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Impact Angle/Time Constraint Guidance Design Based on Fast Terminal Error Dynamics

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Abstract

Considering the problem that the optimal error dynamics can only converge at the terminal time, an impact angle/time constraint missile guidance law with finite-time convergence is designed in this paper, which is based on the pure proportional navigation (PPN) guidance law and the fast terminal error dynamics (FTED) approach. The missile guidance model and FTED equation are given first, and the dynamic equation of impact angle/time error based on PPN is also derived. Then, the guidance law is designed based on FTED, and the guidance error can converge to 0 in a finite time. Furthermore, considering the field of view constraint, the guidance law is improved by using the saturation function mapping method. Finally, a numerical simulation example is given to verify the effectiveness of the guidance law, which shows that the guidance law proposed in this paper can make the missile quickly adjust to the desired states in advance, and effectively relieve the overload saturation pressure of the actuator.

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Abbreviations

a IA :

Biased term to regulate the terminal impact angle

a IT :

Biased term to regulate the terminal impact time

a m :

Guidance acceleration command of the missile

a PPN :

Pure proportional navigation (PPN) term of the acceleration command

(e r, e θ):

Line-of-sight (LOS) frame

M :

Missile

n :

Design parameter controlling the convergence curvature of the saturation function

N :

Proportional navigation gain

p, q :

Regulation parameters of the nonlinear term, which are positive odd numbers and p > q

r :

Vector of the relative distance between the target and the missile

r m :

Position vector of the missile

r t :

Position vector of the target

t :

Current flying time

t 0 :

Initial time

t f :

Terminal time

t d :

Desired impact time

(t m, n m):

Velocity frame

t go :

Remaining flight time

T :

Target

v m :

Velocity vector of the missile

(x 0, y 0):

Position of the missile at the initial time

(x f, y f):

Position of the missile at the terminal time

(X, Y):

Inertial frame

α :

Coefficient of the linear term

β :

Coefficient of the nonlinear term

ε :

Tracking error

ε t :

Impact time error

ε ϕ :

Impact angle error

θ m :

Velocity leading angle

θ max :

Maximum field of view (FOV) angle of the missile

σ :

LOS angle

ϕ 0 :

Flight path angle of the missile at the initial time

ϕ d :

Desired terminal impact angle

ϕ f :

Flight path angle of the missile at the terminal time

ϕ m :

Flight path angle

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Authors and Affiliations

  1. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Xuesheng Qin  (秦雪升), Yuanhe Liu  (刘远贺), Kebo Li  (黎克波) & Yangang Liang  (梁彦刚)

  2. Human Key Laboratory of Intelligent Planning and Simulation for Aerospace Mission, Changsha, 410073, China

    Xuesheng Qin  (秦雪升), Yuanhe Liu  (刘远贺), Kebo Li  (黎克波) & Yangang Liang  (梁彦刚)

Authors
  1. Xuesheng Qin  (秦雪升)
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  2. Yuanhe Liu  (刘远贺)
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  3. Kebo Li  (黎克波)
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  4. Yangang Liang  (梁彦刚)
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Corresponding author

Correspondence to Yangang Liang  (梁彦刚).

Additional information

Foundation item: the National Natural Science Foundation of China (No. 12002370)

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Qin, X., Liu, Y., Li, K. et al. Impact Angle/Time Constraint Guidance Design Based on Fast Terminal Error Dynamics. J. Shanghai Jiaotong Univ. (Sci.) 27, 823–832 (2022). https://doi.org/10.1007/s12204-022-2509-3

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  • DOI: https://doi.org/10.1007/s12204-022-2509-3

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