arXiv subjects

Richard Linares

Publications and source records attributed to Richard Linares.

At least 55 records · Page 3Linked to original sources

arXiv2024

Towards a Machine Learning-Based Approach to Predict Space Object Density Distributions

With the rapid increase in the number of Anthropogenic Space Objects (ASOs), Low Earth Orbit (LEO) is facing significant congestion, thereby posing challenges to space operators and risking the viability of the space environment for varied uses. Current models for examining this evolution, while detailed, are computationally demanding. To address these issues, we propose a novel machine learning-based model, as an extension of the MIT Orbital Capacity Tool (MOCAT). This advanced model is designed to accelerate the propagation of ASO density distributions, and it is trained on hundreds of simulations generated by an established and accurate model of the space environment evolution. We study how different deep learning-based solutions can potentially be good candidates for ASO propagation and manage the high-dimensionality of the data. To assess the model's capabilities, we conduct experiments in long term forecasting scenarios (around 100 years), analyze how and why the performance degrades over time, and discuss potential solutions to make this solution better.

physics.space-ph↗

arXiv2023

Improving Computational Efficiency for Powered Descent Guidance via Transformer-based Tight Constraint Prediction

In this work, we present Transformer-based Powered Descent Guidance (T-PDG), a scalable algorithm for reducing the computational complexity of the direct optimization formulation of the spacecraft powered descent guidance problem. T-PDG uses data from prior runs of trajectory optimization algorithms to train a transformer neural network, which accurately predicts the relationship between problem parameters and the globally optimal solution for the powered descent guidance problem. The solution is encoded as the set of tight constraints corresponding to the constrained minimum-cost trajectory and the optimal final time of landing. By leveraging the attention mechanism of transformer neural networks, large sequences of time series data can be accurately predicted when given only the spacecraft state and landing site parameters. When applied to the real problem of Mars powered descent guidance, T-PDG reduces the time for computing the 3 degree of freedom fuel-optimal trajectory, when compared to lossless convexification, from an order of 1-8 seconds to less than 500 milliseconds. A safe and optimal solution is guaranteed by including a feasibility check in T-PDG before returning the final trajectory.

math.OC↗

arXiv2023

Transformer-based Atmospheric Density Forecasting

As the peak of the solar cycle approaches in 2025 and the ability of a single geomagnetic storm to significantly alter the orbit of Resident Space Objects (RSOs), techniques for atmospheric density forecasting are vital for space situational awareness. While linear data-driven methods, such as dynamic mode decomposition with control (DMDc), have been used previously for forecasting atmospheric density, deep learning-based forecasting has the ability to capture nonlinearities in data. By learning multiple layer weights from historical atmospheric density data, long-term dependencies in the dataset are captured in the mapping between the current atmospheric density state and control input to the atmospheric density state at the next timestep. This work improves upon previous linear propagation methods for atmospheric density forecasting, by developing a nonlinear transformer-based architecture for atmospheric density forecasting. Empirical NRLMSISE-00 and JB2008, as well as physics-based TIEGCM atmospheric density models are compared for forecasting with DMDc and with the transformer-based propagator.

physics.ao-ph↗

arXiv2023

The ReSWARM Microgravity Flight Experiments: Planning, Control, and Model Estimation for On-Orbit Close Proximity Operations

On-orbit close proximity operations involve robotic spacecraft maneuvering and making decisions for a growing number of mission scenarios demanding autonomy, including on-orbit assembly, repair, and astronaut assistance. Of these scenarios, on-orbit assembly is an enabling technology that will allow large space structures to be built in-situ, using smaller building block modules. However, robotic on-orbit assembly involves a number of technical hurdles such as changing system models. For instance, grappled modules moved by a free-flying "assembler" robot can cause significant shifts in system inertial properties, which has cascading impacts on motion planning and control portions of the autonomy stack. Further, on-orbit assembly and other scenarios require collision-avoiding motion planning, particularly when operating in a "construction site" scenario of multiple assembler robots and structures. These complicating factors, relevant to many autonomous microgravity robotics use cases, are tackled in the ReSWARM flight experiments as a set of tests on the International Space Station using NASA's Astrobee robots. RElative Satellite sWarming and Robotic Maneuvering, or ReSWARM, demonstrates multiple key technologies for close proximity operations and on-orbit assembly: (1) global long-horizon planning, accomplished using offline and online sampling-based planner options that consider the system dynamics; (2) on-orbit reconfiguration model learning, using the recently-proposed RATTLE information-aware planning framework; and (3) robust control tools to provide low-level control robustness using current system knowledge. These approaches are detailed individually and in an "on-orbit assembly scenario" of multi-waypoint tracking on-orbit. Additionally, detail is provided discussing the practicalities of hardware implementation and unique aspects of working with Astrobee in microgravity.

cs.RO↗

arXiv2022

A Dynamical Systems Analysis of the Effects of the Launch Rate Distribution on the Stability of a Source-Sink Orbital Debris Model

Future launches are projected to significantly increase both the number of active satellites and aggregate collision risk in Low Earth Orbit (LEO). In this paper, a dynamical systems theory approach is used to analyze the effect of launch rate distribution on the stability of the LEO environment. A multi-shell, three-species source-sink model of the LEO environment, referred to as MOCAT-3 for MIT Orbital Capacity Assessment Tool 3 Species, is used to study the evolution of the species populations. The three species included in the model are active satellites, derelict satellites, and debris. The model's coefficients represent atmospheric drag, collision rate, mean satellite lifetime, post-mission disposal probability, and active debris removal rate. Solutions of the system of differential equations are computed, and an analysis of the stability of the equilibrium points is conducted for numerous launch rate distributions. The stability of the equilibrium points is used to test the sensitivity of the environment to run-away debris growth, known as Kessler syndrome, that occurs at the instability threshold. An analysis of the environment's response to perturbations in launch rate and debris population is conducted. The maximum perturbation in the debris population from the equilibrium state, for which the system remains in a stable configuration, is calculated. Plots of the phase space about the equilibrium points are generated. The results will help to better understand the orbital capacity of LEO and the stability of the space environment, as well as provide improved guidelines on future launch plans to avoid detrimental congestion of LEO.

astro-ph.EP↗

arXiv2022

A Lambert's Problem Solution via the Koopman Operator with Orthogonal Polynomials

Lambert's problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work offers an analytical solution to Lambert's problem using the Koopman Operator (KO). In contrast to previous methods in the literature, the KO provides the analysis of a nonlinear system by seeking a transformation that embeds the nonlinear dynamics into a global linear representation. Our new methodology to solve for Lambert solutions considers the position of the system's eigenvalues on the phase plane, evaluating accurate state transition polynomial maps for a computationally efficient propagation of the dynamics. The methodology used and multiple-revolution solutions found are compared in accuracy and performance with other techniques found in the literature, highlighting the benefits of the newly developed analytical approach over classical numerical methodologies.

math.NA↗

arXiv2022

A Koopman Operator Tutorial with Othogonal Polynomials

The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear combination of the eigenfunctions of the system. Coefficients are evaluated via the Galerkin method, using Legendre polynomials as a set of orthogonal basis functions. This tutorial provides a detailed analysis of the Koopman theory, followed by a rigorous explanation of the KO implementation in a computer environment, where a line-by-line description of a MATLAB code solves the Duffing oscillator application.

math.NA↗

arXiv2022

A Koopman-Operator Control Optimization for Relative Motion in Space

A high order optimal control strategy implemented in the Koopman operator framework is proposed in this work. The new technique exploits the Koopman representation of the solution of the equations of motion to develop an energy optimal inverse control methodology. The operator theory can reformulate a nonlinear dynamical system of finite dimension into a linear system with an infinite number of dimensions. As a results, the state of any nonlinear dynamics is represented as a linear combination of high-order orthogonal polynomials, which creates the state transition polynomial map of the solution. Since the optimal control technique can be reduced to a two-points boundary value problem, the Koopman map is used to connect the state and control variables in time, such that optimal values are obtained through map inversion and polynomial evaluation. The new technique is applied to rendezvous applications in space, where the relative motion between two satellites is modelled with a high-order polynomial series expansion of the Lagrangian of the system, such that the Clohessy-Wiltshire equations represent the reduction of the high-order model to a linear truncation.

math.OC↗

arXiv2022

The Capacity of Low Earth Orbit Computed using Source-sink Modeling

The increasing number of Anthropogenic Space Objects (ASOs) in Low Earth Orbit (LEO) poses a threat to the safety and sustainability of the space environment. Multiple companies are planning to launch large constellations of hundreds or thousands of satellites in the near future, increasing congestion in LEO and the risk of collisions and debris generation. This paper employs a new multi-shell multi-species evolutionary source-sink model, called MOCAT-3, to estimate LEO orbital capacity. In particular, a new definition of orbital capacity based on the stable equilibrium points of the system is provided. Moreover, an optimization approach is used to compute the maximum orbital capacity of the low region of LEO (200-900 km of altitude), considering the equilibrium solutions and the failure rate of satellites as a constraint. Hence, an estimate for the maximum number of satellites that it is possible to fit in LEO, considering the stability of the space environment, is obtained. As a result, considering 7% of failure rate, the maximum orbital capacity of LEO is estimated to be about 12.6 million satellites. Compatibility of future traffic launch, especially in terms of satellite constellations, is also analyzed and a strategy to accommodate for future traffic needs is proposed.

physics.space-ph↗

arXiv2022

A Method for Generating Closely Packed Orbital Shells and the Implication on Orbital Capacity

Shell-wise orbital slotting in Low Earth Orbit (LEO) can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This paper describes two methods to generate 2D Lattice Flower Constellations (2D-LFCs) that are defined with respect to either an arbitrary degree or an arbitrary degree and order Earth geopotential. By generating shells that are quasi-periodic and frozen with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semi-major axis of each shell or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. This helps mitigate the single inclination per shell requirement in prior work by admitting more shells for a given orbital volume while retaining self-safe phasing in each shell. These methods exploit previous work on the Time Distribution Constellation formulation and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these frozen shells are identified. Simplified formulas for estimating shell geometry and thickness are presented. It is shown that sequencing shells to group similar or ascending inclinations improves capacity versus arbitrary inclination ordering.

astro-ph.EP↗

arXiv2022

The RATTLE Motion Planning Algorithm for Robust Online Parametric Model Improvement with On-Orbit Validation

Certain forms of uncertainty that robotic systems encounter can be explicitly learned within the context of a known model, like parametric model uncertainties such as mass and moments of inertia. Quantifying such parametric uncertainty is important for more accurate prediction of the system behavior, leading to safe and precise task execution. In tandem, providing a form of robustness guarantee against prevailing uncertainty levels like environmental disturbances and current model knowledge is also desirable. To that end, the authors' previously proposed RATTLE algorithm, a framework for online information-aware motion planning, is outlined and extended to enhance its applicability to real robotic systems. RATTLE provides a clear tradeoff between information-seeking motion and traditional goal-achieving motion and features online-updateable models. Additionally, online-updateable low level control robustness guarantees and a new method for automatic adjustment of information content down to a specified estimation precision is proposed. Results of extensive experimentation in microgravity using the Astrobee robots aboard the International Space Station and practical implementation details are presented, demonstrating RATTLE's capabilities for real-time, robust, online-updateable, and model information-seeking motion planning capabilities under parametric uncertainty.

cs.RO↗

arXiv2021

Online Information-Aware Motion Planning with Inertial Parameter Learning for Robotic Free-Flyers

Space free-flyers like the Astrobee robots currently operating aboard the International Space Station must operate with inherent system uncertainties. Parametric uncertainties like mass and moment of inertia are especially important to quantify in these safety-critical space systems and can change in scenarios such as on-orbit cargo movement, where unknown grappled payloads significantly change the system dynamics. Cautiously learning these uncertainties en route can potentially avoid time- and fuel-consuming pure system identification maneuvers. Recognizing this, this work proposes RATTLE, an online information-aware motion planning algorithm that explicitly weights parametric model-learning coupled with real-time replanning capability that can take advantage of improved system models. The method consists of a two-tiered (global and local) planner, a low-level model predictive controller, and an online parameter estimator that produces estimates of the robot's inertial properties for more informed control and replanning on-the-fly; all levels of the planning and control feature online update-able models. Simulation results of RATTLE for the Astrobee free-flyer grappling an uncertain payload are presented alongside results of a hardware demonstration showcasing the ability to explicitly encourage model parametric learning while achieving otherwise useful motion.

cs.RO↗

arXiv2021

Dynamics Near the Three-Body Libration Points via Koopman Operator Theory

This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative to the geometric perspective for dynamical systems, where the Koopman Operator formulates the analysis and dynamical systems in terms of observables. This paper explores the use of the Koopman Operator for computing both 2D and 3D periodic orbits near libration points. Further, simulation results show that the Koopman Operator provides analytical solutions with high accuracy for both Lyapunov and Halo orbits, which are then applied to a station-keeping application.

nlin.CD↗

arXiv2021

Approximate Analytical Solution to the Zonal Harmonics Problem Using Koopman Operator Theory

This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly provides the osculating evolution of the system under the effects of any order of the zonal harmonics, and can be automated to obtain any level of accuracy in the approximated solution. Moreover, this paper defines a modified set of orbital elements that can be applied to any kind of orbit and that allows the Koopman operator to have a fast convergence. In that regard, several examples of application are included, showing that the proposed methodology can be used in any kind of orbit, including circular, elliptic, parabolic and hyperbolic orbits.

astro-ph.EP↗

arXiv2021

On the Theory of Uniform Satellite Constellation Reconfiguration

This work focuses on the study of the reconfiguration strategies available for uniformly distributed satellite constellations and slotting architectures. Particularly, this manuscript deals with the cases of reducing, maintaining, and also increasing the number of available positions for satellites in the space structure, and takes into account the potential minimum distances between spacecraft in the configuration to assure the safety of the system. To that end, several approaches to solve the reconfiguration problem are presented based on the properties of Flower Constellations, and more particularly, on the properties of uniformity and symmetries present in these uniform distributions.

astro-ph.EP↗

arXiv2021

Non-self-intersecting trajectories and their applications to satellite constellation design and orbital capacity

This work focuses on the generation of non-self-intersecting relative trajectories, and their applications to satellite constellation design, slotting architectures, and Space Traffic Management. To that end, this paper introduces two theorems to determine when two spacecrafts share the same relative trajectory, and to identify the only conditions that allow the existence of non-self-intersecting relative trajectories. Then, these results are applied first to the estimation of the limits of the orbital capacity at a given altitude, and second, to the design of satellite constellations and slotting architectures that present no conjunctions between any element compliant with these space structures.

astro-ph.EP↗

arXiv2021

Safe and Uncertainty-Aware Robotic Motion Planning Techniques for Agile On-Orbit Assembly

As access to space and robotic autonomy capabilities move forward, there is simultaneously a growing interest in deploying large, complex space structures to provide new on-orbit capabilities. New space-borne observatories, large orbital outposts, and even futuristic on-orbit manufacturing will be enabled by robotic assembly of space structures using techniques like on-orbit additive manufacturing which can provide flexibility in constructing and even repairing complex hardware. However, the dynamics underlying the robotic assembler during manipulation may operate under inertial uncertainties. Thus, inertial estimation of the robot and the manipulated component system must be considered during structural assembly. The contribution of this work is to address both the motion planning and control for robotic assembly with consideration of the inertial estimation of the combined free-flying robotic assembler and additively manufactured component system. Specifically, the Linear Quadratic Regulator Rapidly-Exploring Randomized Trees (LQR-RRT*) and dynamically feasible path smoothing are used to obtain obstacle-free trajectories for the system. Further, model learning is incorporated explicitly into the planning stages via approximation of the continuous system and accompanying reward of performing safe, objective-oriented motion. Remaining uncertainty can then be dealt with using robust tube model predictive control. By obtaining controlled trajectories that consider both obstacle avoidance and learning of the inertial properties of the free-flyer and manipulated component system, the free-flyer rapidly considers and plans the construction of space structures with enhanced system knowledge. The approach naturally generalizes to repairing, refueling, and re-provisioning space structure components while providing optimal collision-free trajectories under e.g., inertial uncertainty.

cs.RO↗

arXiv2020

Rendezvous Mission for Interstellar Objects Using a Solar Sail-based Statite Concept

Using the "statite," or static-satelite, concept -- an artificial satellite capable of hovering in place using a solar sail -- this work proposes to create a dynamic orbital slingshot in anticipation of Interstellar Objects (ISOs) passing through our solar system. The existence of these ISOs offers a unique scientific opportunity to answer fundamental scientific questions about the origin of solar system volatiles, the compositions of exo-solar systems, and the transfer rates of material between solar systems. However, due to their high heliocentric velocities and relatively short lead time, it may be extremely difficult to visit ISOs with current satellite propulsion systems. This work investigates the statite concept as applied to ISO missions and demonstrates potential configurations for optimal ISO flyby and rendezvous missions.

astro-ph.IM↗