Aron A. Wolf

Galileo trajectory design

The Galileo spacecraft was launched by the Space Shuttle Atlantis on October 18, 1989. A two-stage Inertial Upper Stage propelled Galileo out of Earth parking orbit to begin its 6-year interplanetary transfer to Jupiter. Galileo has already received two gravity assists: from Venus on February 10, 1990 and from Earth on December 8, 1990. After a second gravity-assist flyby of Earth on December 8, 1992, Galileo will have achieved the energy necessary to reach Jupiter. Galileos interplanetary trajectory includes a close flyby of asteroid 951-Gaspra on October 29, 1991, and, depending on propellant availability and other factors, there may be a second asteroid flyby of 243-Ida on August 28, 1993. Upon arrival at Jupiter on December 7, 1995, the Galileo Orbiter will relay data back to Earth from an atmospheric Probe which is released five months earlier. For about 75 min, data is transmitted to the Orbiter from the Probe as it descends on a parachute to a pressure depth of 20–30 bars in the Jovian atmosphere. Shortly after the end of Probe relay, the Orbiter ignites its rocket motor to insert into orbit about Jupiter. The orbital phase of the mission, referred to as the satellite tour, lasts nearly two years, during which time Galileo will complete 10 orbits about Jupiter. On each of these orbits, there will be a close encounter with one of the three outermost Galilean satellites (Europa, Ganymede, and Callisto). The gravity assist from each satellite is designed to target the spacecraft to the next encounter with minimal expenditure of propellant. The nominal mission is scheduled to end in October 1997 when the Orbiter enters Jupiters magnetotail.

A Comparison of Powered Descent Guidance Laws for Mars Pinpoint Landing.

I. Abstract In this paper, we formulate and compare a number of powered terminal descent guidance algorithms for Mars pinpoint landing (PPL). The PPL guidance problem involves finding a trajectory that transfers the spacecraft from any g iven state at engine ignition to a desired terminal state (usually within 100m of a desired target) without violating fuel limits or any state constraints and control constraints. Sp ecifically, we first formulate the fuel-optimal guidance problem and show that a direct method can be used to reduce it to a finite-dimensional convex program. Modern interior point methods can then be used to find the global solution to any desired level of accuracy. Nex t, we discuss a class of suboptimal guidance laws based on simple polynomial basis functions. The performance of the sub-optimal guidance laws under a variety of realistic mission constraints are compared to the global fuel-optimal solution.

Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing

In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.

Toward improved landing precision on Mars

Mars landers to date have flown ballistic entry trajectories with no trajectory control after the final maneuver before entry. 12Improvements in landing accuracies (from ∼150 km from the target for Mars Pathfinder to ∼30–40 km for MER and Phoenix) have been driven by approach navigation improvements. MSL will fly the first guided-entry trajectory to Mars, further improving accuracy to ∼10–12 km from the target. For future missions, landing within ∼100m is desired to assure landing safety close to a target of high scientific interest in irregular terrain, or to land near a previously landed asset. Improvements in approach navigation alone are not sufficient to achieve this requirement. If approach navigation error and IMU error are eliminated, the dominant error source is wind drift on the parachute, with map-tie error also significant. Correcting these errors requires terrain-relative navigation (TRN), which can be accomplished with passive imaging supplemented by radar for terrain sensing (with onboard navigation capable of processing measurements from IMU, imaging, and radar). Additionally, near-optimal-ΔV powered descent guidance is needed to minimize the amount of propellant required to reach the target. The capability to land within 100m can be applied in different landing modes depending on how much fuel is carried.

Robust Guidance via a Predictor-Corrector Algorithm with Drag Tracking for Aero-Gravity Assist Maneuvers

An atmospheric guidance algorithm to support Aero-Gravity Assist (AGA) maneuvers is developed. The AGA maneuver is divided into four phases: (i) a capture phase, (ii) a cruise phase, (iii) an exit phase and (iv) a terminal phase. In the capture phase, the vehicle tracks a constant drag reference that controls the plunge of the spacecraft into the atmosphere, trying to protect it from excessive heating. During the cruise and exit phases, a reference trajectory planner based on a numerical predictor-corrector algorithm generates the references the spacecraft should fly, from the current to the atmospheric exit conditions. In the terminal phase, the remaining final orbit inclination error is reduced. The robustness of the guidance algorithm is increased by tracking the drag reference obtained from the reference trajectory planner instead of directly commanding the predicted control profile. Monte Carlo simulation results indicate the viability of the approach for on-board closed-loop guidance in the presence of large dispersions and modeling uncertainties.

Improving the landing precision of an MSL-class vehicle

Prior to Mars Science Laboratory (MSL), Mars landers flew ballistic entry trajectories. Improvements in landing accuracy (from ~150 km from the target for Mars Pathfinder to ~30-40 km for Mars Exploration Rover and Phoenix) were solely due to improved approach navigation. MSL will fly the first guided-entry trajectory to Mars, further improving accuracy to ~10-12 km from the target by modifying the trajectory in the atmosphere using a lift created by slightly offsetting the vehicle center-of-mass. EDL systems of future Mars lander missions are likely to substantially resemble MSL to maximize heritage and minimize cost. Further improvements in landing accuracy are desired for these missions, motivating an investigation into improvements in landing accuracy with minimal impact to the MSL EDL system architecture.

Capabilities of convex Powered-Descent Guidance algorithms for pinpoint and precision landing

The PDG (Powered Descent Guidance) algorithm provides a numerical method for onboard generation of guidance profiles for use during the powered-descent phase of Mars pinpoint or precision landing. The algorithm incorporates both state and control constraints, including minimum and maximum thrust limits, glideslope constraints to avoid impacting the surface, and speed and attitude constraints. These constraints are particularly important for powered-descent scenarios requiring large-divert capabilities to achieve pinpoint or precision landing. Additionally, the constraints ensure that guidance profiles are physically achievable. For instance, the thrust limits are particularly relevant for spacecraft that implement rocket engines that cannot be throttled off after ignition. The formulation of PDG poses the problem as a SoCP (Second-order Cone Program) that can be solved with numerically-efficient interior-point solvers in a finite time to within a prescribed accuracy. This feature is ideal for onboard implementation during powered descent where total flight time is short, thus guidance methods must guarantee convergence to an achievable solution within a short time. If a spacecraft can physically perform maneuvers to achieve pinpoint or precision landing (i.e., the problem is feasible), then the SoCP formulation of PDG will find the solution. Further, this solution will satisfy the prescribed constraints on position, fuel, thrust, speed and attitude.

PARAMETRIC OPTIMIZATION AND GUIDANCE FOR AN AEROGRAVITY ASSISTED ATMOSPHERIC SAMPLE RETURN FROM MARS AND VENUS

Atmospheric lift can increase the bending and the net ∆V achievable during a gravity assist maneuver. This technique is applied to a detailed simulation of a hypothetical atmospheric sample return from Mars and Venus as part of an Earth-Mars-Venus-Earth tour. Reference flyby trajectories for both planets are computed for a waverider vehicle model. The bounding entry conditions are described and compared to those achievable using a recently developed guidance algorithm. for a detailed analysis of the issues associated with accurately guiding a waverider to the exit state required to target the next planet in the tour. Simplifying assumptions are used to generate a reference trajectory through the atmosphere of Mars. Unfortunately, using those same simplifications at Venus resulted in a trajectory that was biased toward one side of the achievable entry corridor. We will describe an approach based on optimal control theory for specifying a reference trajectory that is approximately centered in the available corridor for both Mars and Venus. The reference trajectories will be compared and contrasted for the cases at Mars and Venus. The theoretical bounding cases for Venus will be described and the bounds for Mars will be computed. Earlier papers 1-3,6-23 discuss the history of the waverider concept for interplanetary missions. A guidance algorithm has been developed and implemented in MATLAB. This paper will focus on using angle of attack as the control, while bank angle control and the guidance system development is discussed in a companion paper by Casoliva 2 . The guidance algorithms have been tested using simple models (point mass, spherical planets with exponential atmospheres). The MATLAB based guidance algorithm has been successfully linked into a DSENDS 24 based numerical simulation of the atmospheric flyby segments. DSENDS is a Python based simulator that enables the user to couple complex models of atmospheres, gravity, actuators, sensors, and control mechanisms in a common simulation environment. Monte Carlo simulations of the performance of the guidance algorithm are underway to determine the ability of the guidance algorithm to adapt to errors in entry conditions and to off-nominal atmospheric conditions.

SuperSmart Parachute Deployment Algorithm for Mars Pinpoint Landing

An algorithm for choosing the parachute deployment point has been developed which is designed to reduce delivery errors at powered descent ignition during Entry / Descent / Landing (EDL) on a body with an atmosphere (e.g. Mars), consequently reducing the propellant required to achieve precise landing at a preselected target. This algorithm is designed to improve on the previously developed “Smart Chute” deployment algorithm by modeling the lander’s trajectory during the parachute phase for improved targeting. Performance benefits are influenced by environmental factors, principally winds between chute deployment and ignition, which cause the lander to drift on the parachute.