundant or even primary attitude control systems. This work provides a framework for using manipulators as multipurpose attitude control actuators, with particularly promising applications in in-space assembly and manufacturing when grasping payloads with high relative mass fractions.
Neural inertial odometry increasingly uses networks as learned measurements inside filtering pipelines. Such measurements should transform consistently under arbitrary IMU mounting conventions: their mean must transform as a vector, and their covariance must transform congruently as a second-order tensor. We present GINIO, a geometric SO(3)-equivariant interface for neural inertial odometry under arbitrary rotations of the IMU measurement frame. Given calibrated IMU windows, our framework predicts a motion measurement and uncertainty obeying these tensorial laws. To support efficient sensor-frame learning, we introduce Last-Frame Alignment (LFA), a deterministic preprocessing step that is provably equivalent to world-frame training for SO(3)-equivariant predictors. The connected estimator tracks sensor-local states such as IMU bias, separating nuisance estimation from the geometric law enforced by the learned measurement. We instantiate the same interface in filter-connected NIO, AirIO-style recurrent aerial prediction, EqNIO-style full-SO(3) canonicalization, and ResNet-style temporal backbones. On TLIO, GINIO achieves 2.018 m ID/SO(3) ATE while EqNIO degrades to 76.389 m, using 11.6x fewer FLOPs. On NanoBench, our AirIO-style instantiation improves ATE from 5.579 m to 1.430 m without external attitude input, and our ResNet-style instantiation reaches 0.581 m ATE versus 0.645 m for ResNet1D. On Fetch, GINIO empirically reduces unseen physical-remount ATE from 8.15 m to 0.50 m without retraining, demonstrating robustness beyond the exact coordinate-frame guarantee. For uncertainty, spectral covariance reduces covariance-equivariance error by over three orders of magnitude compared with a diagonal head.