A collision avoidance algorithm for unmanned aerial vehicles (UAVs) based on the conventional proportional navigation (PN) guidance law is investigated The proportional navigation guidance law being applied to a wide range of missile guidance problems is tailored to the collision avoidance of UAVs This can be accomplished by guiding the relative velocity vector of the aircraft to a vector connecting the current aircraft position to the safety boundary of the target aircraft Stability of the proposed algorithm is also studied using the circle criterion The stability condition can be established by choosing the navigation coefficient within a certain bound The guidance law is extended to 3-dimensional maneuver problems Inherent simplicity and robustness of the PN guidance law provides satisfactory collision avoidance performance with different initial conditions

Proportional navigation-based collision avoidance for UAVs

A new gain-varying algorithm for the three-dimensional pure proportional navigation (PPN) guidance problem is presented using the differential geometric (DG) guidance command. To this end, classical differential geometry theory is introduced, firstly, to transform and modify the DG guidance curvature command so as to facilitate the practical implementation and to avoid singularity of the guidance command. Then, a new gain-varying guidance scheme is developed using the modified DG guidance command, as well as the principle of the PPN guidance law, the new guidance law does not need the evaluation of time-to-go information. Furthermore, the capture analysis of the PPN-type guidance law is qualitatively studied in terms of the DG formulations, and a post-launch capture condition is derived and expressed in geometric terms. Simulation results demonstrate that the proposed guidance algorithm performs better than the conventional PPN guidance law in the case of intercepting maneuvering targets.

Gain-Varying Guidance Algorithm using Differential Geometric Guidance Command

Using the recently developed model predictive static programming (MPSP) technique, a suboptimal guidance law is presented in this paper considering the three-dimensional nonlinear engagement dynamics. The main feature of the guidance law is that it accurately satisfies terminal impact angle constraints in both azimuth as well as elevation, in addition to being capable of hitting the target with high accuracy. Moreover, it minimizes the control eort (i.e. the latax demand) throughout the engagement and hence leads to an optimal trajectory as well. The guidance law is primarily based on nonlinear optimal control theory and hence imbeds eective trajectory optimization concept into the guidance law. The performance of the proposed scheme is investigated using nonlinear simulation studies for stationary, moving and maneuvering ground targets, by considering both thrusted as well as unthrusted vehicles. Multiple munition engagement results are also presented to show the eectiveness of the proposed guidance scheme in such a scenario. A comparison plot for the Zero Eort Miss (ZEM) is also included, which reconfirms the superiority of the proposed optimal guidance over an augmented proportional navigation guidance available in the literature to engage maneuvering targets.

A Nonlinear Suboptimal Guidance Law with 3D Impact Angle Constraints for Ground Targets

Purpose – To study the application of three‐dimensional differential geometric (DG) guidance commands to a realistic missile defense engagement, and the application of the Newton's iterative algorithm to DG guidance problems.Design/methodology/approach – The classical differential geometry theory is introduced firstly to transform all the variables in DG guidance commands from an arc length system to the time domain. Then, an algorithm for the angle‐of‐attack and the sideslip angle is developed by assuming the guidance curvature command and guidance torsion command equal to its corresponding value of current trajectory. Furthermore, Newton's iteration is utilized to develop iterative solution of the stated algorithm and the two‐dimensional DG guidance system so as to facilitate easy computation of the angle‐of‐attack and the sideslip angle, which are formulated to satisfy the DG guidance law.Findings – DG guidance law is viable and effective in the realistic missile defense engagement, and it is shown to ...

Iterative solution to differential geometric guidance problem

Geometric approach to capture analysis of PN guidance law

Generalized PN Guidance Law for a Practical Pursuer Evader Engagement

This work deals with Algorithm for In Flight Radome Error Compensation with simulated data of radome test result for both In Plane Error and Cross Plane Error which are obtained as function of kinematic look angles. The se data are generally stored in On -Board Computer of either Interceptor or Seeker for compensation. Accurate information of kinematic look angles is required for proper interpolation of stored data. Measured gimbal angles lag kinematic gimbal angles throug h track loop time constant, which can be time varying depending on noise content and tracking accuracy of measured sight line rate. In this paper, measured gimbal angles are utilized for computation of radome errors from look up table for compensation. Ear lier results suggest that compensation within track loop yields better performance compared to compensation outside track loop. In this paper it is shown that, performance of homing loop for outside track loop compensation when computed radome errors are m odified by a suitable filter, is quite close to performance with radome error compensation inside track loop. This makes Interceptor system more reliable because in the event of any breakage of radome, spare one can fit in and corresponding test data can b e easily inserted in Interceptor OBC for accurate compensation rather than tampering sensitive software of Seeker OBC for inside track loop compensation. Suitable formulae are also derived for radome errors in 3 -D engagement scenario comprising both In -Pla ne and Cross Plane Errors. Additional results are also derived showing how In Plane and Cross Plane Error characteristics of radome covering its full engagement geometry obtained by experiment can be utilized for on -board compensation. In all these results , realistic simulated seeker noise profile, gimbal angle noise are utilized to claim for practical feasibility of this work.

In Flight Radome Error Compensation through Simulated Test Data

Different proportional navigation (PN)-based guidance laws-pure proportional navigation (PPN), true proportional navigation (TPN), and proportional navigation with boost acceleration compensation generally used cannot maintain fundamental parameter of proportional navigation, viz, Navigation constant to the desired value in the presence of significantly high lead angles and missile longitudinal accelerations/decelerations In a real-life situation with sensor noises and hardware constraints, this navigation constant should be maintained tightly at the selected value, which is generally between 3 and 4, for optimum performance In this paper; a new 3-D modified PN guidance law based on a total demand vector concept is presented, which can maintain the navigation constant to the designer-selected value for any 3-D engagement scenario with associated lead angles and any velocity profile with missile longitudinal accelerations1 decelerations Generality of this guidance law is brought out and superiority of this guidance law over the commonly used proportional navigation-based laws like PPN, TPN and PN with boost acceleration compensation has been demonstrated by applying it to the real-life 3-D engagement scenarios of different hypothetical missiles

http://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1992/1029

3-D Modified Proportional Navigation Guidance Law based on a Total Demand Vector Concept

Radio frequency seeker model, including receiver angle error noise modelling and filtering of noise from seeker measurement, is presented in this paper. The effects of eclipsing, radar cross section fluctuation, etc on seeker sight-line rate measurement are highlighted. The formulation for colour noise modelling of sight-line rate noise is derived based on the knowledge of seeker receiver angle error noise model. Two Kalman filter configurations for filtering of noise from seeker output have been considered in this paper, based on sight-line rate kinematics and noise characteristic. It has been  observed from the simulation studies that sight-line rate signal varies slowly at higher interceptor-target ranges; with severe colour noise in sight line rate measurement, and therefore higher weightage for noise attenuation is beneficial in Kalman filter configuration. So, kinematic plus state augmentation for colour noise are considered for adequate filtering for higher interceptor-target ranges. Whereas for lower interceptor-target ranges, sight-line rate changes appreciably, which have been tracked by a simplified/modified spherical coordinate model, which uses knowledge of interceptor-target  engagement dynamics. For both the filters, benefits of colour noise modelling and process model augmentation through coloured noise states, for filtering severe colour noise of seeker, has been demonstrated.

http://publications.drdo.gov.in/ojs/index.php/dsj/article/download/1997/1034

Radio Frequency Seeker Modelling and Seeker Filter Design

The Mach number, angle of attack and altitude of operation for an interceptor vary widely during the course of its trajectory. As a result, the interceptor Center of Pressure (CP) locations move significantly around a given Center of Gravity (CG) location at these operating conditions. This results in an inevitable variation in aerodynamic static stability leading to stable and unstable operating regions. In order to ensure good speed of response during the interceptor homing phase, lesser static stability is desirable. Hence the requirement to handle aerodynamic instability at some other operating conditions in the interceptor envelope become inevitable. Since flexibility has a strong bearing on autopilot design, it becomes necessary to control unstable operating points in the presence of flexibility modes. Despite the static stability variation, aerodynamic design can control the level of maximum instability of the configuration. Hence the maximum static instability the autopilot can handle has to be specified for aerodynamic configuration design. This paper brings out the limitations of autopilot design in controlling an unstable interceptor with low bending mode frequencies in terms of maximum instability the autopilot design can handle, which serves as an important input for aerodynamic design.

P.K. Tiwari

Papers

Generalized PN Guidance Law for a Practical Pursuer Evader Engagement

In Flight Radome Error Compensation through Simulated Test Data

3-D Modified Proportional Navigation Guidance Law based on a Total Demand Vector Concept

Radio Frequency Seeker Modelling and Seeker Filter Design

Limitations of autopilot design for controlling a statically unstable flexible interceptor