Gimbal-Lock Escape via Orthogonal Torque                                                         Compensation

Leve, Frederick A.; Muñoz, Josué; Fitz-Coy, Norman

doi:10.2514/6.2010-8069

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…The GSR inverse uses explicitly timevarying dither inside E shown in (17) to bump out of the local extrema of a gimbal-lock singularity. Another method that is not found through local optimization of the BI cost function can be seen in [9]. This method analytically proves that the system will never get locked at gimbal-lock.…”

Section: ) Generalized Inverse Steering Law (Gisl)mentioning

confidence: 98%

“…The linearity of the perturbation in the methods in [9] makes it possible to prove that gimbal-lock will always be avoided.…”

Section: ) Generalized Inverse Steering Law (Gisl)mentioning

confidence: 98%

“…These singularity parameters consider whether the singularity is hyperbolic or elliptic and thus, provide torque error and no (or less) null-motion at elliptic singularity and null-motion and no (or less) torque error at hyperbolic singularities. It should be noted that this steering algorithm, as well as, all previously defined except the GSR inverse, are susceptible to gimbal-lock and a method such as the one in [9] should be used in addition to the HSL in (38). In [14], the projection matrix P is made to be nonsingular as a function of the right singular values matrix V, of the singular value decomposition of A, as follows:…”

Section: ) Hybrid Steering Logicmentioning

confidence: 99%

“…At singularity, for a four-SGCMG pyramid arrangement this system has a singularity definition matrix M ∈ 2×2 (see [7], [9]) and therefore, the det(M) will be zero or negative (i.e., Q is semidefinite or indefinite) for hyperbolic internal singularities and positive (i.e., Q is definite) for elliptic singularities. Considering, parameters α and β are defined as follows:…”

Section: ) Hybrid Steering Logicmentioning

confidence: 99%

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Evaluation of Steering Algorithm Optimality for Single-Gimbal Control Moment Gyroscopes

Leve

2014

IEEE Trans. Contr. Syst. Technol.

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Analytic optimization methods typically used to derive optimal steering algorithms for single-gimbal control moment gyros do not consider the structure of the Jacobian matrix mapping the gimbal rates onto the desired torque within their cost function. Many of the steering algorithms resulting from these optimization methods systematically take first and second derivatives, forming the Jacobian and Hessian matrices to obtain a solution. However, the optimality is usually a local result and cannot be mapped back to its resulting performance. It is shown that the majority of steering algorithms are optimal with respect to one specific cost function previously published and that the design of the weighting matrices within the cost is what distinguishes steering algorithms. The author analytically shows how the blended inverse, Moore-Penrose pseudoinverse, generalized inverse steering law, singularity robust inverse, generalized singularity robust inverse, singular direction avoidance, local-gradient methods, and the hybrid steering logic are derived from the same optimizations but their sense of optimality is lost because the structure of singularities is not considered in the optimization process. In addition, the author also points out that the design of the quadratic costs weighting matrix used for optimization and desired gimbal rate is of the highest importance in differentiation between steering law performance.

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Section: ) Generalized Inverse Steering Law (Gisl)mentioning

confidence: 98%

“…The linearity of the perturbation in the methods in [9] makes it possible to prove that gimbal-lock will always be avoided.…”

Section: ) Generalized Inverse Steering Law (Gisl)mentioning

confidence: 98%

Section: ) Hybrid Steering Logicmentioning

confidence: 99%

Section: ) Hybrid Steering Logicmentioning

confidence: 99%

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Evaluation of Steering Algorithm Optimality for Single-Gimbal Control Moment Gyroscopes

Leve

2014

IEEE Trans. Contr. Syst. Technol.

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“…One of the few steering laws that escapes from every singularity when properly tuned for each maneuver is the offdiagonal singularityrobust (o-DSR) steering law developed by Wie [1], which modifies the pseudoinverse to enforce escape. Other methods enhance existing steering laws by perturbing the reference moment [16,17]. In either of these approaches, the pseudoinverse is used to both enforce escape and to damp excessive gimbal rates, presenting a tradeoff between minimizing escape time and minimizing oscillatory error moments and gimbal rates [18].…”

Section: Introductionmentioning

confidence: 99%

Directional Singularity Escape and Avoidance for Single-Gimbal Control Moment Gyroscopes

Valk

Berry

2018

Journal of Guidance, Control, and Dynamics

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Inertia parameters M d Gyroscopic moment due to satellite rotation τ, τ c Gyroscopic moment due toγ orγ c τ s Gyroscopic moment due toγ s τ ref , e Gyroscopic moment reference and error J, P, Q Cost function and weighing matrices Ω c , µ Rate and momentum magnitude of one flywheel b i Projection ofτ ref on plane orthogonal toĝ i ψ i Angle betweenĥ i and b i p i , d i Gimbal potential and escape potential δ man Manipulability measure δ track , δ pot Tracking index and total gimbal potential z j , κ j Tracking index parameters σ min Singular value below which damping is applied σ acp Singular value for tracking with acceptable rates kγ, k Ω Gimbal and flywheel motor gainṡ ω c Body acceleration for computing motor torques β, k p , k v Satellite and attitude control constants τ min , τ max Minimum and maximum moment magnitude η, d 0 , ζ DSEA control parameters λ, φ, , W i o-DSR control parameters RA Left superscript denoting evaluation at nearest reference-aligned singularity 1

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