Maximum Torque and Momentum Envelopes for Reaction Wheel Arrays

Abstract

Spacecraft reaction wheel maneuvers are limited by the maximum torque and/or angular momentum which the wheels can provide. For an n-wheel configuration, the torque or momentum envelope can be obtained by projecting the ndimensional hypercube, representing the domain boundary of individual wheel torques or momenta, into three dimensional space via the 3xn matrix of wheel axes. In this paper, the properties of the projected hypercube are discussed, and algorithms are proposed for determining this maximal torque or momentum envelope for general wheel configurations. Practical implementation strategies for specific wheel configurations are also considered.

A simple approach for predicting time-optimal slew capability

“…The spin axis of each wheel is also offset from the X-Y plane by η ¼ 35:261. The value of parameter η is chosen as the value which maximizes the inscribed sphere of the reaction wheel torque envelope [13]. The reaction wheel alignment matrix for this configuration is given by …”

“…The smallest maximum torque can be found as the radius of the largest inscribed sphere of the reaction wheel torque envelope. For the four wheel system considered here, the radius of this sphere is 1:63τ max where τ max ¼ 0:11 Nm is the torque capability of a single wheel [13]. The acceleration limit for maneuver design is therefore…”

“…7 shows the three-dimensional torque envelope for the reaction wheel configuration under consideration in this paper. As mentioned earlier, the skew angle of the array was configured in order to maximize the inscribed sphere [13]. While the radius of the inscribed sphere is 1:63τ max ¼ 0:18 N m, the maximum torque that can be developed is along the Z axis and is equal to 2.31 τ max ¼ 0:25 N m. Thus, Fig.…”

“…In this paper, however, it is assumed that L 1 allocation of torques to the individual RWs is used so that the entire torque envelope is accessible for conventional maneuvering. This ideal case can be realized in practice using an iterative method developed by Markley et al [13].…”

Kinematic Steering Law for Conically Constrained Torque-Limited Spacecraft Attitude Control

“…The algorithm for computing this minimum torque capacity is given in Reference [21]. An N RW -wheel system has an N RW -dimensional torque vector u s feasible set that fills the interior of a hypercube of dimension N RW , where each side has a length of twice the maximum torque (2u smax ).…”