orbital trajectory modeling

Modeling spacecraft–manipulator systems in non-inertial orbital reference frames remains challenging due to strong couplings among spacecraft attitude, orbital motion, and manipulator deformation dynamics. Method: This paper proposes the Lagrange–Poincaré–Kepler (LPK) framework—a novel geometric formulation that integrates Keplerian orbital dynamics and exponential joint parameterization into the Lagrange–Poincaré theory. Built upon the Lagrange–d’Alembert principle on principal bundles, it yields closed-form structural matrices explicitly incorporating orbital perturbations and external symmetry-breaking torques. Contribution/Results: The LPK framework ensures both geometric rigor and computational tractability, enabling hardware-in-the-loop simulation and autonomous control integration. Validation via a 7-DOF manipulator demonstrates significantly improved dynamical fidelity and numerical efficiency under orbital conditions compared with conventional approaches—providing a high-fidelity, computationally efficient dynamical foundation for on-orbit autonomous operations.

This work addresses the simulation inconsistencies in Basilisk arising from heterogeneous development environments due to variations in dependencies, operating systems, and configurations. To resolve this, the authors propose and implement the first containerized workflow specifically designed for Basilisk. By leveraging Docker, the approach encapsulates the complete build environment, dependencies, and simulation infrastructure into a portable, self-contained package. Integrated with Basilisk’s BSKSim class hierarchy, modular dynamics modeling, and flight software integration, this framework enables reproducible end-to-end simulations—from orbital dynamics to complex Monte Carlo attitude control scenarios. The resulting environment significantly enhances the repeatability of multi-layered simulations and provides researchers with a standardized, ready-to-use Basilisk simulation platform.

This work addresses the high computational cost of optimal control solvers typically required for evaluating fuel consumption and accessibility in low-thrust orbit transfers. To overcome this limitation, the authors propose a neural network–based surrogate model trained on a large-scale dataset generated via a homotopy ray strategy. By incorporating scaling laws inherent to low-thrust trajectories, the method introduces a self-similar coordinate transformation that enables cross-domain generalization across varying semi-major axes, inclinations, and central bodies—eliminating the need for retraining. The approach demonstrates high accuracy and efficiency in predicting performance for both single- and multi-revolution transfers, with validation on public datasets as well as complex missions involving multiple asteroid flybys and rendezvous. The implementation code and associated data are publicly released.

Satellite constellations face significant challenges in maintaining trajectory tracking and setpoint stability under multiple concurrent actuator failures—jeopardizing space sustainability. To address this, this paper proposes a Fault-Tolerant Model Predictive Control (FT-MPC) framework. The approach models actuator faults as time-varying constraints and ensures closed-loop asymptotic stability and recursive feasibility via online constrained optimization. Its key innovations include integrated fault awareness, robust constraint handling, and real-time receding-horizon optimization. The method is rigorously validated on the ATMOS testbed and an open-source high-fidelity simulation environment. Results demonstrate that the proposed FT-MPC enables stable navigation of spacecraft to service or collision-avoidance orbits under complex, persistent multi-actuator failure scenarios. It thus significantly enhances autonomous fault resilience, supporting long-term constellation operations and safe end-of-life disposal.

Modeling the long-term evolution of the space environment remains challenging due to complex, stochastic interactions among orbital objects. Method: This study proposes a stochastic dynamic network framework: space objects are categorized as nodes, while probabilistic collision events and orbital coupling relationships constitute edges. Drawing an analogy to ecological networks, we establish a space carrying capacity theory; sustainable capacity is defined via stability analysis of the network’s equilibrium state, and policy interventions—such as collision avoidance and post-mission disposal—are quantified accordingly. The approach integrates stochastic processes, dynamic network theory, nonlinear dynamical systems analysis, and orbital mechanics. Contribution/Results: The model successfully reproduces historical debris growth trends, identifies critical node categories—including defunct satellites and spent rocket upper stages—and pinpoints high-risk regions, notably the LEO–SSO intersection zone. It significantly improves predictive accuracy for long-term impacts of launch traffic and mitigation strategies, thereby enhancing policy-relevant decision support.

This paper addresses the six-degree-of-freedom (6-DOF) pose trajectory planning problem for satellite rendezvous and docking under no-fly zone constraints. We propose a dual-quaternion-based RRT* motion planning method that uniformly models translation and rotation directly in the SE(3) manifold. By embedding dual-quaternion algebra into the RRT* framework, our approach enables natural screw-motion interpolation, ensuring global C¹ continuity of the generated pose trajectories. Unlike conventional decoupled approaches—separately optimizing translation and quaternion rotation—our method significantly improves trajectory smoothness and obstacle avoidance capability. Simulation experiments in multi-obstacle scenarios demonstrate a 12.7% increase in collision-free success rate and a 38.5% reduction in pose jitter. The entire algorithm is implemented in Python, confirming its feasibility and robustness for onboard real-time trajectory planning.

This work proposes an end-to-end approach leveraging large language models to automatically translate natural language descriptions of space mission intent into solvable trajectory optimization formulations, substantially reducing reliance on domain experts. It represents the first application of large language models to the semantic-to-formal modeling pipeline in spacecraft trajectory optimization, integrating natural language understanding, convex optimization, and spacecraft rendezvous dynamics to generate executable optimization code directly from high-level mission specifications. Evaluated in spacecraft rendezvous scenarios, the system demonstrates a high success rate in reconstructing feasible convex optimization problems, thereby validating its effectiveness, practical utility, and significant enhancement of both mission design flexibility and development efficiency.

To address the escalating collision risk and inefficiency of manual collision avoidance planning caused by the rapid increase in low Earth orbit (LEO) satellite density, this paper proposes an autonomous low-thrust collision avoidance maneuver planning algorithm. Methodologically, the non-convex quadratically constrained quadratic program (QCQP) formulation is converted into a tight convex semidefinite program (SDP) via Shor relaxation, and a minimum-risk mechanism is incorporated to ensure robust responses under infeasible conditions. The key contributions are: (i) the first recovery of globally optimal collision avoidance solutions within an SDP framework for short-term LEO rendezvous scenarios; and (ii) validation via high-fidelity orbital simulations and Conjunction Data Messages (CDM), demonstrating simultaneous optimization of minimum energy consumption and minimum collision probability. The algorithm generates feasible maneuver strategies in milliseconds, significantly enhancing both response speed and avoidance reliability.

This study investigates whether large language models (LLMs) can autonomously perform multi-stage planning in high-dimensional, physics-constrained aerospace missions, exemplified by the GTOC 12 asteroid mining competition. Leveraging the MLE-Bench framework and the AIDE agent architecture, the work presents the first application of LLMs to real-world orbital mechanics challenges, enabling autonomous generation and optimization of mission designs. It introduces an “LLM-as-a-Judge” evaluation paradigm that aligns with expert scoring criteria to assess strategic feasibility. Experimental results show that state-of-the-art models released in the past two years—such as GPT-4-Turbo, Gemini 2.5 Pro, and o3—achieve average scores rising from 9.3 to 17.2 out of 26. However, persistent errors in unit handling and boundary condition management reveal a significant gap between strategic reasoning and engineering implementation in current LLM capabilities.

This study challenges the conventional view of robotic manipulators as mere disturbance sources in spacecraft attitude control by systematically demonstrating their potential as redundant or even primary actuators. Focusing on scenarios involving high relative-mass payload capture, the work proposes a multifunctional control framework leveraging the manipulator for complex attitude maneuvers without propellant consumption. A nonlinear trajectory optimization problem is formulated, incorporating joint limits and collision-avoidance constraints, and solved via an interior-point method. Momentum-torque envelope analysis is employed to quantitatively compare the attitude control authority of the manipulator against that of a reaction wheel assembly. Simulation results generate diverse detumbling and reorientation trajectories, validating the feasibility of achieving intricate spacecraft attitude maneuvers solely through manipulator motion.