Attitude Determination for NPS Three-Axis Spacecraft Simulator

Abstract

This paper presents the attitude determination method for the Bifocal Relay Mirror Spacecraft Simulator. The simulator simulates three-axis motion of a spacecraft and has an optical system emulating a bifocal space telescope. The simulator consists of three control moment gyroscopes, rate gyros, two-axis analog sun sensor, and two inclinometers. The five-foot diameter platform is supported on a spherical air bearing to offer a low-torque environment. This paper demonstrates two attitude determination methods employing the measurements from a two-axis analog IR sensor, two inclinometers, and a triaxial gyroscope. The first method implements the conventional Kalman filter algorithm. The second method uses a nonlinear observer derived from the Lyapunov's direct method. Analytical and experimental results are presented to validate the proposed algorithm. The TASS simulates spacecraft three-axis motion and has an optical system simulating a single space telescope. The five- foot diameter TASS platform is supported on a spherical air bearing to offer a low- torque environment. The simulator consists of three variable speed control moment gyroscopes as actuators, rate gyros for angular rate, two-axis analog sun sensor and two inclinometers for attitude sensors. Detailed description of the TASS hardware is given in Ref. 2. This paper focuses on the development and validation of the attitude determination algorithm of the TASS using two inclinometers, two-axis IR sensor, and a triaxial rate gyroscope. Although inclinometers cannot be used in a spacecraft, they can still be employed in testbeds to get useful attitude information with good accuracy at low cost. Also, if the light source is not far enough, the effect of transitional motion of the IR sensor during the rotation of the testbed should be taken into account when calibrating the IR sensor. Quaternion attitude parametrization offers a singularity-free method to represent three-dimensional rota- tions using four-dimensional unit vectors. But the four elements of the unit quaternion cannot be estimated independently because of the normality constraint. It is a standard approach to include the gyro bias in the overall kinematics model and to estimate the actual attitude by Extended Kalman Filter (EKF) techniques. The EKF, as an extension of the Kalman Filter (KF) to nonlinear models, works satisfactorily when the linearized model exhibits sufficient accuracy. Since the EKF utilizes a linearization at each step, the nonlinear normality constraint of the quaternions cannot be rigidly enforced within the EKF computational structure. Various methods have been developed to overcome this deficiency and are described in Refs. 3, 4, 5, and 6. The nominal attitude determination method used for the TASS is a basic six-state attitude estimation filter known as the Multiplicative EKF (MEKF). 4 In the MEKF formulation of the TASS, the Modified Ro- drigues Parameters (MRPs) are used as an unconstrained representation of the attitude error with quaternion