Variational Technique for Spacecraft Trajectory Planning

Henshaw, Carl Glen; Sanner, Robert M.

doi:10.1061/(asce)as.1943-5525.0000019

Cited by 12 publications

(10 citation statements)

References 18 publications

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“…(6) can be transformed (11) with c τ − τ a the central anomaly and a and b to be defined in Sec. IV.A.…”

Section: Apocentral Coordinates and Transformationmentioning

confidence: 99%

“…(11) which shows, on the left side, the conventional, Cartesian expression, and on the right, motion on an ellipse in the first two coordinates, with the third coordinate zero. The two sides of this equation are mathematically equivalent, but the elliptical form makes manifest solutions to maneuver problems presented in the second half of the paper.…”

Section: Introductionmentioning

confidence: 99%

“…Richards et al [10] use relative motion dynamics to formulate a mixed-integer linear programming approach that provides minimum delta-v collision-free trajectories by numerical optimization. Henshaw and Sanner [11] used an optimal variational technique and the full gravitating-body orbit dynamics; while fully general, in practice, solutions are difficult to obtain due to small basins of convergence.…”

Section: Introductionmentioning

confidence: 99%

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Trajectory Guidance Using Periodic Relative Orbital Motion

Healy

Henshaw

2015

Journal of Guidance, Control, and Dynamics

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Relative motion of one satellite about another in circular orbit, where the two objects have the same semimajor axis, is periodic in the linearized approximation. A set of orbital elements, the geometric relative orbital elements, which are an exact geometric analogy to the classical orbital elements, can be defined. The relative orbit is manifestly seen to be an ellipse or circle in apocentral coordinates, analogous to perifocal coordinates in inertial motion and different from the local-vertical local-horizontal Cartesian coordinates customarily used for analysis of relative motion problems. These provide a way to do relative motion trajectory design and guidance that stands in contrast to the use of Cartesian coordinates. Algorithms are presented for computing the delta-v and timing for impulsive maneuvers to change a single element: two that change the plane and one that changes the size of the relative orbit. The change in size is a two-maneuver transfer and uses the solution of the three-point periodic boundary value problem, also solved and presented here. This solution permits the direct computation, with no iteration or searching, of the periodic relative orbit that connects two points. Optimization to minimize fuel use can be done with a one-dimensional search.

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“…(6) can be transformed (11) with c τ − τ a the central anomaly and a and b to be defined in Sec. IV.A.…”

Section: Apocentral Coordinates and Transformationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Trajectory Guidance Using Periodic Relative Orbital Motion

Healy

Henshaw

2015

Journal of Guidance, Control, and Dynamics

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“…This principle is also used by the authors of [15] to analytically formulate the optimal control problem for minimum-time and minimum-energy rendezvous trajectories between a controlled chaser spacecraft and a tumbling target object with collision avoidance. A trajectory planning algorithm for minimum-fuel direct docking with a tumbling target is also developed in [16].…”

Section: Introductionmentioning

confidence: 99%

“…The primary evaluation method for rendezvous and docking algorithms is the numerical simulation, with examples given in [7][8][9]11,[14][15][16]. Numerical simulations typically consider three-dimensional six-degree-of-freedom trajectories [7,[14][15][16], although some are limited to planar three-degree-of-freedom (3-DOF) trajectories [8][9][10] or 3-DOF translation-only trajectories [11]. The simulations are quick, do not require expensive equipment, and produce instant results without the need to statistically analyze experimental data.…”

Section: Introductionmentioning

confidence: 99%

Experimental Characterization of Inverse Dynamics Guidance in Docking with a Rotating Target

Wilde

Ciarcià

Grompone

et al. 2016

Journal of Guidance, Control, and Dynamics

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The performance of an inverse dynamics guidance and control strategy is experimentally evaluated for the planar maneuver of a "chaser" spacecraft docking with a rotating "target." The experiments were conducted on an airbearing proximity maneuver testbed. The chaser spacecraft simulator consists of a three-degree-of-freedom autonomous vehicle floating via air pads on a granite table and actuated by thrusters. The target consists of a docking interface mounted on a rotational stage with the rotation axis perpendicular to the plane of motion. Given a preassigned trajectory, the guidance and control strategy computes the required maneuver control forces and torque via an inverse dynamics operation. The recorded data of 150 experimental test runs were analyzed using two-way analysis of variance and post hoc Tukey tests. The metrics were maneuver success, vehicle mass change, maneuver duration, thruster duty cycle, and maneuver work. The results showed that the guidance and control algorithm provided robust performance over a range of target rotation rates from 1 to 4 deg ∕s. = maximum available torque, N · m T z = chaser torque about z axis of laboratory coordinate system, N · m t = maneuver time, s t D = total duration of docking maneuver, s t DA = duration of final docking approach, s t FF = duration of free-flight phase, s t f = final maneuver time, s W = maneuver work, J x C ; y C T = planar position vector of chaser center of mass in laboratory coordinate system, m x T ; y T T = planar position vector of the target center of rotation in laboratory coordinate system, m x; y; z = Cartesian coordinate system fixed in laboratory x 0 ; y 0 ; z 0 = Cartesian coordinate system fixed to chaser spacecraft simulator x 0 0 ; y 0 0 ; z 0 0 = Cartesian coordinate system fixed to target object γ = auxiliary maneuver targeting angle, rad Δm = chaser mass change, kg Δr = positioning tolerance for completion of docking maneuver, m Δt DA = extended maneuver time beyond nominal maneuver time, s Δt G = time step of the guidance algorithm, s ζ = auxiliary maneuver targeting angle, rad θ C = chaser orientation angle in relation to laboratory coordinate system, rad θ T = target orientation angle in relation to laboratory coordinate system, rad χ ij = thruster activity for thruster j at time step ∈ 0; 1, s ω T = target object angular rate, rad∕s

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