GNC Algorithms Research Articles

On-ground validation of orbital GNC: Visual navigation assessment in robotic testbed facility

AbstractCubeSats have become versatile platforms for various space missions (e.g., on-orbit servicing and debris removal) owing to their low cost and flexibility. Many space tasks involve proximity operations that require precise guidance, navigation, and control (GNC) algorithms. Vision-based navigation is attracting interest for such operations. However, extreme lighting conditions in space challenge optical techniques. The on-ground validation of such navigation systems for orbital GNC becomes crucial to ensure their reliability during space operations. These systems undergo rigorous testing within their anticipated operational parameters, including the exploration of potential edge cases. The ability of GNC algorithms to function effectively under extreme space conditions that exceed anticipated scenarios is crucial, particularly in space missions where the scope of errors is negligible. This paper presents the ground validation of a GNC algorithm designed for autonomous satellite rendezvous by leveraging hardware-in-the-loop experiments. This study focuses on two key areas. First, the rationale underlying the augmentation of the robot workspace (six-degree-of-freedom UR10e robot + linear rail) is investigated to emulate relatively longer trajectories with complete position and orientation states. Second, the control algorithm is assessed in response to uncertain pose observations from a vision-based navigation system. The results indicate increased control costs with uncertain navigation and exemplify the importance of on-ground testing for system validation before launch, particularly in extreme cases that are typically difficult to assess using software-based testing.

Tianwen-1 Entry, Descent, and Landing Guidance, Navigation, and Control System Design and Validation

On 15 May 2021, the Tianwen-1 mission delivered a lander and the Zhurong rover to the Mars surface, which made China the second nation to successfully land and place a rover on that planet. The guidance, navigation, and control (GNC) system for the entry, descent, and landing (EDL) of the Tianwen-1 mission play keys role in guaranteeing a successful landing. In this paper, the Tianwen-1 EDL GNC system design is presented, including the GNC architecture, scheme, and algorithm; additionally, the system is validated through experimental tests, numerical simulations, and actual flight results from telemetry data.

A Graduated Non-Convexity Technique for Dealing Large Point Spread Functions

This paper focuses on reducing the computational cost of a GNC Algorithm for deblurring images when dealing with full symmetric Toeplitz block matrices composed of Toeplitz blocks. Such a case is widespread in real cases when the PSF has a vast range. The analysis in this paper centers around the class of gamma matrices, which can perform vector multiplications quickly. The paper presents a theoretical and experimental analysis of how γ-matrices can accurately approximate symmetric Toeplitz matrices. The proposed approach involves adding a minimization step for a new approximation of the energy function to the GNC technique. Specifically, we replace the Toeplitz matrices found in the blocks of the blur operator with γ-matrices in this approximation. The experimental results demonstrate that the new GNC algorithm proposed in this paper reduces computation time by over 20% compared with its previous version. The image reconstruction quality, however, remains unchanged.

Design of the landing guidance for the retro-propulsive vertical landing of a reusable rocket stage

Launcher reusability is the most effective way of reducing access to space costs, but remains a great technical challenge for the European aerospace industry. One of the challenges lies in the recovery GNC strategy and algorithms, in particular those of the powered-landing phase, which must enable a precise landing with low fuel margins and significant dispersions. While state-of-the-art solutions for Navigation and control problems can be applied, namely, hybrid Navigation techniques and robust control, for the powered descent guidance problem novel techniques are required to enable on-board optimization, that is necessary to achieve the landing accuracy required to recover the first stage of a launcher. This paper presents the GNC solution currently in development by DEIMOS Space for RETALT (Retro Propulsion Assisted Landing Technologies), an EU Horizon 2020 funded project for studying launch system re-usability technologies for different classes of vertical take-off vertical-landing vehicles. At first, the architecture of the GNC solution identified for the return mission of the launcher is presented. Then, the paper focuses on the landing phase guidance solution, whose performance is critical to enable the recovery and, therefore, the reusability of the launcher making use of retro-propulsion. The guidance strategy is based on direct optimal control methods via on-board optimization, which is necessary to satisfy the pinpoint landing requirement in a high uncertain dynamic system, such as a booster recovery mission. Online convex optimization and successive convexification are explored for the design of the guidance function. The proposed guidance solution was integrated and tested in a high-fidelity simulator and the performance was preliminary assessed. The guidance assessment allowed selecting the best algorithms to be further consolidated and integrated in an end-to-end GNC solution for the return mission.

The Tianwen-1 Guidance, Navigation, and Control for Mars Entry, Descent, and Landing

Tianwen-1, the first mission of China’s planetary exploration program, accomplished its goals of orbiting, landing, and roving on the Mars. The entry, descent, and landing (EDL) phase directly determines the success of the entire mission, of which the guidance, navigation, and control (GNC) system is crucial. This paper outlines the Tianwen-1 EDL GNC system design by introducing the GNC requirements followed by presenting the GNC system architecture and algorithms to meet such requirements. The actual flight results for the whole EDL phase are also provided in this paper.

Autonomous GNC strategy for an asteroid impactor mission

The Solar System features thousands of Near-Earth Asteroids that could be at collision risk with our planet in the future. Scientists are investigating the possibility of deflecting asteroids from their trajectory by means of a hyper-velocity impactor spacecraft. The aim of this research is to develop and simulate a GNC strategy to control the spacecraft towards its impact with the asteroid. The navigation is based on the use of a camera to estimate the relative position through image analysis and a filtering process. A zero-effort error strategy is adopted for the control. A simulator has been developed to render the simulated images online and test the GNC algorithms. The simulator is used to assess the performance of the strategy on different scenarios and to perform a sensitivity analysis with respect to the environmental and design parameters.

GNC & robotics for on orbit servicing with simulated vision in the loop

Complex robotics missions require complex GNC and Robotics algorithms, often using vision sensors. The problem of vision-in-the-loop GNC is addressed using photorealistic simulated images and simple computer vision algorithms, coupled with relative estimation and control of a servicing satellite in close proximity operations with a customer satellite. In the near future it will be required to simulate the behavior of automated servicing missions comprehending also vision data, hence the request for vision-in-the-loop simulations. In this article is proposed a GNC and Robotics scheme for proximity operations between a servicer and a customer satellite through the use of adaptive control and computer vision. The scheme is then put to test through simulation of orbital robot dynamics, sensors and camera inputs, and computer vision algorithm in the loop.

A DPS extension to restore blurred and noisy piecewise constant signals

In this paper, we are interested in restoring piecewise constant signals obtained from a linear operator A (e.g. a blurring operator) and degraded by a white Gaussian noise. The number of plateaus and their values are unknown. So the problem could be tackled as a joint restoration and unsupervised segmentation in the context of linear inverse problems. The DPS algorithm is a combinatorial algorithm proposed to solve the classical case, where the linear operator is reduced to I. The solution is computed as a global minimizer of an energy function that contains a quadratic fidelity term and a non-convex pairwise potential term. DPS offers a faster alternative to the GNC algorithm that minimizes the same energy in a continuation deterministic approach. We present an extension to the DPS algorithm for the general case. This extension only requires the regularity of the matrix , unlike the GNC extension that needs further computation of its smallest eigenvalue in order to formulate a convex relaxation. Also, we present a message passing and shared memory implementation to speed up the running time for high dimension signals. The parallelization is possible since DPS evaluate the energy on a set of nodes in a given hypercube, and in each level of the hypercube, the nodes are independents.

Difference of convex functions algorithms (DCA) for image restoration via a Markov random field model

In this paper, we introduce a novel approach in the nonconvex optimization framework for image restoration via a Markov random field (MRF) model. While image restoration is elegantly expressed in the language of MRF’s, the resulting energy minimization problem was widely viewed as intractable: it exhibits a highly nonsmooth nonconvex energy function with many local minima, and is known to be NP-hard. The main goal of this paper is to develop fast and scalable approximation optimization approaches to a nonsmooth nonconvex MRF model which corresponds to an MRF with a truncated quadratic (also known as half-quadratic) prior. For this aim, we use the difference of convex functions (DC) programming and DC algorithm (DCA), a fast and robust approach in smooth/nonsmooth nonconvex programming, which have been successfully applied in various fields in recent years. We propose two DC formulations and investigate the two corresponding versions of DCA. Numerical simulations show the efficiency, reliability and robustness of our customized DCAs with respect to the standard GNC algorithm and the Graph-Cut based method—a more recent and efficient approach to image analysis.

Quasi optimal spacecraft formation maneuvering via Lyapunov functions

Space mission concepts based on satellite formations feature several interesting and demanding design requirements. During formation deployment, re-sizing and re-orientation, the spacecraft must reach their desired positions without incurring in collisions or interfering with each other. Conventional GNC algorithms cannot support the degree of flexibility, the accuracy in the relative positioning and the fine pointing attitude requirements of future missions. The potential function method, based upon Lyapunov’s second theorem on stability, brings the advantage of robustness and flexibility, along with a light workload for the control system. The aim of this paper is to foster the understanding of existing algorithms based on this method. In particular, the attention is focused on reducing the fuel consumption through the parametric optimization of the Lyapunov function that defines the control algorithm.

Optimal control and practical GNC algorithms for autonomous low-and high-glide-ratio delivery systems

The paper addresses development of control algorithms for two different autonomousaerial delivery systems. The first one is based on a solid circular parachute and the second one - on a ram-air parafoil. While the first, low-glide-ratio system is crucially dependent on the accuracy of the wind prediction, the second, high-glide-ratiosystem is capable of effectively rejecting moderate winds. This fundamental difference dictates different control laws described in this paper. The paper applies optimal control analysis to both systems and proceeds with thedevelopment of the practical guidance and control algorithms. Simulation results forboth systems as well as flight test results for the parachute-based system are included.

DEIS UAV: GNC Design and Avionics Implementation Issues

The School of Aerospace Engineering of the Forli Branch of the University of Bologna is currently developing an Unmanned Aerial Vehicle (UAV) which, thanks to a partially autonomous flight capability, aims to be a very low cost and compact flying platform capable of performing significant flight tests of general GNC algorithms or mission oriented experiments. The development activity includes the project, the synthesis and the assembly of the on-board avionics equipment, together with the software implementation for both data collection and some basic GNC algorithms. A demonstrative application will be the test of some integrity monitoring functions and algorithms using data collected during some flights.

A GNC algorithm for constrained image reconstruction with continuous-valued line processes

Image reconstruction is formulated as the problem of minimizing a non-convex functional F(ƒ) in which the smoothness stabilizer implicitly refers to a continuous-valued line process. Typical functionals proposed in the literature are considered. The minimum of F(ƒ) is computed using a GNC algorithm that employs a sequence F (p)(ƒ) of approximating functionals for F(ƒ), to be minimized in turn by gradient descent techniques. The results of a simulation evidence that GNC algorithms are computationally more efficient than simulated annealing algorithms, even when the latter are implemented in a simplified form. A comparison between the performance of these functionals and that of a functional that refers to an implicit binary line process is also carried out; this shows that assuming a continuous-valued line process gives a better reconstruction of the smooth, planar or quadratic regions of the image, even with first-order models.

Master index of volumes 11–15

Image reconstruction is formulated as the problem of minimizing a non-convex functional F(ƒ) in which the smoothness stabilizer implicitly refers to a continuous-valued line process. Typical functionals proposed in the literature are considered. The minimum of F(ƒ) is computed using a GNC algorithm that employs a sequence F(p)(ƒ) of approximating functionals for F(ƒ), to be minimized in turn by gradient descent techniques. The results of a simulation evidence that GNC algorithms are computationally more efficient than simulated annealing algorithms, even when the latter are implemented in a simplified form. A comparison between the performance of these functionals and that of a functional that refers to an implicit binary line process is also carried out; this shows that assuming a continuous-valued line process gives a better reconstruction of the smooth, planar or quadratic regions of the image, even with first-order models.

Mean field annealing: a formalism for constructing GNC-like algorithms

Optimization problems are approached using mean field annealing (MFA), which is a deterministic approximation, using mean field theory and based on Peierls's inequality, to simulated annealing. The MFA mathematics are applied to three different objective function examples. In each case, MFA produces a minimization algorithm that is a type of graduated nonconvexity. When applied to the ;weak-membrane' objective, MFA results in an algorithm qualitatively identical to the published GNC algorithm. One of the examples, MFA applied to a piecewise-constant objective function, is then compared experimentally with the corresponding GNC weak-membrane algorithm. The mathematics of MFA are shown to provide a powerful and general tool for deriving optimization algorithms.