Kenneth D. Mease

Design and Evaluation of an Acceleration Guidance Algorithm for Entry

The design and performance evaluation of an entry guidance algorithm for future space transportation vehicles is presented. The guidance concept is to plan and track aerodynamic acceleration. This concept, on which the longitudinal entry guidance for the Space Shuttle Orbiter is based, is extended to integrated longitudinal and lateral guidance. With integrated longitudinal and lateral guidance, more extreme points in the landing footprint can be reached accurately; in particular, the cross-range capability is extended. The guidance algorithm consists of two components: a trajectory planner and a trajectory tracking law. The planner generates reference drag acceleration and heading angle profiles, along with reference state and bank angle profiles. The planner executes onboard and is capable of generating updates as the entry evolves. The tracking law, based on feedback linearization, commands the angles of bank and attack required to follow the reference drag and heading angle profiles. The planner and tracking law are described, along with additional higher level logic included in the algorithm. Extensive simulations for a set of return-from-orbit entries, including ones requiring large cross range, demonstrate that this algorithm consistently achieves the desired target conditions within allowable tolerances and satisfies all other entry constraints.

Shuttle Entry Guidance Revisited Using Nonlinear Geometric Methods

The entry guidance law for the Space Shuttle Orbiter is revisited using nonlinear geometric methods. The Shuttle guidance concept is to track a reference drag trajectory that has been designed to lead to a specified range and velocity. The current guidance law provides exponential tracking locally. We show that the approach taken in the original derivation of the Shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, we are led to an alternative, potentially superior, guidance law. To compare the two guidance laws, stability and performance domains in state space are defined, taking into account the nonlinear dynamics, a state constraint, and a control constraint. The stability and performance domains for the Shuttle law and the alternative law are constructed numerically. The effects of increasing the control capability and changing a parameter in the guidance laws are illustrated. The alternative guidance law achieves the desired performance over a larger domain of the state space; the stability domains for the two laws are similar. For the current operating domain of the Shuttle, the performance improvement offered by the alternative guidance law is probably not significant. With a larger operating domain for the Shuttle or some other entry vehicle, the alternative guidance law should be considered. A more comprehensive comparison taking into account important factors not considered here, such as robustness, would be necessary to decide whether or not the alternative guidance law is superior.

Drag-Based Predictive Tracking Guidance for Mars Precision Landing

Future Mars missions require precision landing capability. An entry guidance law is developed for a lander with flying capabilities consistent with those expected for the lander in the 2001 mission. The lander flight path is controlled by bank angle adjustments. The guidance law belongs to the class of drag-based predictive tracking guidance laws which includes the entry guidance law for the Space Shuttle Orbiter. Modifications relative to the Shuttle entry guidance law are introduced to accommodate the very low lift capability and the combination of a low bandwidth attitude control system and a fixed trim angle of attack. Monte Carlo results show that even with a maximum lift-to-drag ratio of only 0.12 a specified parachute deployment latitude/longitude point can be achieved with 99% certainty to within 13.2 km under the assumed worst case dispersions. The dynamic pressure and Mach number constraints for parachute deployment are also satisfied with 99% certainty.

Feasible Trajectory Generation for Atmospheric Entry Guidance

Author(s): Leavitt, JA; Mease, KD | Abstract: An atmospheric entry trajectory planner is developed that generates a feasible trajectory and associated bank angle profile. Feasibility denotes that the initial and final state conditions, the path and control constraints, and the nominal equations of motion are all satisfied. Feasible trajectories are easier to track, and thus enhanced performance is expected when the trajectory planner is combined with a tracking law for entry guidance. Insights from computing maximum crossrange trajectories are factored into the design of the planner, and as a result that it can generate trajectories to most of the landing footprint Drag profile design is central in the planning approach, but in addition both longitudinal and lateral motions are accounted for, including bank reversal planning, and the assumption of zero flight path angle is not required. Comparisons of trajectories created by the new planner and optimal trajectories and guidance simulation results using an algorithm based on the new planner demonstrate the performance improvements.

Competitive tracking of molecular objectives described by quantum mechanics

The control of molecular events by optical fields is sought with the methods of asymptotic inverse tracking, local track generation (model matching), and competitive tracking which are extensions of exact inverse tracking. The methodology is applied to infrared dissociation of a diatomic molecule and selective dissociation of the stronger bond in a highly coupled linear triatomic system. The major appeal of these methods is that they do not require costly iterations unlike other control studies in which optimization techniques are used to design fields to achieve desired molecular objectives. It is found that in exact inverse tracking where a requisite external field is obtained to exactly track a prescribed objective expectation value as a function of time, a high degree of intuition is required to find an a priori objective track such that the required fields are reasonable in terms of intensity and bandwidth. Furthermore, exact inverse tracking does not allow for tracking of multiple observables. The extensions of the inverse tracking method presented in this work help to alleviate these drawbacks. In all of these extensions the requisite field is computed locally in time through minimization of a cost functional which contains terms designed to minimize the error between the objective and actual tracks and also minimize the field fluence. The objective tracks can be prescribed a priori as in exact inverse tracking or from the present evolving system state (local track generation). Competitive tracking allows for the following of multiple observables although none will be tracked exactly. Locally generated tracks (model matching) require less physical intuition because it is easier to specify an objective track with current knowledge of the state of the system. However, the tradeoff with this method is that prediction of the behavior of the tracked observables may be elusive.

Reachable and Controllable Sets for Planetary Entry and Landing

Author(s): Benito, J; Mease, KD | Abstract: Understanding the envelope of entry trajectories that a given planetary lander is capable of flying can be an important aid for mission analysis and design. Two characteristics of this envelope are considered: 1) the set of states reachable from a given entry state and 2) the set of entry states controllable to a given final state. Precise definitions of these sets are given and methods for computing them are presented. To illustrate their use, the sets are employed to characterize the performance of two vehicle configurations, a low lift-to-drag-ratio capsule and a mid lift-to-dragratio ellipsled, for Mars entry. Roles for the sets in evaluating entry trajectory planning algorithms, choosing a nominal entry state, and planning skip entries are described. Copyright

Eigenvector approximate dichotomic basis method for solving hyper‐ sensitive optimal control problems

The dichotomic basis method is further developed for solving completely hyper-sensitive Hamiltonian boundary value problems arising in optimal control. For this class of problems, the solution can be accurately approximated by concatenating an initial boundary-layer segment, an equilibrium segment, and a terminal boundary-layer segment. Constructing the solution in this composite manner alleviates the sensitivity. The method uses a dichotomic basis to decompose the Hamiltonian vector field into its stable and unstable components, thus allowing the missing initial conditions needed to specify the initial and terminal boundary-layer segments to be determined from partial equilibrium conditions. The dichotomic basis reveals the phase-space manifold structure in the neighbourhood of the optimal solution. The challenge is to determine a sufficiently accurate approximation to a dichotomic basis. In this paper we use an approximate dichotomic basis derived from local eigenvectors. An iterative scheme is proposed to handle the approximate nature of the basis. The method is illustrated on an example problem and its general applicability is assessed. Copyright

Minimum-Fuel Powered Descent for Mars Pinpoint Landing

Motivated by the requirement for pinpoint landing in futureMarsmissions, we consider the problemofminimumfuel powered terminal descent to a prescribed landing site. The first-order necessary conditions are derived and interpreted for a point-mass model with throttle and thrust angle control and for rigid-bodymodel with throttle and angular velocity control, clarifying the characteristics of the minimum-fuel solution in each case. The optimal thrust magnitude profile is bang–bang for bothmodels; for the point-mass, the most general thrust magnitude profile has a maximum–minimum–maximum structure. The optimal thrust direction law for the point-mass model (alignment with the primer vector) corresponds to a singular solution for the rigid-bodymodel.Whether the point-mass solution accurately approximates the rigid-body solution depends on the thrust direction boundary conditions imposed for the rigid-body model. Minimum-fuel solutions, obtained numerically, illustrate the optimal strategies.

Landing Footprint Computation for Entry Vehicles

A method is developed for generating landing footprints for entry vehicles in near realtime, as needed for an on-board flight management system. The method described in the paper is built around a previously developed, acceleration-based trajectory planner. The boundary of the footprint is constructed from the endpoints of extreme downrange or crossrange trajectories generated by the planner. The strengths of the method include fast computation time, respecting path constraints such as vehicle heating limits, accounting for Coriolis effects and constructing angle of attack profiles that are nearly optimal for long range glide. The accuracy of the landing footprint generator is determined by direct comparison with footprints computed with a general purpose optimization program.

Sliding Mode Observer for Drag Tracking in Entry Guidance

A sliding mode state and perturbation observer is used in conjunction with a feedback linearizing drag tracking law for application to entry guidance. The observer estimates the drag and drag rate required by the tracking law and estimates the modeling error in the drag dynamics. The modeling error estimate is used in the drag tracking law to more exactly cancel the nonlinearities; thus rendering the drag tracking adaptive to o-nominal conditions. Mars entry simulations for a capsule-type lander are carried out to assess and compare the performance of the adaptive tracking law relative to straight feedback linearizing tracking law. The results show that the adaptive drag tracking guidance oers performance improvement.