Receding Horizon Guidance Research Articles

Receding horizon guidance and control using sequential convex programming for spacecraft 6-DOF close proximity

This paper presents a receding horizon implementation of sequential convex programming for the spacecraft six-degree-of-freedom close proximity to a non-cooperative target satellite. With linearized relative translational dynamics and newly derived discrete rotational equations in terms of modified Rodrigues parameters, nonlinear system dynamics of the original optimal guidance and control problem for proximity are converted into convex ones for sequentially planning. The nonconvex constraint on field-of-view of the visual sensor pointing with coupled attitude and relative position is then approximately relaxed as a convex standard second-order cone, and concave spherical and ellipsoidal obstacle regions respectively around the target's body and solar arrays are convexified by affine constraints in terms of tangent planes. The original nonlinear optimal guidance and control problem is accordingly transformed into a series of second-order cone programming sub-problems via iteratively successive convexification with the trust region constraints, and sequentially solved using disciplined convex programming method. A close-loop guidance and control using the proposed sequential convex programming scheme is then demonstrated by means of receding horizon to robustly drive the spacecraft maneuvering close to the target. Numerical simulations and results reveal that the proposed method provides rapid and reliable guidance and control performance for six-degree-of-freedom close proximity and shows the potential for on-board implementations in real-time applications.

Receding horizon guidance of a small unmanned aerial vehicle for planar reference path following

This paper describes a novel lateral guidance law for an unmanned aerial vehicle using nonlinear receding horizon optimization and shows its flight test results. The guidance law uses an extended Kalman filter which estimates steady wind velocities in order to follow a pre-specified reference path defined in a ground-fixed coordinate system. The guidance law can be applied to arbitrary reference path as long as the path is represented as a differentiable function of x and y in a ground-fixed coordinate system. A small-scale research vehicle developed by the Japan Aerospace Exploration Agency is used for flight tests, and the results demonstrate the high guidance performance of the proposed method.

Nonlinear receding horizon guidance for spacecraft formation reconfiguration on libration point orbits using a symplectic numerical method

This paper studies a nonlinear receding horizon control guidance strategy for spacecraft formation reconfiguration on libration orbits in the Sun–Earth system. For comparison, a linear quadratic soft terminal control strategy is also considered for the same reconfiguration missions. A novel symplectic iterative numerical algorithm is proposed to obtain the optimal solution for the nonlinear receding horizon control strategy at each update instant. With the aid of the quasilinearization method, a high-efficiency structure-preserving symplectic method is introduced in the iterations, and the optimal control problem is replaced successfully by a series of sparse symmetrical linear equations. Several typical spacecraft formation reconfiguration missions including resizing, rotating and slewing reconfigurations and their combinations are numerically simulated to show the effectiveness of the nonlinear receding horizon guidance strategy based on the proposed symplectic algorithm. Through these simulations, the nonlinear receding horizon control strategy is shown to have obvious advantages in convergence and parameter sensitivity compared with a linear quadratic soft terminal control strategy. Monte Carlo stochastic simulations are used to test the robustness of the nonlinear receding horizon control guidance in dealing with measurement and execution errors.

Simultaneous Optimization Method for Trajectory and Sequence for Receding Horizon Guidance in Terminal Area

The target of this study is to develop the simultaneous optimization method for trajectory and sequence in the airspace near airports (terminal area). Traditionally, the arrival sequence optimizati...

Optimal guidance based on receding horizon control for low-thrust transfer to libration point orbits

This paper addresses the design and computation of a guidance law for a transfer mission from an orbit near the Earth to a halo orbit around the libration point L2 in the Sun–Earth system. The guidance law, which is designed based on receding horizon control and compensates for launch velocity errors that are introduced by inaccuracies of the launch vehicle, is solved using the generating function method. During the design of the closed-loop guidance law, the entire transfer mission, which is considered a nonlinear optimal control problem, is evaluated to obtain a nominal reference trajectory. Using the launch velocity errors and the uncertainty of the model, a spacecraft controlled by the proposed guidance law tracks the reference trajectory. Furthermore, the original Riccati differential equation in the receding horizon control algorithm is replaced by an equivalent convenient form of the Riccati differential equation that is based on the generating function. The high-efficiency solution of the equivalent equation avoids the online direct integration of the original Riccati differential equation, which significantly increases the computational efficiency for the receding horizon control problem. Numerical simulations using a nonlinear bicircular four-body model demonstrate the capabilities of the proposed receding horizon guidance law for the transfer mission. In addition, the generating function method improves the computational efficiency by at least one order of magnitude over the backward sweep method in solving the receding horizon control problem.

Software-Enabled Receding Horizon Control for Autonomous Unmanned Aerial Vehicle Guidance

This paper describes autonomous unmanned aerial vehicle (UAV) guidance technologies developed and demonstrated in a flight test sponsored by the DARPA Software Enabled Control program. The flight experiment took place in June 2004 using a Boeing UAV testbed and demonstrated important autonomy capabilities enabled by a receding horizon guidance controller and fault detection filter. The receding horizon controller (RHC) design process is presented in detail as well as demonstration scenarios which were designed to exercise and evaluate the primary functionalities of the control system. Simulation results of the key capabilities are shown and compared with recorded flight data for evaluation purposes. Hardware-in-the-loop simulations and other high-fidelity test run results illustrate secondary capabilities such as controller reconfiguration due to actuator fault and maneuvering limit enforcement using output constraints in the receding horizon approach.

Hybrid Model for Receding Horizon Guidance of Agile Autonomous Rotorcraft

This paper presents a novel framework for full-envelope guidance of agile, autonomous rotorcraft. A velocity control mode is combined with a maneuver scheduler that enables execution of pre-programmed, agile maneuvers. The closed-loop dynamics in the body-axis frame are described by a hybrid model, consisting of a set of constrained, linear, time-invariant modes and discrete transitions in the state space. Optimal trajectories through cluttered environments are then computed using mixed integer linear programming. A receding horizon formulation is presented that is feasible for real-time guidance.

Game optimal receding horizon guidance laws and its equivalence to receding horizon guidance laws

In this paper, a game optimal receding horizon guidance law (GRHG) is proposed, which does not use information of the time-to-go and target maneuvers. It is shown that by adjusting design parameters appropriately, the proposed GRHG is identical to the existing receding horizon guidance law (RHG), which can intercept the target by keeping the relative vertical separation less than the given value, within which the warhead of the missile is detonated, after the appropriately selected time in the presence of arbitrary target maneuvers and initial relative vertical separation rates between the target and missile. Through a simulation study, the performance of the GRHG is illustrated and compared with that of the existing optimal guidance law (OGL).

Receding horizon guidance laws for constrained missiles with autopilot lags

Abstract In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear continuous time-invariant systems with input and state constraints. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix subject to constraints. A new algorithm is suggested to implement the RHC scheme for a constrained receding horizon guidance law (CRHG). The proposed CRHG, which does not use information on the time-to-go, is obtained by using linear matrix inequality (LMI) optimization. Through simulation examples, the performance of the proposed CRHG is illustrated.

Modified receding horizon guidance law with information on small accurate time-to-go

A modified receding horizon guidance law (MRHG), which is useful when the accurate time-to-go is available only for a short time before the final time, is proposed. The proposed MRHG is based on the receding horizon strategy and optimal control theory. In the presence of arbitrary target maneuvers and an initial lateral miss distance (MD) rate between a target and a missile, it is shown that the proposed MRHG guarantees not only to keep the lateral MD less than a given value, within which the warhead of the missile is detonated, from the appropriately selected time to the intercept time, but also to render the terminal MD zero. Through simulations when the time-to-go is accurate only for a short time, the performance of MRHG is compared with the optimal guidance law (OGL) and the receding horizon guidance law (RHG) in terms of the terminal MD, the lateral MD, and the missile acceleration.

Receding Horizon Guidance Laws with No Information on the Time-to-Go

In this paper a modie ed optimal guidance law is proposed that does not use information on the time-to-go. The proposed receding horizon guidance law (RHG) is based on the receding horizon strategy and optimal control theory. In the presence of arbitrary target maneuvers and an initial lateral miss distance (MD) rate between the target and the missile, the proposed RHG is shown to guarantee to keep the lateral MD less than the given value, within which the warhead of the missile is detonated, from the appropriately selected time to the intercept time. Through threesimulation examples theability oftheRHGto interceptthetarget isillustrated. The performanceof theRHGiscompared with theoptimalguidancelawin termsoftheterminal MDwhen thetime-to-goisinaccurate, and in terms of the lateral MD and the missile acceleration when the time-to-go is accurate.

Modified Receding Horizon Guidance Law

In this paper, a modified receding horizon guidance law (MRHG) is proposed which can be a proper guidance law when the accurate time-to-go is available only for a short time before the final time. In the proposed MRHG, RHG is used before the accurate time-to-go is available and after that, OGL is used until the missile intercepts the target using the accurate time-to-go given for a short time. The proposed MRHG makes the lateral miss distance (MD) below the pre-described value before the accurate time-to-go is available and makes the terminal MD zero using the accurate time-to-go even in the presence of target maneuvers and an initial relative normal velocity between the target and the missile. Through simulation, the performance of MRHG is illusrtated in terms of the terminal MD the lateral MD and the missile normal acceleration.