Elliptic Guidance

Livermore, Riley A.; Tsalik, Ronny; Shima, Tal

doi:10.2514/1.g003565

Cited by 24 publications

(12 citation statements)

References 29 publications

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“…In this paper, an ellipse whose main axis is parallel to a certain axis of the reference frame is called a ''standard ellipse''. The ''standard ellipse'' equation is solved at a specific rotation angle in [37], [38], that is, the flight path angle at the launch point or the target point, without a general analytical expression. In fact, there is at most one ''standard ellipse'' after an arbitrary rotation angle is determined.…”

Section: A Elliptic Guidance Law 1) Elliptical Trajectory Designmentioning

confidence: 99%

“…Inspired by [38], this paper guarantees the tracking effect by enforcing the sum of the distance between the vehicle and two foci constant. This simple guidance concept is the reason why the ellipse is chosen as a nominal trajectory.…”

Section: ) Improved Sliding Mode Guidance Lawmentioning

confidence: 99%

“…where k 1 and k 2 are adjustable parameters. From (37), (38) and (42), the curve is eventually formulated as:…”

Section: B Bézier Curve Guidance Lawmentioning

confidence: 99%

“…In [37], a nominal elliptical trajectory and the normal acceleration along it in the rotated frame are proposed, but the rotation angle is specific corresponding to flight path angle. In [38], Livermore developed the elliptic guidance law into a threepoint guidance concept and applied a proportional-integralderivative (PID) controller to track the ellipse. In conclusion, the three-point guidance concept is simple to implement and suitable for trajectory planning.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, a smooth geometric trajectory is designed in advance to achieve desired impact angle. The motion in vertical plane is to track elliptical trajectory, which is partly derived from [38], but the judgment method of ellipse existence is exactly given. To avoid undesired acceleration commands which frequently change signs, an improved SMC method based on a position-dependent weight is developed.…”

Section: Introductionmentioning

confidence: 99%

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Three-Dimensional Geometric Descent Guidance With Impact Angle Constraint

et al. 2020

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A novel trajectory-shaping guidance law with impact angle constraint is proposed for attacking stationary targets in a three-dimensional environment. The guidance concept, derived from the inverse dynamic method, is to design an analytical curve trajectory satisfying the impact angle in advance and obtain reasonable control commands. The vehicle motion is decomposed in the horizontal and vertical planes of the inertial coordinate system. Firstly, the trajectory in the vertical plane is designed as ellipse, which can be shaped by adjusting its axis direction. An improved sliding mode control (SMC) method, which adds position-dependent correction to the weight in sliding mode surface, is adopted to track the nominal trajectory. Therefore, the vehicle approaches the ellipse quickly and smoothly in the early stage and hits the stationary target accurately. Secondly, a third-order Bézier curve with adjustable parameters is employed as the prior nominal trajectory in the lateral plane. When the vehicle deviates from the original trajectory due to perturbation or self-limitation, it will turn to the updated curve in real time according to its own condition. Moreover, coupling of acceleration commands in the two planes is resolved through acceleration decomposition, which qualifies independent trajectory design in two planes and paves a new way to more curve combinations. Nominal testing and Monte Carlo simulations on the proposed method are carried out. Simulation results demonstrate that the proposed guidance law is highly designable and strongly robust.

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Section: A Elliptic Guidance Law 1) Elliptical Trajectory Designmentioning

confidence: 99%

Section: ) Improved Sliding Mode Guidance Lawmentioning

confidence: 99%

“…where k 1 and k 2 are adjustable parameters. From (37), (38) and (42), the curve is eventually formulated as:…”

Section: B Bézier Curve Guidance Lawmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%