Implementation Of Guidance Laws Research Articles

Dynamic Encircling Cooperative Guidance for Intercepting Superior Target with Overload, Impact Angle and Simultaneous Time Constraints

This paper proposes a dynamic encircling cooperative guidance (DECG) law to enable multiple interceptors to cooperatively intercept a superior target, considering low velocity, limited overload, impact angle and simultaneous arrival constraints. First, the feasible escaping area of the target is analyzed and a dynamic encircling strategy for the target is established. This strategy efficiently provides virtual escaping points, allowing interceptors to dynamically encircle the target without excessive energy consumption, ultimately leading to a successful interception. Second, to enhance the physical feasibility of the kinematic equations governing the interaction between interceptors and target at the virtual escaping points, the independent variable is substituted and the kinematic equations are remodeled. Convex optimization is employed to address the multi-constraint optimal guidance problem for each interceptor, thereby facilitating simultaneous interception. Compared with the existing guidance laws, DECG has a more practical and feasible cooperative strategy, is able to handle more constraints including the interceptor’s own constraints and cooperative constraints, and does not rely on the precise calculation of explicit remaining flight time in the guidance law implementation. Lastly, the effectiveness, superiority and robustness of the DECG law are evaluated through a series of numerical simulations, and its performance is compared with that of the cooperative proportional navigation guidance law (CPNG).

Differentiator-Based Incremental Three-Dimensional Terminal Angle Guidance With Enhanced Robustness

In this article, an incremental guidancelaw with terminal angle constraint is proposed against maneuvering targets in the 3-D space. First, a sliding surface is constructed such that its first-order dynamics excludes the relative range and line-of-sight angles in the perturbation. This manipulation avoids unboundedperturbations induced by target maneuvers near collision. Then, a benchmark guidance law is derived via the nonlinear dynamic inversion (NDI) based sliding mode control (NDI-SMC). To further enhance guidance system robustness, an incremental nonlinear dynamic inversion (INDI) based SMC (INDI-SMC) 3-D guidance law is developed. The INDI-SMC guidance law exploits the first-order derivative of the sliding variable and guidance command output at the latest step, which leads to reduced perturbation and thus requires smaller gains than the NDI-SMC guidance law. A multivariable continuous differentiator is employed to estimate the sliding variable's first-order derivative for guidance law implementation. Moreover, the stability of the differentiator is analyzed and the guidance robustness under uncertainties is compared. Extensive numerical simulations and a Monte Carlo test are conducted to verify effectiveness and robustness of the proposed method.

An Iterative Guidance and Navigation Algorithm for Orbit Rendezvous of Cooperating CubeSats

Modern space missions often require satellites to perform guidance, navigation, and control tasks autonomously. Despite their limited resources, small satellites are also involved in this trend, as in-orbit rendezvous and docking maneuvers and formation flying have become common requirements in their operational scenarios. A critical aspect of these tasks is that these algorithms are very much intertwined with each other, although they are often designed completely independently of one another. This paper describes the design and simulation of a guidance and relative navigation architecture for the rendezvous of two cooperating CubeSats. The integration of the two algorithms provides robustness to the solution, by simulating realistic levels of noise and uncertainty in the guidance law implementation. The proposed guidance law is derived based on the linearized equations of orbital motion, written in terms of spherical coordinates. The trajectory is iteratively corrected at a fixed time step, so that errors from the navigation and the initial orbital condition can be recovered. The navigation algorithm processes the bearing and range measurements from a camera and an intersatellite link through an unscented filter to provide the information required from the guidance law. A Monte Carlo campaign based on a 3-DOF simulation demonstrates the effectiveness of the proposed solution.

Wingman-Based Estimation and Guidance for a Sensorless PN-Guided Pursuer

A novel wingman-based estimation and guidance concept is proposed for a sensorless pursuer. The pursuer is guided towards a maneuvering aerial target using proportional navigation (PN) guidance law. The wingman is assumed to acquire bearings-only measurements of the target and to accurately track the wingman-pursuer relative position. The pursuer-target relative states, needed for the pursuer guidance law implementation, are estimated from the available data to the wingman. The proposed state estimator is implemented using extended Kalman filter equations and transformed wingman's measurements into the moving pursuer frame. Analytical observability analysis of the proposed wingman-based measuring concept suggests an optimal wingman trajectory in terms of the wingman-pursuer relative geometry. The resulting wingman trajectory ensures maximum observability of the pursuer-target line-of-sight (LOS) angle, which is a crucial parameter needed for the PN guidance law implementation. The resulting trajectory can be directly related to the well-known LOS guidance concept. Monte Carlo simulation results validate the analytical findings and demonstrate the potential of the proposed concept.

A novel three‐dimensional guidance law implementation using only line‐of‐sight azimuths

SummaryA novel three‐dimensional guidance law using only line‐of‐sight azimuths based on input‐to‐state stability and robust nonlinear observer is proposed for interception of maneuvering targets. The proposed guidance law does not need any prior information of unknown bounded target maneuvers and uncertainties. Since in practice the line‐of‐sight rate is difficult for a pursuer to measure accurately, a nonlinear robust observer is introduced to estimate it. A three‐dimensional guidance law with bearing only measurement is obtained for interception of maneuvering targets. The presented algorithm is tested using computer simulations against a maneuvering target. Copyright © 2014 John Wiley & Sons, Ltd.

Guidance law implementation with performance recovery using an extended high-gain observer

Guidance law of a homing missile is implemented using an extended high gain observer without the model assumptions on target maneuvers. First, for a class of multi-input–multi-output nonlinear systems, extended high-gain observers are used for output feedback control with partial practical stabilization. Then the method is applied to the guidance law implementation of a homing missile with bearing only measurement. Simulation results show satisfactory performance.

Evaluation of optimal-guidance algorithm for aeroassisted orbit transfer

In this paper we perform an evaluation of a guidance algorithm for aeroassisted orbit transfer based on the method of matched asymptotic expansions (MAEs). It is shown that, by exploiting the structure of the matched asymptotic expansion solution procedure, the original problem, which requires the solution of a set of 20 implicit algebraic equations, can be reduced to a problem of 6 implicit equations in 6 unknowns. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the MAE problem to obtain the feedback controls.

Optimal Guidance for Aerodynamically Controlled Re-Entry Vehicles

Linear optimal control theory is applied to develop terminal guidance laws for aerodynamically controlled re-entry vehicles. The quadratic performance function minimized includes the terminal state error, the integral of the state deviation from the nominal trajectory, and the integral of control corrections, where the weighting coefficients are trajectory dependent parameters. The vehicle is assumed to be controlled by lift acceleration magnitude and bank angle. By use of linear regulator theory, perturbation feedback control gains are calculated and used with state errors to compute corrections to the commanded nominal lift acceleration and bank angle. A four-state perturbation model is used to approximate the six-state trajectory dynamics for the derivation of the guidance feedback gain matrix. The notable feature of the approach described in this paper stems from the elimination of the velocity magnitude state in the flight dynamics perturbation model. In addition, time is eliminated as the independent variable in favor of distance, resulting in a four-state perturbation model. With these and other assumptions, the control variables are lift acceleration and bank angle, which are the natural ones for an acceleration controlled vehicle using accelerometers for measurement. This unique approach to modeling avoids the need for consideration of angle of attack and aerodynamic drag in the guidance equations. The guidance law implementation is thus independent of vehicle parameters such as mass and surface area, atmospheric density, and the aerodynamic coefficients of lift and drag. The resulting guidance law is evaluated using a three-degree-of-freedom simulation, in which the angle of attack and accelerations are limited and the trajectory dynamics are described by a six-state set of differential equations. Good performance is obtained for a variety of initial state errors, and off-nominal conditions in atmospheric density and vehicle aerodynamic lift and drag coefficients.