Bailey and Christopher J. Heiberg, SN [Docket No. A66 17215]; A Continuous Attitude Control Which Avoids CMG Array Singularities, by David A. Bailey, Christopher J.

Heiberg and Bong Wie, SN [Docket No. A66 17025 ; Escaping Singularities In A Satellite Attitude Control, by Christopher J. Heiberg and David A. Bailey, SN [Docket No. A66 17216].

Technical Field of the Invention This invention relates to satellites and robotic systems, for example controlling the orientation of a satellite using a plurality of control moment gyros (CMG).

Background of the Invention The attitude of an agile spacecraft or satellite is often maintained and adjusted with a control moment gyro array because those devices provide high torque and torque amplification. A typical CMG is a rotating mass suspended on a gimbal with an actuator to rotate it on the gimbal axis, producing torque and accumulating angular momentum.

Angular momentum is the integral of torque over time. An array of n>3 CMGs is often used, allowing attitude control with some redundancy. Each CMG has an angular momentum (h) constrained essentially to a plane, the angular momentum vector of the gyro is nearly orthogonal to the gimbal axis. The error in orthogonality is small enough that it does not affect the operation of the CMG, the array of CMGs, or the attitude control of the satellite. The wheel speed of the CMG is essentially constant in most applications, but does not have to be for this invention to work. The torque produced by <BR> <BR> <BR> <BR> <BR> <BR> the CMG, Q is the result of the cross product Q = 8xh, where 8 is the gimbal rate and h is the angular momentum of the rotor, if varying wheel speed is incorporated then

there is an additional term Q = 8xh + h, where the angular momentum h is defined as h = JQ, and h = JQ, where J is the moment of inertia of the rotating wheel and 0 is the rotational rate of the wheel.

Classically the attitude control calculates the desired attitude rates for the satellite c3 c, being the three axis attitude rates. The gimbal angle (8) rates for the CMG array are calculated using the pseudo inversc control law, <BR> <BR> <BR> <BR> <BR> Jsisthesatellitemomentofinertiamatrix,andAis#=AT(AAT)-1JS#c, where <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> <BR> 5h the Jacobian of CMG array angular momentum with respect to gimbal angle, A = ah where h is the sum of the angular momentum of the CMG array, Since the A matrix is a function of the gimbal angles and the gimbal angels change in order to produce torque on the spacecraft the rank of A can drop from 3 to 2, which is a singular condition and the pseudo inverse cannot be calculated.

The SN 08,923,742 application, referenced above, provides a solution that primarily uses and an open loop to maintain the desired trajectory. In this invention, CMG angles are controlled directly instead of controlling only the rate of change of gimbal angle DISCLOSURE OF THE INVENTION An object of the present invention is to significantly increase the speed in reorienting a satellite between two objects by utilizing more of the available angular momentum from the CMGs.

According to the invention, the attitude control calculates the angular momentum for the CMGs, instead of the desired torque. The angular momentum is directly used to calculate the gimbal angles of the CMGs. Based on mapping the angular momentum into three regions.

One is within the largest singularity free region surrounding the origin, the second is region that is beyond the angular momentum capability of the CMG array, and the third lies between the first two. If the angular momentum lies within the singularity free ellipsoid, the value of the angular momentum is used to calculate the gimbal angles.

Otherwise the gimbal angles are calculated for the point on the ellipsoid that lies on a line between the angular momentum and the origin. The saturation angular momentum in the direction of the desired angular momentum is calculated along with gimbal angles. If the commanded angular momentum is greater than the saturation angular momentum then the saturation gimbal angles are used, otherwise the gimbal angles are the interpolated values between the saturation gimbal angles and the ellipsoid gimbal angles.

A feature of this approach is that it allows for the use of the full angular momentum envelope.

Another feature is that CMG control is free from the singularities that are caused by the use of a pseudo inverse in the CMG control law.

Another feature is that the invention can be used to avoid singularities in robotic systems with similar control problems.

Other objects, benefits and features of the invention will be apparent from the following discussion of one or more embodiments.

BRIEF DESCRIPTION OF THE DRAWING Fig 1. is a functional block diagram showing a control embodying the present invention to rotate a satellite in response to commanded rotation signal q,.

Fig 2 is a block diagram showing a satellite with CMGs that are rotated to change the satellite's attitude in response to individually produce angular rate signals.

Fig. 3 illustrates two possible paths for reorienting between two objects.

BEST MODE FOR CARRYING OUT THE INVENTION It will be appreciated that Fig. 1 shows function blocks that may be implemented through hardware or software, preferably the latter in a computer based satellite control containing one or more signal processors programmed to produce output signals to control CMGs on the satellite as explained hereafter. Fundamentally the process is shown for a single signal path between two points, but it should be understood that single lines represent vector data which is 3 dimensional for the satellite attitude, attitude rate and torque, and n dimensional for the signals related to the n CMGs. Fig 2 shows three (n=3) CMGs. The control scheme shown in Fig. 1 is used to pan or rotate

the satellite on its axis from the line of sight view of an object A to a line of sight view of object B in Fig. 3. A typical closed loop control follows an eigen axis rotation path "old"by controlling the CMG's based on the actual (determined) from the attitude determination system ADS as in Fig. 3) and the desired path attitude. The invention, however, is not constrained to follow an eigen axis path as will be explained.

In the embodiment shown in Fig. 1, the desired attitude 10 for a satellite 11 is generated by a mission planner in a usual form, a quaternion, although any method can be used with the invention. The desired attitude 10 is compared at 12 with actual satellite attitude 14, producing an error 16 that is applied to an attitude control 17 according to <BR> <BR> <BR> <BR> <BR> the following: Ho = J (k Iqe + k2coe) where Hsis the desired angular momentum of the satellite, J is the moment of inertia tensor of the satellite, que vis the first three terms of the quaternion error, cotis the angular error rate, and k, and k2 are gains. The base angular momentum Hbjas 22 is added at 40 to the desired satellite angular momentum Hs 20, resulting in the total angular momentum delivered by the CMGs 24. The desired angular momentum is mapped at 26 to get, at 28, the desired CMG angles 8, (as opposed to CMG rate). This process involves three exclusive criteria for a given desired angular momentum. There are three regions of angular momentum that define a calculation method for the desired gimbal angle. The smallest region is if the angular momentum falls within an ellipsoid containing a singularity free space. The largest region is if the commanded angular momentum is greater than the saturation angular momentum of the CMG array. Then the saturation angular momentum is used to calculate the gimbal angles. The middle region is an interpolated value from the smallest and largest regions.

The mapping from angular momentum to gimbal angle is done differently, in three regions. If the angular momentum HC, ng is within the singularity free ellipsoid, <BR> <BR> <BR> <BR> h ; hz h2<BR> <BR> <BR> z 2 + 2 < 1, where h ; is the angular momentum component in the particular a, 2 a3 direction and ai is the radius in the ith direction, then the desired angular momentum Hdesjred is set equal to HCmg If, however, the angular momentum HCmg is outside that

ellipsoid, Hdesired is Hdesired so that gimbal angles are based the singularity free ellipsoid <BR> <BR> <BR> <BR> 8 = starting angle<BR> <BR> <BR> <BR> <BR> H = A (8)<BR> <BR> <BR> <BR> <BR> Do<BR> <BR> <BR> <BR> <BR> aH<BR> A=<BR> @@<BR> A =<BR> ##<BR> <BR> <BR> <BR> <BR> #n+1=#n+AT(AAT+kI)-1(Hdesired-Hn) Hn+1 = A(#n+1) Hdesired-Hn+1en+1= hile + > tolerance.

The invention has been explained in the context of a satellite control, but it can be used in systems, such as robotic systems, which can encounter singularities. With the benefit of the previous discussion of the invention, one of ordinary skill in the may be able to modify the invention and the components and functions that have been described in whole or in part without departing from the true scope and spirit of the invention.