arXiv subjects

Koki Ho

Publications and source records attributed to Koki Ho.

At least 19 recordsLinked to original sources

arXiv2026

Spare Strategy for Large-Scale Satellite Constellations Under Dual Resupply Channels Using Markov Chain

This paper presents a Markov-chain-based method for the early-phase analysis and design of hybrid spare-management architectures for large-scale satellite constellations.} The hybrid strategy combines two channels: an indirect path that stages spares in parking orbits via heavy launch for later transfer to constellation planes, and a direct path that delivers spares to in-plane orbits using small launch vehicles. {To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as a Markov chain:} the indirect channel follows a periodic-review reorder-point/order-quantity policy, while the direct channel uses a standard reorder-point/order-quantity policy. These coupled chains yield a periodic steady state over the right ascension of the ascending node cycle via fixed-point iteration, and the stationary distributions provide rigorous cost and resilience metrics. By directly modeling the stochastic, multi-echelon dynamics governed by orbital mechanics, our framework avoids the aggregation assumptions of prior works and remains valid across a wider operating domain. We also introduce an approximate analysis that preserves delay statistics while significantly reducing model size. Building on this fast, accurate analysis, we formulate a cost minimization problem with resilience constraints and solve it using a genetic algorithm. The framework is channel-neutral; the optimization autonomously selects the preferred path and roles. {A case study validates the analysis against Monte Carlo simulations and demonstrates the practical value of the framework in identifying the conditions under which the hybrid policy outperforms pure strategies.

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arXiv2026

Integrated Routing and Trajectory Design for Satellite Servicing

This paper studies the integrated spacecraft routing and trajectory optimization problem for satellite servicing missions involving partial en-route propellant replenishment. Unlike terrestrial routing problems, spacecraft operate in a dynamic environment, and we need to optimize the spacecraft routing over a network with nonlinear and time-dependent trajectory costs. In this paper, we tackle this problem using two different formulations. The first formulation, referred to as the arc-based formulation, defines variables based on arcs and employs an iterative decoupling scheme that alternates between mixed-integer linear programming and sequential nonlinear trajectory optimization. The second formulation, referred to as the path-based formulation, defines variables based on paths/routes and leverages column generation and a labeling algorithm to accelerate the identification of promising routes. Through a geosynchronous satellite servicing case study and numerical experiments, we quantify the computational trade-offs between these two formulations in terms of the solution optimality, computational time, and robustness against non-converging or trivial solutions.

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arXiv2025

Spare Strategy Analysis and Design for Mega Satellite Constellations Using Markov Chain

This paper presents a Markov-chain-based method for the early-phase analysis and design of spare-management architectures for large-scale satellite constellations. To assess the long-run viability of such concepts of operations, satellite failure and replenishment processes are modeled as Markov chains and analyzed through their stationary solution. We reinvestigate an indirect spare strategy, modeled as a multi-echelon periodic-review reorder-point/order-quantity policy, in which spares are first delivered to parking orbits and then transferred to constellation planes. The stock levels in constellation and parking orbits are each modeled as independent Markov chains, and a fixed-point iteration yields a consistent joint stationary solution that describes the strategy's average behavior. This approach accurately captures the stochastic interplay within a multi-echelon model driven by orbital mechanics, avoiding the aggregation assumptions of prior works and remaining valid across a wider operating domain. Building on this fast, accurate analysis, we formulate an optimization problem and solve it via a genetic algorithm. Finally, we demonstrate the practical value of both the analysis method and the optimization framework in a real-world mega-constellation case study.

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arXiv2025

Analysis and Design of Spare Strategy for Large-Scale Satellite Constellation Using Direct Insertion under (r,q) Policy

This paper introduces a Markov chain-based approach for the analysis and optimization of spare-management policies in large-scale satellite constellations. Focusing on the direct strategy, we model spare replenishment as a periodic-review reorder-point/order-quantity policy, where spares are deployed directly to constellation planes. The stochastic behavior of satellite failures and launch vehicle lead times is captured through Markov representations of both failure and replenishment dynamics. Based on this efficient and accurate framework, we construct and solve an optimization problem aimed at minimizing operational costs. The effectiveness of the proposed method is demonstrated through a case study using a real-world mega-constellation.

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arXiv2025

Optimizing Flexible Complex Systems with Coupled and Co-Evolving Subsystems under Operational Uncertainties

The paper develops a novel design optimization framework and associated computational techniques for staged deployment optimization of complex systems under operational uncertainties. It proposes a local scenario discretization method that offers a computationally efficient approach to optimize staged co-deployment of multiple coupled subsystems by decoupling weak dynamic interaction among subsystems. The proposed method is applied to case studies and is demonstrated to provide an effective and scalable strategy to determine the optimal and flexible systems design under uncertainty. The developed optimization framework is expected to improve the staged deployment design of various complex engineering systems, such as water, energy, food, and other infrastructure systems.

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arXiv2025

Concurrent Optimization of Satellite Phasing and Tasking for Cislunar Space Situational Awareness

Recently, renewed interest in cislunar space spurred by private and public organizations has driven research for future infrastructure in the region. As Earth-Moon traffic increases amidst a growing space economy, monitoring architectures supporting this traffic must also develop. These are likely to be realized as constellations of patrol satellites surveying traffic between the Earth and the Moon. This work investigates the concurrent optimization of patrol satellite phasing and tasking to provide information-maximal coverage of traffic in periodic orbits.

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arXiv2025

Orbital Depot Location Optimization for Satellite Constellation Servicing with Low-Thrust Transfers

This paper addresses the critical problem of co-optimizing the optimal locations for orbital depots and the sequence of in-space servicing for a satellite constellation. While most traditional studies used network optimization for this problem, assuming a fixed set of discretized nodes in the network (i.e., a limited number of depot location candidates), this work is unique in that it develops a method to optimize the depot location in continuous space. The problem is formulated as mixed-integer nonlinear programming, and we propose a solution methodology that iteratively solves two decoupled problems: one using mixed-integer linear programming and the other using nonlinear programming with an analytic transfer solution. To demonstrate the effectiveness of our approach, we apply this methodology to a case study involving a GPS satellite constellation. Numerical experiments confirm the stability of our proposed solutions.

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arXiv2025

Revolution-Spaced Output-Feedback Model Predictive Control for Station Keeping on Near-Rectilinear Halo Orbits

We develop a model predictive control (MPC) policy for station keeping on a Near-Rectilinear Halo Orbit (NRHO). The proposed policy achieves full-state tracking of a reference NRHO via a multiple-maneuver control horizon, each spaced one revolution apart to abide by typical mission operation requirements. We prove that the proposed policy is recursively feasible, and perform numerical evaluation in an output-feedback setting by incorporating a navigation filter and realistic operational uncertainties, where the proposed MPC is compared against the state-of-the-art station-keeping algorithm adopted for the Gateway. Our approach successfully maintains the spacecraft in the vicinity of the reference NRHO at a similar cumulative cost as existing station-keeping methods without encountering phase deviation issues, a common drawback of existing methods with one maneuver per revolution.

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arXiv2024

Optimisation of Categorical Choices in Exploration Mission Concepts of Operations Using Column Generation Method

Space missions, particularly complex, large-scale exploration campaigns, can often involve many discrete decisions or events in their concepts of operations. Whilst a variety of methods exist for the optimisation of continuous variables in mission design, the inherent presence of discrete events in mission ConOps disrupts the possibility of using methods that are dependent on having well-defined, continuous mathematical expressions to define the systems. Typically, mission architects will circumvent this problem by solving the system optimisation for every permutation of the categorical decisions if practical, or use metaheuristic solvers if not. However, this can be prohibitively expensive in terms of computation time. Alternatively, categorical decisions in optimisation problems can be expressed using binary variables. If implemented naively, commercially available MILP solvers are still slow to solve such a problem. Problems of this class can be solved more efficiently using column generation methods. Here, restricted problems are created by removing significant numbers of variables. The restricted problem is solved, and the unused variables are priced to test which, if any, could improve the objective of the restricted problem if they were to be added. Column generation methods are problem-specific, and so there is no guaranteed solution to these categorical problems. As such, the following paper proposes guidelines for defining restricted problems representing space exploration mission concepts of operations. The column generation process is described and then applied to two case studies: a ConOps for a crewed Mars mission, in which the design, assembly, and staging of the trans-Martian spacecraft is modelled using discrete decisions; and the payload delivery scheduling of translunar logistics in the context of an extended Artemis surface exploration campaign.

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arXiv2024

Real-Time Stochastic Terrain Mapping and Processing for Autonomous Safe Landing

Onboard terrain sensing and mapping for safe planetary landings often suffer from missed hazardous features, e.g., small rocks, due to the large observational range and the limited resolution of the obtained terrain data. To this end, this paper develops a novel real-time stochastic terrain mapping algorithm that accounts for topographic uncertainty between the sampled points, or the uncertainty due to the sparse 3D terrain measurements. We introduce a Gaussian digital elevation map that is efficiently constructed using the combination of Delauney triangulation and local Gaussian process regression. The geometric investigation of the lander-terrain interaction is exploited to efficiently evaluate the marginally conservative local slope and roughness while avoiding the costly computation of the local plane. The conservativeness is proved in the paper. The developed real-time uncertainty quantification pipeline enables stochastic landing safety evaluation under challenging operational conditions, such as a large observational range or limited sensor capability, which is a critical stepping stone for the development of predictive guidance algorithms for safe autonomous planetary landing. Detailed reviews on background and related works are also presented.

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arXiv2024

Terminal Soft Landing Guidance Law Using Analytic Gravity Turn Trajectory

This paper presents an innovative terminal landing guidance law that utilizes an analytic solution derived from the gravity turn trajectory. The characteristics of the derived solution are thoroughly investigated, and the solution is employed to generate a reference velocity vector that satisfies terminal landing conditions. A nonlinear control law is applied to effectively track the reference velocity vector within a finite time, and its robustness against disturbances is studied. Furthermore, the guidance law is expanded to incorporate ground collision avoidance by considering the shape of the gravity turn trajectory. The proposed method's fuel efficiency, robustness, and practicality are demonstrated through comprehensive numerical simulations, and its performance is compared with existing methods.

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arXiv2024

Optimal Strip Attitude Command of Earth Observation Satellite using Differential Dynamic Programming

This paper addresses the optimal scan profile problem for strip imaging in an Earth observation satellite (EOS) equipped with a time-delay integration (TDI) camera. Modern TDI cameras can control image integration frequency during imaging operation, adding an additional degree of freedom (DOF) to the imaging operation. On the other hand, modern agile EOS is capable of imaging non-parallel ground targets, which require a substantial amount of angular velocity and angular acceleration during operation. We leverage this DOF to minimize various factors impacting image quality, such as angular velocity. Initially, we derive analytic expressions for angular velocity based on kinematic equations. These expressions are then used to formulate a constrained optimal control problem (OCP), which we solve using differential dynamic programming (DDP). We validate our approach through testing and comparison with reference methods across various practical scenarios. Simulation results demonstrate that our proposed method efficiently achieves near-optimal solutions without encountering non-convergence issues.

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arXiv2024

Time Efficient Rate Feedback Tracking Controller with Slew Rate and Control Constraint

This paper proposes a time-efficient attitude-tracking controller considering the slew rate constraint and control constraint. The algorithm defines the sliding surface, which is the linear combination of command, body, and regulating angular velocity, and utilizes the sliding surface to derive the control command that guarantees finite time stability. The regulating rate, which is an angular velocity regulating the attitude error between the command and body frame, is defined along the instantaneous eigen-axis between the two frames to minimize the rotation angle. In addition, the regulating rate is shaped such that the slew rate constraint is satisfied while the time to regulation is minimized with consideration of the control constraint. Practical scenarios involving Earth observation satellites are used to validate the algorithm's performance.

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arXiv2024

Analysis and Design of Satellite Constellation Spare Strategy Using Markov Chain

This paper introduces the analysis and design method of an optimal spare management policy using Markov chain for a large-scale satellite constellation. We propose an analysis methodology of spare strategy using a multi-echelon $(r,q)$ inventory control model with Markov chain, and review two different spare strategies: direct resupply, which inserts spares directly into the constellation orbit using launch vehicles; and indirect resupply, which places spares into parking orbits before transferring them to the constellation orbit. Furthermore, we propose an optimization formulation utilizing the results of the proposed analysis method, and an optimal solution is found using a genetic algorithm.

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arXiv2024

Cislunar Space Situational Awareness Constellation Design and Planning with Facility Location Problem

Driven by the surmounting interest for dedicated infrastructure in cislunar space, this work considers the satellite constellation design for cislunar space situational awareness (CSSA). We propose a mixed-integer linear programming (MILP)-based formulation that simultaneously tackles the constellation design and sensor-tasking subproblems surrounding CSSA. Our approach generates constellation designs that provide coverage with considerations for the field-of-view of observers. We propose a time-expanded p-Median problem (TE-p-MP) which considers the optimal placement of p space-based observers into discretized locations based on orbital slots along libration point orbits, simultaneously with observer pointing directions across discretized time. We further develop a Lagrangian method for the TE-p-MP, where a relaxed problem with an analytical solution is derived, and customized heuristics leveraging the orbital structure of candidate observer locations are devised. The performance of the proposed formulation is demonstrated with several case studies for CSSA constellations monitoring the cislunar Cone of Shame and a periodic time-varying transit window for low-energy transfers located in the Earth-Moon L2 neck region. The proposed problem formulation, along with the Lagrangian method, is demonstrated to enable a fast assessment of near-optimal CSSA constellations, equipping decision-makers with a critical technique for exploring the design trade space.

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arXiv2024

Generalizing Space Logistics Network Optimization with Integrated Machine Learning and Mathematical Programming

Recent growing complexity in space missions has led to an active research field of space logistics and mission design. This research field leverages the key ideas and methods used to handle complex terrestrial logistics to tackle space logistics design problems. A typical goal in space logistics is to optimize the commodity flow to satisfy some mission objectives with the lowest cost. One of the successful space logistics approaches is network flow modeling and optimization using mixed-integer linear programming (MILP). A caveat of the conventional MILP-based network approach for space logistics is its incapability of handling nonlinearity. For example, in the MILP formulation, the spacecraft structure mass and fuel/payload capacity are approximated by a linear relationship. However, this oversimplified relationship cannot characterize a realistic spacecraft design. Other types of nonlinearity can appear when a nonlinear time-dependent trajectory model is considered in an event-driven network, where the time step of each event itself is a variable. In response to this challenge, this Note develops a new systematic general framework to handle nonlinearity in the MILP-based space logistics formulation using machine learning (ML). Specifically, we replace the nonlinear constraints in the space logistics formulation with trained ML models that are compatible with MILP. The MILP-compatible ML model includes linear regression, PWL approximations, neural networks (NN) with Rectified Linear Unit (ReLU) activations, decision tree regression, and random forest regression, among others; these models can be translated into MILP formulations with a definition of additional variables and constraints while maintaining the linearity. This Note provides the first demonstration of using such trained ML models directly in a MILP-based space logistics optimization formulation.

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arXiv2024

Sensitivity Analysis of Separation Time Along Weak Stability Boundary Transfers

This study analyzes the sensitivity of the dynamics around Weak Stability Boundary Transfers (WSBT) in the elliptical restricted three-body problem. With WSBTs increasing popularity for cislunar transfers, understanding its inherently chaotic dynamics becomes pivotal for guiding and navigating cooperative spacecrafts as well as detecting non-cooperative objects. We introduce the notion of separation time to gauge the deviation of a point near a nominal WSBT from the trajectory's vicinity. Employing the Cauchy-Green tensor to identify stretching directions in position and velocity, the separation time, along with the Finite-Time Lyapunov Exponent are studied within a ball of state uncertainty scaled to typical orbit determination performances.

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arXiv2024

Deterministic Multistage Constellation Reconfiguration Using Integer Programming and Sequential Decision-Making Methods

In this paper, we address the problem of reconfiguring Earth observation satellite constellation systems through multiple stages. The Multi-stage Constellation Reconfiguration Problem (MCRP) aims to maximize the total observation rewards obtained by covering a set of targets of interest through the active manipulation of the orbits and relative phasing of constituent satellites. In this paper, we consider deterministic problem settings in which the targets of interest are known a priori. We propose a novel integer linear programming formulation for MCRP, capable of obtaining provably optimal solutions. To overcome computational intractability due to the combinatorial explosion in solving large-scale instances, we introduce two computationally efficient sequential decision-making methods based on the principles of a myopic policy and a rolling horizon procedure. The computational experiments demonstrate that the devised sequential decision-making approaches yield high-quality solutions with improved computational efficiency over the baseline MCRP. Finally, a case study using Hurricane Harvey data showcases the advantages of multi-stage constellation reconfiguration over single-stage and no-reconfiguration scenarios.

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