Equilibria, periodicity, and chaotic behavior in spherically constrained relative orbital motion

Harris, Matthew W.; Woodford, Nathaniel

doi:10.1007/s11071-022-07941-2

Cited by 3 publications

(12 citation statements)

References 34 publications

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“…This work is concerned with the control of a spacecraft constrained to remain a fixed distance from another spacecraft. Recent work, [12], studied this problem and identified six unstable equilibrium points and provided stabilizing proportional derivative (PD) control laws. This work builds upon [12] by finding an estimate of the RoA of each of the PD control laws.…”

Section: Contributionsmentioning

confidence: 99%

“…Recent work, [12], studied this problem and identified six unstable equilibrium points and provided stabilizing proportional derivative (PD) control laws. This work builds upon [12] by finding an estimate of the RoA of each of the PD control laws. Through a Lagrangian approach, equations of motion are derived that are identical to the equations of motion described in [12]; however, the Lagrangian approach leads to the natural identification of a constant of motion.…”

Section: Contributionsmentioning

confidence: 99%

“…In this section, linear control laws for stabilization are specified and RoAs for the control laws are computed. Specification of control laws was done in [12]. They are repeated here without proof for completeness.…”

Section: Linear Control and Numerical Roamentioning

confidence: 99%

“…The spherically constrained relative motion problem has been studied recently in the context of exact, convex control relaxations [10], computation of trajectories using splines [11], and nonlinear systems analysis identifying equilibria, periodicity, and chaotic behavior [12]. In the broader context of general spherically constrained motion, there is related work on balltype absorbers [13,14].…”

mentioning

confidence: 99%

“…For the unconstrained relative motion described by linear CW equations, five first integrals were found [21]. Identification of motion constants for nonlinear systems is more challenging, though a single constant has been reported for the spherically constrained CW equations [12].…”

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confidence: 99%

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Lyapunov Functions and Regions of Attraction for Spherically Constrained Relative Orbital Motion

Woodford

Harris

2023

Preprint

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This paper considers the problem of a deputy spacecraft constrained to remain a fixed distance from another spacecraft. The relative dynamics of the deputy spacecraft are derived from a velocity-dependent potential function. A constant of motion is presented that aids in the development of multiple Lyapunov functions and stabilizing control laws. Through both numerical and analytical methods, estimates of the region of attraction are presented for each of the control laws. These regions of attraction serve as domains on which it is conclusively known that the equilibrium points are stabilizable. Lastly, a control law with a spatially maximal region of attraction is presented that can be used to track a time-varying trajectory.

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Section: Contributionsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Section: Linear Control and Numerical Roamentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Lyapunov Functions and Regions of Attraction for Spherically Constrained Relative Orbital Motion

Woodford

Harris

2023

Preprint

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Lyapunov functions and regions of attraction for spherically constrained relative orbital motion

Woodford,

Harris

2024

Nonlinear Dyn

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Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range

Jansson

Harris

2023

Aerospace

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This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex optimization problem and the other requires solving a sequence of convex optimization problems. The approaches are applied to two practical problems in aerospace engineering: a constrained relative orbital motion problem and an attitude control problem. The solve times for both problems and approaches are on the order of seconds. It is concluded that these techniques are rigorous and of practical use in solving nonlinear trajectory design and control problems.

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Equilibria, periodicity, and chaotic behavior in spherically constrained relative orbital motion

Cited by 3 publications

References 34 publications

Lyapunov Functions and Regions of Attraction for Spherically Constrained Relative Orbital Motion

Lyapunov Functions and Regions of Attraction for Spherically Constrained Relative Orbital Motion

Lyapunov functions and regions of attraction for spherically constrained relative orbital motion

Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range

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