Recent advances in space robotics have underscored the need for modeling, estimation, and control frameworks that respect the intrinsic geometry of rigid-body motion. Traditional Euclidean formulations or small-angle approximations often fail to capture the coupled rotational–translational dynamics encountered in complex space operations, including multibody or perturbed dynamical regimes such as those found in cislunar or planetary environments. Geometric mechanics provides a principled, coordinate-free foundation for such problems, unifying attitude, pose, and momentum dynamics on Lie groups. In parallel, developments in invariant filtering, Riemannian optimization, and structure-preserving integration have bridged analytical mechanics with modern robotic autonomy and AI-based perception. These approaches enable globally consistent estimation and control laws that preserve physical invariants, enhance stability, and extend autonomy to highly nonlinear regimes. Bringing these developments together within a unified framework is timely for advancing next-generation guidance, navigation, and control (GNC) in intelligent space robotics.

This Research Topic aims to consolidate emerging advances in geometric mechanics and learning-based methods for modeling, dynamics, estimation, and autonomy of space robotic systems. Although substantial progress has been achieved across individual areas, current GNC frameworks often remain disconnected from the underlying geometric and variational structure of rigid-body motion. By uniting developments in geometric control theory, invariant and manifold-based filtering, Riemannian optimization, and learning-driven estimation and control, this collection seeks to establish a common foundation that ensures global consistency, robustness, and physical interpretability. The overarching goal is to promote cross-disciplinary integration between analytical mechanics, estimation theory, and robotic intelligence—enabling next-generation space systems capable of precise, reliable, and adaptive operation in nonlinear, uncertain, and dynamically coupled environments. Particular emphasis will be placed on contributions that demonstrate the integration of geometric principles with computational autonomy frameworks, bridging theoretical advances and real-world robotic performance in space.

This Research Topic welcomes contributions that advance geometric and learning-informed approaches to modeling, dynamics, estimation, and control of space robotic systems. Topics of interest include, but are not limited to:
– Geometric mechanics and variational formulations for rigid-body and multibody dynamics;
– Invariant and manifold-based estimation or filtering techniques;
– Riemannian optimization and learning-based control on nonlinear manifolds;
– Structure-preserving integration and geometric numerical methods;
– Geometric optimal control, constrained motion coordination, and formation dynamics;
– Integration of geometric frameworks with perception, planning, and AI-driven autonomy;
– Applications to space robotics, on-orbit servicing, autonomous assembly, and mobility in complex dynamical environments.

Both theoretical and computational studies are encouraged, including algorithmic developments, simulation analyses, and experimental validations. Works that bridge geometric modeling and learning-based autonomy are particularly encouraged to foster synergy between classical mechanics, robotics, and modern AI-enabled GNC architectures in space.

Topic Editor Morad Nazari receives financial support from a NASA-funded SBIR Phase II project conducted through a private company. Topic Editor Sean Phillips is employed by AFRL. All other Topic Editors declare no competing interests with regards to the Research Topic subject.

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Geometric Mechanics and Learning-Based Methods for Modeling and Autonomy in Space Robotics