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.
Abstract
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.
Attitude estimation based on inertial sensing requires measurements of local angular velocities and local gravity via gyroscopes and accelerometers. However, during the motion of a mobile system the inertial measurement unit (IMU) will be subject to additional accelerations which skews the measurement of local gravity. This effect gets amplified the further away the IMU is from the base of the system. Many attitude estimation filters, such as "Madgwick" or "Mahony", account for this by relying more on gyroscope integration for periods of high angular velocity. However, this approach is prone to accumulate long term error especially around the gravity vector. In this work we utilize the gyroscope measurements to compensate the additional accelerations induced by the motion of the system, i.e., centripetal- and tangential-accelerations. Additionally, we introduce a calibration method that estimates intrinsic IMU parameters such as axes misalignment, bias, scale, as well as the extrinsic base-to-IMU vector without the necessity for additional external equipment. Our evaluation in simulation as well as in the real-world shows that this method improves any attitude filter that relies on the direction of gravity. Furthermore we demonstrate the effectivenes on highly dynamic systems, and systems that are unable to put the IMU at the center of rotation, using our real-world spherical mobile mapping system.