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Dual Quaternion Visual Servo Control

This paper focuses on a dual quaternion-based estimation and control approach for position-based visual servoing (PBVS). The pose estimation of the camera is achieved using a dual quaternion-based Extended Kalman Filter (EKF), which estimates the position and orientation of the camera based on feature points acquired through a sequence of camera images. Based on the estimation, a dual quaternion control law is developed to regulate the camera to the desired pose. Leveraging the local exponential stability of the EKF and the global exponential stability of the designed controller, a nonlinear separation principle is used to prove the stability of the joint estimation and control for PBVS. The method is distinguished from other PBVS methods in the sense that a compact representation of dual quaternion is used to represent the pose, and a joint stability of estimator and controller for PBVS in dual quaternion space is presented. The proposed dual quaternion PBVS method is validated using a simulation.

Quaternions↗

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

In this study, a powered descent guidance algorithm using a unit dual quaternion represen- tation 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 DQG’s 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.

GN&C↗

Hardware in the Loop Performance of Terrestrial Powered Descent Dual Quaternion Guidance With A Custom First-Order Solver

The Safe & Precise Landing Integrated Capabilities Evolution (SPLICE) program continues to push the development of advanced descent and landing technologies. This paper will focus on the improvements made to the SPLICE Dual Quaternion Guidance (DQG) algorithm, which is a critical software component for generating approach phase and hazard avoidance trajectories. The trajectory performance of SPLICE DQG will be evaluated in preparation for a terrestrial flight test that incorporates a hazard avoidance maneuver. Additionally, the implementation of a customized first order Proportional-Integral Projected Gradient solver will be reviewed, along with preliminary execution results on the SPLICE Descent and Landing Computer (DLC).

SPLICE↗

Performance Analysis of A Dual Quaternion Guidance Algorithm Applicable During Lunar Approach With A Hazard Avoidance Maneuver

There is currently a need for advanced guidance and targeting algorithms that can provide real-time trajectories in the presence of state and vehicle constraints during powered descent. The Safe & Precise Landing Integrated Capabilities Evolution (SPLICE) program aims to mature Hazard Detection (HD) technology along with advanced navigation and guidance algorithms. This paper will report the overall performance of the SPLICE Dual Quaternion Guidance (DQG) algorithm which is a 6-Degree-of-Freedom (6-DOF) convex optimization-based guidance algorithm that can enforce multiple vehicle and state constraints required for Hazard Detection Lidar (HDL) scans during the approach phase. DQG was tested in a closed-loop lunar descent simulation with realistic HDL sensing constraints in a Monte Carlo assessment of 1000 dispersed runs.

Guidance↗

Application of A Dual-Quaternion Six Degree-of-Freedom Guidance to Human-Scale Mars Entry, Descent, and Landing

Landing humans on Mars comes with many challenges, including the execution of a safe and precise entry, descent, and landing (EDL) sequence. Various NASA studies have shown that there are a variety of EDL guidance methods that potentially offer solutions to the human-scale EDL precision landing problem and work is ongoing to assess new and novel methods. As part of these ongoing studies, a dual-quaternion-based six degree-of-freedom guidance algorithm was implemented in the Program to Optimize Simulated Trajectories II (POST2), a NASA-and industry-standard spacecraft trajectory and vehicle design tool. This algorithm considers both translational and rotational dynamics and casts the trajectory optimization problem as a quadratically constrained quadratic program (QCQP) with various constraints at discrete nodes throughout the trajectory. The QCQP problem is solved via an alternating direction method of multipliers (ADMM) approach, and the output is a discretized optimal trajectory. The guidance is applied to a NASA reference human-scale Mars EDL system, and results are compared and discussed.

Optimization↗

Application of A Dual-Quaternion Six Degree-of-Freedom Guidance to Human-Scale Mars Entry, Descent, and Landing

Landing humans on Mars comes with many challenges, including the execution of a safe and precise entry, descent, and landing (EDL) sequence. Various NASA studies have shown that there are a variety of EDL guidance methods that potentially offer solutions to the human-scale EDL precision landing problem and work is ongoing to assess new and novel methods. As part of these ongoing studies, a dual-quaternion-based six degree-of-freedom guidance algorithm was implemented in the Program to Optimize Simulated Trajectories II (POST2), a NASA-and industry-standard spacecraft trajectory and vehicle design tool. This algorithm considers both translational and rotational dynamics and casts the trajectory optimization problem as a quadratically constrained quadratic program (QCQP) with various constraints at discrete nodes throughout the trajectory. The QCQP problem is solved via an alternating direction method of multipliers (ADMM) approach, and the output is a discretized optimal trajectory. The guidance is applied to a NASA reference human-scale Mars EDL system, and results are compared and discussed.

Optimization↗

Safe and Precise Landing Integrated Capabilities Evolution (SPLICE) Imagery of Sensors

Collection of imagery of SPLICE hardware and software visualization. Descent Landing Computer ETU Open Frame Chassis (OFC). ETU pictures of the GSFC Hazard Detection Lidar during assembly. Prototype picture of the delivered Psionic Navigation Doppler Lidar, including testing with a three-dimensional mobile target. Visualization of a lunar lander simulation using the Dual Quaternion Guidance, demonstrating pointing of a mounted hazard lidar, and then diverting to a selected safe site.

Guidance Navigation and Control↗

Tele-Autonomous control involving contact

Object localization and its application in tele-autonomous systems are studied. Two object localization algorithms are presented together with the methods of extracting several important types of object features. The first algorithm is based on line-segment to line-segment matching. Line range sensors are used to extract line-segment features from an object. The extracted features are matched to corresponding model features to compute the location of the object. The inputs of the second algorithm are not limited only to the line features. Featured points (point to point matching) and featured unit direction vectors (vector to vector matching) can also be used as the inputs of the algorithm, and there is no upper limit on the number of the features inputed. The algorithm will allow the use of redundant features to find a better solution. The algorithm uses dual number quaternions to represent the position and orientation of an object and uses the least squares optimization method to find an optimal solution for the object's location. The advantage of using this representation is that the method solves for the location estimation by minimizing a single cost function associated with the sum of the orientation and position errors and thus has a better performance on the estimation, both in accuracy and speed, than that of other similar algorithms. The difficulties when the operator is controlling a remote robot to perform manipulation tasks are also discussed. The main problems facing the operator are time delays on the signal transmission and the uncertainties of the remote environment. How object localization techniques can be used together with other techniques such as predictor display and time desynchronization to help to overcome these difficulties are then discussed.

Shao, Lejun↗

Quaternions for Galileo scan platform control

The application of quaternions for the articulation control of the Galileo scan platform is presented in this paper. The purpose of selecting quaternions is to minimize onboard computation time and program size. Attention has been focused on performing inertial pointing while the spacecraft is in a dual spin configuration. Target quaternion and relative target quaternion are introduced and used to specify the target position of the scan platform for point-to-point absolute slews and mosaic relative slews, respectively. The pointing error of the platform is represented by an error quaternion which is converted into gimbal angular errors defining the attitude change. For path control, a moving target quaternion is generated; the corresponding tracking error quaternion and the related spacecraft motion compensation capability are also addressed. A sample slew case is used to demonstrate the implementation of these concepts.

Breckenridge, W. G.↗

Inertial attitude determination for a dual-spin planetary spacecraft

Design and performance evaluations of an onboard inertial attitude determination system for a dual-spin planetary spacecraft are presented. A quaternion integration algorithm and a rate estimator sequentially determine the scan platform's inertial attitude and rate from the drift and misalignment compensated gyro outputs. A least-squares estimator algorithm processes the star transit data from a rotor-mounted star scanner, and provides periodic updates of the scan platform's attitude as a means of correcting the drift of the quaternion integration algorithm. Computer simulated algorithm performance in the presence of nutation and sensor noise are presented.

Wong, E. C.↗

Miniature wide field-of-view star trackers for spacecraft attitude sensing and navigation

Introducing a family of miniature, wide field-of-view star trackers for low cost, high performance spacecraft attitude determination and navigation applications. These devices, derivative of the WFOV Star Tracker Camera developed cooperatively by OCA Applied Optics and the Lawrence Livermore National Laboratory for the Brilliant Pebbles program, offer a suite of options addressing a wide range of spacecraft attitude measurement and control requirements. These sensors employ much wider fields than are customary (ranging between 20 and 60 degrees) to assure enough bright stars for quick and accurate attitude determinations without long integration intervals. The key benefit of this approach are light weight, low power, reduced data processing loads and high information carrier rates for wide ACS bandwidths. Devices described range from the proven OCA/LLNL WFOV Star Tracker Camera (a low-cost, space-qualified star-field imager utilizing the spacecraft's own computer and centroiding and position-finding), to a new autonomous subsystem design featuring dual-redundant cameras and completely self-contained star-field data processing with output quaternion solutions accurate to 100 micro-rad, 3 sigma, for stand-alone applications.

Mccarty, William↗

An attitude reorientation algorithm for the Galileo spacecraft

This paper presents an onboard closed loop attitude reorientation algorithm for a dual-spin spacecraft, Galileo. The basic concept for the design uses the despun stator as a reference and fires a sequence of fixed duration thruster pulses to precess the angular momentum vector to its commanded orientation. The error signals used to despin the stator and to perform the turn are derived from the stator error quaternion which is computed using gyro outputs. Constraints considered in the design include gyro rate saturation, plume impingement effects, system parameter variations, as well as software reliability and flexibility. The performance of the algorithm was predicted by analysis and confirmed by computer simulation results. It was concluded that a reorientation accuracy of better than 1 milliradian with a nutation angle of less than 1 degree during the turn can be achieved.

Lin, H.-S.↗