Curvature Constrained Cubic Spline Impact Angle Guidance for Intercepting Stationary Targets

In this paper, a cubic spline guidance law is proposed for intercepting a stationary target at a desired impact angle in surface-to-surface engagement scenarios. An inverse method is used, which represents the altitude as a cubic polynomial of the downrange. The paper addresses many shortcomings of earlier work in this area. In particular, an explicit guidance expression is derived, which makes the guidance law effective and accurate in the presence of disturbances and uncertainties. It is also shown that the guidance command can be obtained using a single cubic spline polynomial even for impact angles greater than and equal to $\pi / 2$ , while resulting in substantial improvement in terms of lateral acceleration and length of the trajectory. The paper also obtains an analytically derived capture region. The proposed guidance law is conceptually simple, independent of time-to-go, computationally inexpensive, and does not need linearization.

[1]  Min-Jea Tahk,et al.  Analytic Solutions of Generalized Impact-Angle-Control Guidance Law for First-Order Lag System , 2013 .

[2]  F. Nesline,et al.  Missile guidance design tradeoffs for high-altitude air defense , 1983 .

[3]  Michael E. Hough.  Explicit guidance along an optimal space curve , 1989 .

[4]  Jang Gyu Lee,et al.  Biased PNG law for impact with angular constraint , 1998 .

[5]  Debasish Ghose,et al.  Impact Angle Constrained Interception of Stationary Targets , 2008 .

[6]  J. Page,et al.  Guidance and control of maneuvering reentry vehicles , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[7]  Gary D. Knott,et al.  Interpolating Cubic Splines , 2001, J. Approx. Theory.

[8]  R. Esmaelzadeh,et al.  Near optimal guidance law for descent to a point using inverse problem approach , 2008 .

[9]  Mohammad Reza Mortazavi,et al.  Near optimal re-entry guidance law using inverse problem approach , 2008 .

[10]  David B. Doman,et al.  Adaptive Terminal Guidance for Hypervelocity Impact in Specified Direction , 2005 .

[11]  Youan Zhang,et al.  Guidance law with impact time and impact angle constraints , 2013 .

[12]  Min-Jea Tahk,et al.  Optimality of Linear Time-Varying Guidance for Impact Angle Control , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Debasish Ghose,et al.  Impact Angle Constraint Guidance Law using Cubic Splines for Intercepting Stationary Targets , 2012 .

[14]  M. Tahk,et al.  Bias-Shaping Method for Biased Proportional Navigation with Terminal-Angle Constraint , 2013 .

[15]  Taek Lyul Song,et al.  Impact angle control for planar engagements , 1999 .

[16]  Debasish Ghose,et al.  State-Dependent Riccati-Equation-Based Guidance Law for Impact-Angle-Constrained Trajectories , 2009 .

[17]  Debasish Ghose,et al.  Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets , 2010 .

[18]  K-S Kim,et al.  Practical guidance law controlling impact angle , 2007 .

[19]  Min-Jea Tahk,et al.  Guidance law to control impact time and angle , 2005, 2005 International Conference on Control and Automation.

[20]  Andrey V. Savkin,et al.  Circular navigation guidance law for precision missile/target engagements , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[21]  Min-Jea Tahk,et al.  Time-to-go Polynomial Guidance with Trajectory Modulation for Observability Enhancement , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[22]  Debasish Ghose,et al.  Terminal Impact Angle Constrained Guidance Laws Using Variable Structure Systems Theory , 2013, IEEE Transactions on Control Systems Technology.

[23]  Frederick H. Lutze,et al.  Fixed-trim re-entry guidance analysis , 1982 .

[24]  M. Kim,et al.  Terminal Guidance for Impact Attitude Angle Constrained Flight Trajectories , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[25]  Yuri Ulybyshev.  Terminal Guidance Law Based on Proportional Navigation , 2005 .

[26]  James E. Lebensohn,et al.  A Treatise on Conic Sections. , 1954 .

[27]  Myung-Gon Yoon.  Relative circular navigation guidance for the impact angle control problem , 2008, IEEE Transactions on Aerospace and Electronic Systems.

[28]  Min-Jea Tahk,et al.  Augmented Polynomial Guidance With Impact Time and Angle Constraints , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[29]  Samir Chabra.  Fuzzy Logic-based Terminal Guidance with Impact Angle Control , 2007 .

[30]  T. Shima,et al.  Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle , 2008 .

[31]  Debasish Ghose,et al.  Intercepting maneuvering target with specified impact angle by modified SDRE technique , 2012, 2012 American Control Conference (ACC).

[32]  Koray S. Erer,et al.  Indirect Impact-Angle-Control Against Stationary Targets Using Biased Pure Proportional Navigation , 2012 .

[33]  Chang-Hun Lee,et al.  Polynomial Guidance Laws Considering Terminal Impact Angle and Acceleration Constraints , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[34]  Gregg A. Harrison,et al.  Hybrid Guidance Law for Approach Angle and Time-of-Arrival Control , 2012 .

[35]  Taek Lyul Song,et al.  Time-optimal impact angle control for vertical plane engagements , 1999 .

[36]  J. M. Cameron.  Explicit guidance equations for maneuvering re-entry vehicles , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[37]  W. Marsden.  I and J , 2012 .

[38]  Thor I. Fossen,et al.  Integral LOS Path Following for Curved Paths Based on a Monotone Cubic Hermite Spline Parametrization , 2014, IEEE Transactions on Control Systems Technology.

[39]  Shashi Ranjan Kumar,et al.  Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints , 2012 .

[40]  Min-Jea Tahk,et al.  Generalized Formulation of Weighted Optimal Guidance Laws with Impact Angle Constraint , 2012, IEEE Transactions on Aerospace and Electronic Systems.