Showing papers in "Journal of Guidance Control and Dynamics in 2017"

Model Predictive Path Integral Control: From Theory to Parallel Computation

Abstract: In this paper, a model predictive path integral control algorithm based on a generalized importance sampling scheme is developed and parallel optimization via sampling is performed using a graphics...

Customized Real-Time Interior-Point Methods for Onboard Powered-Descent Guidance

Abstract: This paper presents a new onboard-implementable, real-time convex optimization-based powered-descent guidance algorithm for planetary pinpoint landing. Earlier work provided the theoretical basis of convexification, the equivalent representation of the fuel-optimal pinpoint landing trajectory optimization problem with nonconvex control constraints as a convex optimization problem. Once the trajectory optimization problem is convexified, interior-point method algorithms can be used to solve the problem to global optimality. Though having this guarantee of convergence motivated earlier convexification results, there were no real-time interior point method algorithms available for the computation of optimal trajectories on flight computers. This paper presents the first such algorithm developed for onboard use and flight-tested on a terrestrial rocket with the NASA Jet Propulsion Laboratory and the NASA Flight Opportunities Program in 2013. First, earlier convexification results are summarized and the result...

Constrained Trajectory Optimization for Planetary Entry via Sequential Convex Programming

Abstract: In this paper, the highly nonlinear planetary-entry optimal control problem is formulated as a sequence of convex problems to facilitate rapid solution. The nonconvex control constraint is avoided ...

Constrained Autonomous Precision Landing via Dual Quaternions and Model Predictive Control

Abstract: The problem of powered descent guidance and control for autonomous precision landing for next-generation planetary missions is addressed. The precision landing algorithm aims to trace a fuel-optimal trajectory while keeping geometrical constraints such as the line of sight to the target site. The design of an autonomous control algorithm managing such mission scenarios is challenging due to fact that critical geometrical constraints are coupled with the translational and rotational motions of the lander spacecraft, leading to a complex motion-planning problem. This problem is approached within the model predictive control framework by representing the dynamics of the rigid body in a uniform gravity field via a piecewise affine system taking advantage of the unit dual-quaternion parameterization. Such a parameterization in turn enables a six-degree-of-freedom motion planning in a unified framework while also admitting a quadratic cost on the required control commands to minimize propellant consumption. A n...

Pseudospectral Convex Optimization for Powered Descent and Landing

Abstract: Over the last years, two new technologies to solve optimal-control problems were successfully developed: that is, pseudospectral optimal control and convex optimization, with the former for solving...

Propellant-Optimal Powered Descent Guidance

Abstract: The problem of guiding a rocket-powered vehicle to land on a planet (or the Moon) with pinpoint precision and minimum propellant usage is the focus of this work. Three related but different version...

Implementation and Experimental Demonstration of Onboard Powered-Descent Guidance

Abstract: Onboard, fuel-optimal, constrained powered-descent guidance based on the theory of lossless convexification has been implemented as the Guidance for Fuel-Optimal Large Diverts (G-FOLD) algorithm. Here, “guidance” means generating feedforward reference trajectories for control systems. This paper presents terrestrial flight-test demonstrations of large diverts planned by G-FOLD onboard a vertical-takeoff/vertical-landing rocket. The G-FOLD parser, which transforms the guidance problem into a second-order cone program and so encodes the divert constraints, is described at an engineering level, including new and modified constraints incorporated for these flight tests. Several practical issues, such as discretization effects, are addressed, and the flight-test architecture is presented. A total of eight flight tests were performed. In the first three, the rocket executed diverts of increasing size preplanned by G-FOLD on the ground. Then G-FOLD was demonstrated running onboard five times. Three qualitatively...

New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

Abstract: This paper presents new state transition matrices that model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J2 and differential drag for three state definitions ...

Safety Control for Spacecraft Autonomous Rendezvous and Docking Under Motion Constraints

Abstract: This paper addresses the translational control problem for the final phase of spacecraft rendezvous and docking. For safety concerns, during the approach process, the pursuer spacecraft is required...

Rapid Generation of Time-Optimal Trajectories for Asteroid Landing via Convex Optimization

Abstract: This paper presents a new method for rapid generation of time-optimal trajectories for asteroid landing via convex optimization. To overcome the nonconvex difficulty due to the free-flight time, a ...

Contact Dynamics Modeling and Simulation of Tether Nets for Space-Debris Capture

Abstract: A proposed method for containing the growth of space debris, which jeopardizes operation of spacecraft, is the active debris removal of massive derelict spacecraft and launcher upper stages by means of tether nets. The behavior of nets in space is not well known; therefore, numerical simulation is needed to gain understanding of deployment and capture dynamics. In this paper, a lumped-parameter approach for modeling the net and different models of contact dynamics are presented. A continuous compliant approach for the normal contact force and a modified damped bristle model for the friction force are chosen. The capability of the developed simulation tool to represent multiple dynamic conditions is demonstrated in this paper, and the results of a deployment dynamics simulation are presented; this reveals a snapping behavior of tension. Simulation of net-based capture of cylindrical debris in microgravity and vacuum conditions is performed with the presented tool. The effect of employing different contact ...

Verification of a Fully Numerical Entry Guidance Algorithm

Abstract: The process, methodology, and results of a two year effort are presented in this paper on verification of an advanced entry guidance algorithm, called Fully Numerical Predictor-corrector Entry Guidance (FNPEG). FNPEG is a model-based numerical guidance algorithm capable of performing both direct (orbital or suborbital) entry and skip entry missions. Few vehicle-dependent adjustments are necessary, and no reference trajectory or mission-dependent planning is required. The algorithm is applicable to a wide range of vehicles with different lift-to-drag ratios and includes state-of-the-art capability to effectively control g load and damp out phugoid oscillations, without adversely affecting the guidance precision. FNPEG has undergone extensive testing and evaluation in the high-fidelity simulation environment for the Orion spacecraft at NASA Johnson Space Center. In this paper, the verification methodology and process are described. The metrics for verification are defined. Extensive testing and simulation r...

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem

Abstract: Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto.

Fast and Near-Optimal Guidance for Docking to Uncontrolled Spacecraft

Abstract: This paper proposes a guidance scheme for autonomous docking between a controlled spacecraft and an uncontrolled tumbling target in circular orbit. The onboard trajectory planning consists of a direct optimization method based on the inversion of the system dynamics. The trajectory components of the controlled spacecraft are imposed by using polynomial functions. Some of the polynomial coefficients are constrained to satisfy path constraints, whereas the remaining coefficients are varied parameters to be optimized. The optimal control problem is converted into a nonlinear programming problem by inverting the system dynamics. The proposed guidance scheme, based on the closed-loop implementation of this optimization problem, is applied to several scenarios. The resulting trajectories closely match the solutions of the correspondent optimal control problems. The guidance scheme is shown to perform precise maneuvers in most maneuvering situations, even in the presence of orbital perturbations. The sensitivity...

Dual-Quaternion-Based Spacecraft Autonomous Rendezvous and Docking Under Six-Degree-of-Freedom Motion Constraints

Abstract: This paper addresses the integrated attitude and position control problem for the final phase proximity operations of spacecraft autonomous rendezvous and docking, in which important motion constra...

Cooperative Nonlinear Guidance Strategies for Aircraft Defense

Abstract: This paper presents nonlinear guidance strategies for scenarios where an aircraft launches a defender missile as a countermeasure against an incoming attacking missile. The guidance system offers an additional degree of freedom due to two available controls, the lateral accelerations of defender and aircraft. This extra degree of freedom is used in various ways to design guidance strategies. These guidance strategies, in addition to each ensuring interception of missile, also individually allow: 1) to reduce sensitivity of guidance law to erroneous time-to-go estimates, 2) the aircraft to perform optimal evasive maneuvers, and 3) either of the aircraft or the defender to maneuver independently with their maximum limit small as compared to that of missile. The design of guidance strategies is performed in a nonlinear framework, using sliding-mode control technique, with relevant zero-effort miss variables as switching surfaces. For reduction of sensitivity against time-to-go, an additional zero-effort velo...

Robust Aircraft Trajectory Planning Under Wind Uncertainty Using Optimal Control

Abstract: Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future air traffic management system. Therefore, understanding and managing uncertainty will be necessa...

Adaptive Disturbance-Based High-Order Sliding-Mode Control for Hypersonic-Entry Vehicles

Abstract: In this paper, an adaptive, disturbance-based sliding-mode controller for hypersonic-entry vehicles is proposed. The scheme is based on high-order sliding-mode theory, and is coupled to an extended...

Dynamics Analysis and Controller Design for Maneuverable Tethered Space Net Robot

Abstract: Space robots are considered as a promising solution to active space-debris capture and removal. In this paper, a brand new space robot system called the maneuverable tethered space net robot is pro...

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

Abstract: The impact time control problem can be stated as the requirement to hit the target with no other terminal constraint than achieving a specified final time. This specific terminal constraint HE impact time control problem can be stated as the requirement to hit the target with no other terminal constraint could provide survivability against close-in weapon systems by facilitating a salvo attack capability. In addition, impact time control could be employed to force the missile pass through a certain waypoint at a specified time. With rising interest over recent years, the literature on impact time control laws has been growing rapidly. One ofthe earliest studies was presented in [1], which was based on proportional navigation (PN) involving the difference of the desired and estimated time-to-go values as a bias term. The same authors extended the previous work, in which the design was based on linearized kinematics, in [2] to nonlinear kinematics. Another impact time control method via biased PNwas considered in [3] for cooperative attacks. The bias term was a time-varying navigation gain that was adjusted based on the time to go of the individual missile and the times to go of the cooperating missiles. As well as PN-based impact time guidance laws, there exist numerous studies based on the nonlinear control theory. ALyapunovbased approach was considered in [4] using the same time-to-go estimation as in [1]. The sliding mode was applied in [5], using a switching surface as a combination of the impact time error and the line-of-sight (LOS) rate. In [6], a sliding surface that was only a function of the impact time error was provided. In addition, several modifications were made to deal with the singularity of the guidance command. The common disadvantage of these guidance laws designed via the nonlinear control theory is the high acceleration demand at the beginning of the flight. As exemplified thus far, many of the impact time guidance laws in the literature require the time to go as feedback. Thus, the estimation of this quantity might turn into a source of error. However, there are also several studies where the impact time problem is solved without relying on this information. In [7], second- and third-order polynomial guidance laws were proposed, where the guidance gain was to be calculated by solving an integral equation in order to satisfy the requirement of a zero miss distance. Also, the third-order approach is shown to produce trajectories close to optimal ones. The guidance law in [8] was derived by shaping the range as a quartic polynomial. The nonlinear design results in a closed-loop guidance law with constant coefficients, showing robustness under lagged response and seeker noise. In addition to these, guidance laws effective against moving targets were presented in [9,10]. The study in [9] adopted the vector guidance approach, directing the total acceleration to ensure the capture at the specified time. In [10], a twophased PN guidance scheme is constructed, where the switching instant was calculated with respect to the desired impact time. Both of these guidance laws require a controlled change of missile velocity. In addition to the impact time control problem alone, simultaneous control of the impact time and angle should also be mentioned here because it can also lead to a designated impact time. In [11], the guidance command was composed of two parts, where the first part was for the impact-angle constraint with zero miss distance and the second part was for the impact time constraint. The sliding-mode control theory was used in [12] for simultaneous control ofthe impact time and angle. A second-order sliding-mode control law was introduced using a backstepping concept to provide robustness in the presence of uncertainties. The work in [13] provided a three-phased practical guidance law to control the impact time or/and the impact angle under look-angle and acceleration constraints. The key assumption in all of these studies is that the velocity ofthe missile was either constant or, on a few occasions, controllable. In contrast, the velocity is not even controllable in most missile applications. Besides, it changes under the action of drag, thrust, and the trajectory being followed. The works presented in [14,15] considered the impact time control problem under changing velocity. In [14], which devised a quadsegment polynomial method via parameterizing the trajectories in terms of the downrange, doing a preflight analysis was proposed as a first step in coping with the velocity change. In [15], on the other hand, integral sliding-mode control was performed, taking into account the rate of change of the velocity and its limits. However, a preflight analysis as in [14] might not always be feasible, and having the terminal acceleration systematically diverging away from zero as in [15] could be prohibitive. Moreover, varying velocity is assuredly a problem, not only for the impact time problem but also for the optimal guidance laws too. There are several studies that concentrated on this issue. An energy-optimized guidance law was presented in [16], where the guidance gain was varied via a time-to-go-like function. This function considered the future missile velocity and adjusted the guidance gain with respect to the predicted velocity. In [17], an extension to the previous study was presented while providing two schemes for updating the velocity and general-case cost functions for varying velocity. The study in [18] used a time-varying linear game model for an interception scenario with a knownvelocity profile and a lateral acceleration constraint. In addition to these studies, adaptive guidance schemes are also applied to provide robustness under varying conditions. Here, adaptation means updating the guidance gains with respect to those conditions, and no connection with the conventional adaptive control is implied. In this extent, the impact-angle control problem was studied in the literature. In [19], a nonlinear parameter adaptation scheme for impact-angle control was presented for a hypersonic gliding vehicle. The study in [20] developed two adaptive impactangle guidance laws: one ofwhich was based on the conventional PN guidance and the other one based on controlling the turn rate of the relative velocity vector. In both of these studies, the guidance gains were updated in a closed-loop manner; therefore, they were able to deal with varying conditions. In this study, a feasible impact time control algorithm is proposed. The guidance laws in [7] are generalized using an nth order polynomial of the look angle. Unlike [7], the linearized kinematics is used to obtain an analytical solution for the guidance gain as a function of the range, the look angle, and the duration until impact. This solution is then extended to the nonlinear domain by considering an adaptive guidance scheme. Such adaptation through periodically updating the guidance gain is not only able to overcome the unmodeled nonlinearities but it also provides robustness against disturbing factors such as autopilot lag. However, adaptation will only be sufficient as long as the velocity of the missile remains constant. As mentioned previously, the velocity is generally neither constant nor controllable. What makes the situation more problematic is that the velocity profile eventually depends on the trajectory, which is indeed the result of the guidance law itself. If the future velocity profile or, equivalently, the mean value of this profile can somehow be predicted, this information can be used to feed the adaptive guidance process. The approach adopted in this work for predicting the meanvelocity uses the analytical results extracted from the linearized guidance loop. At each guidance step, in which the eventual objective is the adaptation of the guidance gain, the mean velocity is predicted for the interval between the current time and the final time using an iterative process. The prediction algorithm involves a mathematical model of how the velocity is expected to change. In this predictive-adaptive guidance scheme, the guidance gain is updated based on the predicted mean velocity. The outline of the Note is organized as follows: In Sec. II, the impact time control problem is described and the general form of the guidance command is presented. In Sec. III, the solution of the guidance gain is presented based on linearized kinematics. Afterward, adaptive and predictive-adaptive guidance schemes for impact time control are introduced. Last, the performance of the proposed guidance technique is demonstrated with simulations in Sec. IV. After presenting idealized examples with constant velocity, more realistic ground-to-ground and air-to-ground scenarios with nonconstant velocity profiles and autopilot lag are exemplified. In addition to these simulations, which also include comparisons with optimal solutions, a case that involves drag uncertainty is investigated.