Non-Symmetric Gyroscope Skewed Pyramids

Abstract

The novel contribution in this manuscript is an expansion of the current state-of-the-art in the geometric installation of control moment gyroscopes beyond the benchmark symmetric skewed arrays and the four asymmetric arrays presented in recent literature. The benchmark pyramid symmetrically skewed at 54.73 degrees mandates significant attention to singularity avoidance, escape, and penetration, while the most recent four asymmetric arrays are strictly useful in instances where space is available to mount at least one gyro orthogonal to the others. Skewed arrays of gyros and the research-benchmark are introduced, followed by the present-day box-90 and “roof” configurations, where the roof configuration is the first prevalently used asymmetric geometry. Six other asymmetric options in the most recent literature are introduced, where four of the six options are obviously quite useful. From this inspiration, several dozen discrete options for asymmetric installations are critically evaluated using two figures of merit: maximum momentum (saturation) and maximum singularity-free momentum. Furthermore, continuous surface plots are presented to provide readers with countless (infinite) options for geometric installations. The manuscript firmly establishes many useful options for engineers who learn that the physical space on their spacecraft is insufficient to permit standard installations.

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

“…Hailey [25] performed experimental verification of the analytical results for PD and linear-quadratic regulator (LQR), and additionally tested a classic bang-bang controller, furthermore implementing control input shaping to eliminate an undesirable spike in the response of the PD controller. Harrington later performed [26] multivariate control (using LQG) with piezoelectric sensors [16] and actuators along the length of the flexible appendage. Burke performed experimental verification of Harrington's technique.…”

“…While translation is straightforward (a second-order ordinary differential equation), rotation is complex since the governing equations are nonlinear and coupled and remain unsolved in general form without simplifying assumptions. Thus, rotational motion remains an area of considerable recent developments [14][15][16][17][18][19], where [14][15][16] are recent works in the control of rotational mechanics, while [17][18][19] represent very recent developments in system identification, in particular, identification of material properties and system parameters (e.g., modal properties like natural frequencies and moment of inertia) that permit control design of highly flexible multi-body systems. New research in kinematic representations of the motion is presented in [20].…”

Lasers for Satellite Uplinks and Downlinks

“…Substantial developments in acquisitions, tracking, and fine pointing evolved in the twenty first century and continue to this day including substantial development in target acquisition [61,64,65,[67][68][69][70][71][72], target tracking [62,63,75,76,78,81,[83][84][85][86][87][89][90][91], and fine pointing [60,73,74,77,79,80,82,88] at the Naval Postgraduate School amongst several other institutions achieving microradian pointing accuracy and closely pursuing nano-radian accuracy.…”

Preparing for Satellite Laser Uplinks and Downlinks

“…Substantial developments in acquisitions, tracking, and fine pointing evolved in the twenty-first century and continue to this day including substantial development in target acquisition [86,89,90,[92][93][94][95][96][97], target tracking [87,88,100,101,103,106,[108][109][110][111][112][114][115][116], and fine pointing [85,98,99,102,104,105,107,113] at the Naval Postgraduate School amongst several other institutions achieving microradian pointing accuracy and closely pursuing nano-radian accuracy.…”