IFAC PapersOnLine 51-1 (2018) 47–52 ScienceDirect ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.05.009 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Guidance, Impact angle, Dynamic inversion, Sliding mode control, Maneuvering targets, Three-dimensional engagements 1. INTRODUCTION Guidance is a directing algorithm which helps the vehicle to come closer and closer to a goal point, using the in- formation gathered from its environment, Ghose (2010). As the interception always occurs in three-dimensional (3D) space, it is desirable to design guidance using 3D engagement kinematics. In order to enhance the effective- ness of missile, kill probability and also to reduce the collateral damage, impact angle constraints are beneficial. In practice, the 3D engagement dynamics are coupled in nature. Nonlinear guidance design, without decoupling the dynamics, is expected to have better performance. Sliding mode control (SMC) has become popular due to its robustness against uncertainties, Utkin (2009). In Kumar (2017), the guidance law was designed using SMC and 3D coupled engagement dynamics, but limited to stationary targets. In Weimeng (2007); Hu (2011); Biming (2013), the authors decoupled the 3D engagement dynamics in two mutually perpendicular planes and then guidance laws were designed for every plane using SMC. But the performance of the guidance laws degrade under large heading errors due to the assumption of decouple dynamics in guidance design. In Lee (2013), SMC based guidance law was proposed using dual sliding surfaces. Although the performance of the guidance law was satisfactory, it does not guarantee finite convergence of the error. In Lianzheng (2008), the author first developed a mathematical model for head pursuit in space and then designed a guidance law with robustness against matched uncertainties. An impact angle guidance law was designed using SMC in Gu (2007). However, the paper does not provide the analysis of the sliding mode dynamics. A 3D optimal sliding guidance law was proposed in Chen (2014). As the authors used the decoupled dynamics of the system, it cannot capture the original engagement scenario. In WJ (2010), a SMC based impact angle guidance law was developed for the anti-ship missile. But, the errors and its derivatives do not converge within the finite time. Apart from SMC, there are various other nonlinear control techniques, for example dynamic inversion (DI), which can be used for guidance design. In recent past, DI is being widely used to design the guidance and control system. A robust integrated guidance and control law was proposed in Shu (2012), where the authors derived the guidance law using DI. Later, the observer is used to estimate the compound disturbances and compensate them. In Shi- cheng (2016), an impact time guidance law was developed using the concept of virtual leader and DI. Kim (2013) introduced a conjunction among navigation, guidance, and control for an unmanned hovercraft. Furthermore, the line- of-sight (LOS) guidance law was adopted and a neural network based adaptive DI was used to design the control algorithm. It was shown that the vehicle properly follow the prescribed path but it was unable to achieve the desired surge speed initially. In Song (2011), a robust nonlinear control system incorporating DI and SMC was proposed to control the attitude of RLV re-entry process. In the literature, there exist vast amount of works on impact angle guidance for planar engagements. In Ku- mar (2012), SMC based impact angle guidance law was proposed. Impact angle was redefined in terms of the desired LOS angle. However, this guidance law encounters Abstract: Guidance system, which is an integral part of missile flight control system, plays a key role in achieving a desired performance subjected to various criteria. This paper focuses on the design of terminal impact angle constrained guidance laws, against maneuvering targets, for three- dimensional engagements. Impact angles are defined by the elevation and azimuth angles of line-of-sight with respect to the inertial frame of reference. The derivation of guidance strategies are performed with the nonlinear coupled engagement kinematics using dynamic inversion and sliding mode control techniques. The proposed guidance laws are applicable even for large heading angle errors. The comparative study of performance of both guidance laws is done using numerical simulations for various engagement scenarios. * Indian Institute of Technology Bombay, Powai, Mumbai, 400076 India (bhaskar.aero13@gmail.com). ** Indian Institute of Technology Bombay, Powai, Mumbai, 400076 India (srk@aero.iitb.ac.in). *** Indian Institute of Technology Bombay, Powai, Mumbai, 400076 India (arnab@aero.iitb.ac.in). Bhaskar Biswas, * Shashi Ranjan Kumar, ** Arnab Maity *** Three-Dimensional Nonlinear Impact Angle Guidance for Maneuvering Targets