Lloyd Strohl

Bio: Lloyd Strohl is an academic researcher. The author has contributed to research in topics: Computer science & Algorithm. The author has an hindex of 1, co-authored 3 publications receiving 6 citations.

Post-Flight Performance Analysis of Navigation and Advanced Guidance Algorithms on a Terrestrial Suborbital Rocket Flight

Abstract: There is currently renewed interest in robotic and crewed landers for a return to the lunar surface. Advanced guidance and navigation algorithms are essential to accurately delivering cargo and crew safely to the moon successfully. This paper reports the overall performance of an integrated set of navigation and guidance algorithms flown on a terrestrial suborbital rocket up to an altitude of approximately 100km. The navigation algorithm consists of an onboard extended Kalman Filter (EKF) that ingests multiple sensor measurements, one of which is the output from a terrain relative navigation (TRN) algorithm that cross-references camera images to on-board satellite imagery to perform feature correlation within the camera image. The guidance algorithm solves for a 6-degree-of-freedom (DoF) optimal trajectory using a successive convexification method during powered descent. The altitude range as well as the landing dynamics experienced during this test flight are realistic for an extraterrestrial landing and provide an invaluable data set to gauge the current development of these landing algorithms in an effort to advance the overall software readiness levels (SRL). This paper will delve into different aspects of each algorithm and present an analysis of the in-flight performance of the algorithms. This flight was conducted under the National Aeronautics and Space Administration (NASA) Safe and Precise Landing Integrated Capabilities Evolution (SPLICE) project focused on technology advancement for landing applications.

Implementation of a Six Degree of Freedom Precision Lunar Landing Algorithm Using Dual Quaternion Representation

Abstract: In this study, a powered descent guidance algorithm using a unit dual quaternion representation of the vehicle dynamics is implemented in a high-fidelity simulation and on representative flight hardware. This Dual-Quaternion Guidance (DQG) algorithm is applied to the precision lunar landing problem which levies complex constraints upon the trajectory, including state triggered attitude constraints to enable terrain-relative navigation and hazard detection as well as real-time requirements for landing site re-designation. The investigation explores DQGs usefulness as a mission design tool as well as a real-time guidance algorithm and defines real-time performance requirements for the hazard detection and avoidance (HDA) re-targeting phase of precision lunar landing. The experiment is presented in two parts. First, DQG is implemented within a high-fidelity Monte Carlo simulation to tune the algorithm’s parameters for the simulated vehicle, to refine the mission design, and to develop guidance update timing requirements to perform the HDA maneuver. DQG generates trajectories online for the divert which are tracked by the vehicle’s inner-loop controllers to the targeted landing site. Second, DQG is run on representative hardware to demonstrate real-time operation through a divert maneuver. These results allow for rapid, flexible, optimal mission design satisfying complex constraints, and for the definition of real-time performance requirements for the HDA operations inherent in precision lunar landing. The HDA divert maneuver is found to require guidance trajectory updates in less than three seconds. DQG is found to be too slow to meet this update timing on the descent and landing computer (DLC) in its current implementation. DQG running on alternative hardware can meet the update rate requirement. Algorithm implementation improvements are also recommended which are expected to speed up computation sufficiently to meet requirements on the DLC.

Lossless Convex Guidance for Lunar Powered Descent

Abstract: This paper builds upon a convex programming approach to propellant-optimal planetary landing guidance originally developed for Mars landings and adapts it to lunar soft landings. These novel adaptations include the addition of state and control constraints that were previously not part of the lossless convexification framework: maximum tilt rate, maximum tilt acceleration, maximum thrust ramp rate, and a terminal vertical descent phase. Additionally, we have included an inverse square central gravity model and a minimum altitude constraint in the Moon-centered, Moon-fixed (MCMF) frame. These constraints are convexified and the resulting second-order cone program is solved for an Apollo-like sample case.

Customized Real-Time First-Order Methods for Onboard Dual Quaternion-based 6-DoF Powered-Descent Guidance

Abstract: The dual quaternion-based 6-DoF powered-descent guidance algorithm (DQG) was selected as the candidate powered-descent guidance algorithm for NASA’s Safe and Precise Landing — Integrated Capabilities Evolution (SPLICE) project. DQG is capable of handling state-triggered constraints that are of the utmost importance in terms of enabling technologies such as terrain relative navigation (TRN). In this work, we develop a custom solver for DQG to enable onboard implementation for future rocket landing missions. We describe the design and implementation of a real-time-capable optimization framework, called sequential conic optimization (SeCO), that blends together sequential convex programming and first-order conic optimization to solve difficult nonconvex trajectory optimization problems, such as DQG, in real-time. This framework is entirely devoid of matrix factorizations/inversions, making it suitable for safety-critical applications. Under the hood, the SeCO framework leverages a first-order primal-dual conic optimization solver, based on the proportional-integral projected gradient method (PIPG), that combines the ideas of projected gradient descent and proportional-integral feedback of constraint violation. Unlike other conic optimization solvers, PIPG effectively exploits the sparsity and geometric structure of the constraints, avoids expensive equation solving, and is suitable for both real-time and large-scale applications. We describe the implementation of this solver, and develop customizable first-order methods, including an analytical preconditioning algorithm, to solve the nonconvex DQG optimal control problem in real-time. Strategies such as warm-starting and extrapolation are leveraged to further accelerate convergence. We show that the DQG-customized solver is able to solve the problem significantly faster than other state-of-the-art convex optimization solvers, and thus demonstrate the viability of SeCO for real-time, mission-critical applications onboard computationally constrained flight hardware.

Nonlinear Multiplicative Smoothing Applied to Trajectory Recovery for GPS/INS-Aided Navigation

Abstract: A multiplicative continuous-discrete Rauch-Tung-Striebel (RTS) smoother is presented in this work. Traditional nonlinear smoothing formulations are extended to apply to states exhibiting multiplicative error, such as the quaternion. This new framework mirrors the form of the multiplicative extended Kalman filter, which is often used in aerospace vehicle navigation. This work demonstrates the effectiveness of the new smoother to accurately recover `ground truth' attitude, position, and velocity during GPS/INS-aided navigation scenarios. The smoother's capability is then extended to inertial sensor noise quantification and approximation of external inertial accelerations acting on the vehicle. Validation of the proposed algorithms is achieved through application to data obtained from the Blue Origin New Shepard De-Orbit, Descent, and Landing Tipping Point test campaign.

Implementation of a Six Degree of Freedom Precision Lunar Landing Algorithm Using Dual Quaternion Representation

Abstract: In this study, a powered descent guidance algorithm using a unit dual quaternion representation of the vehicle dynamics is implemented in a high-fidelity simulation and on representative flight hardware. This Dual-Quaternion Guidance (DQG) algorithm is applied to the precision lunar landing problem which levies complex constraints upon the trajectory, including state triggered attitude constraints to enable terrain-relative navigation and hazard detection as well as real-time requirements for landing site re-designation. The investigation explores DQGs usefulness as a mission design tool as well as a real-time guidance algorithm and defines real-time performance requirements for the hazard detection and avoidance (HDA) re-targeting phase of precision lunar landing. The experiment is presented in two parts. First, DQG is implemented within a high-fidelity Monte Carlo simulation to tune the algorithm’s parameters for the simulated vehicle, to refine the mission design, and to develop guidance update timing requirements to perform the HDA maneuver. DQG generates trajectories online for the divert which are tracked by the vehicle’s inner-loop controllers to the targeted landing site. Second, DQG is run on representative hardware to demonstrate real-time operation through a divert maneuver. These results allow for rapid, flexible, optimal mission design satisfying complex constraints, and for the definition of real-time performance requirements for the HDA operations inherent in precision lunar landing. The HDA divert maneuver is found to require guidance trajectory updates in less than three seconds. DQG is found to be too slow to meet this update timing on the descent and landing computer (DLC) in its current implementation. DQG running on alternative hardware can meet the update rate requirement. Algorithm implementation improvements are also recommended which are expected to speed up computation sufficiently to meet requirements on the DLC.

Performance Analysis of Terrain Relative Navigation Using Blue Origin New Shepard Suborbital Flight Telemetry

Abstract: As part of a NASA Tipping Point Partnership with Blue Origin to mature precision lunar landing technologies, two test flights of the Blue Origin New Shepard vehicle carrying a NASA-developed sensor suite were conducted on 10/13/2020 and 08/26/2021 at the West Texas Launch Site (LS-1). Part of the acquired datasets, comprising data from an inertial measurement unit and a downward facing camera, was postprocessed through a JPL-developed prototype Visual Odometry and Map Relative Localization software (TRNVOSIM), and compared against ground truth acquired by the host vehicle navigation system. In this paper, we provide a description of the algorithms, the test setup, and the processed results.