GPU-Accelerated Reachability Analysis for Tumbling Space Objects

The goal of this internship is to develop a high-performance implementation of this reachability framework using CUDA C++ in order to enable real-time reachable-set computation for tumbling space objects.

Your Contribution

We are seeking a motivated student interested in high-performance computing and space robotics to implement GPU-accelerated reachability algorithms for uncertain rigid-body attitude dynamics.

You will:

• Study the existing reachability framework based on Lipschitz constant estimation for rigid-body attitude dynamics on SO(3).
• Implement numerical evaluation of the rigid-body dynamics flow map (see Sec. 4.1.3-4.1.4 in [1]) and associated Lipschitz constant.
• Develop a CUDA C++ implementation to evaluate large numbers of samples in parallel.
• Implement GPU kernels for estimating local Lipschitz constants and constructing convex hull reachable-set over-approximations.
• Optimize memory layout, kernel execution, and parallel workload distribution.
• Validate the implementation on realistic tumbling satellite scenarios inspired by ESA's ENVISAT case studies.
• Benchmark computational performance and analyze scalability with respect to the number of sampled trajectories., * Implementation of existing forward reachability analysis method for rigid body attitude dynamics using CUDA C++.
• Validation using simulated tumbling debris scenarios.
• Performance analysis with respect to runtime, scalability, and suitability for real-time applications.

• Enrolled in a Bachelor's or Master's program in Aerospace Engineering, Computer Science, Robotics, Applied Mathematics, or a related field.
• Strong programming skills in C++.
• Strong interest or experience in parallel computing or GPU programming.
• Interest in space robotics or spacecraft dynamics.
• Ability to work independently and systematically., * Hands-on experience with GPU programming and high-performance scientific computing.
• Work on a real research problem relevant to autonomous space missions.
• Collaboration within a leading research institute in space robotics.
• Insight into advanced reachability analysis methods for safety-critical systems.
• Opportunity to contribute to ongoing research publications (subject to approval).

This internship is ideal for students interested in GPU computing, numerical simulation, and space applications, and who enjoy translating advanced algorithms into efficient high-performance implementations.

Supervisors: Alessandro Melone, Roberto Lampariello.

At the Institute of Robotics and Mechatronics of the German Aerospace Center (DLR), we develop advanced autonomy algorithms for robotic proximity operations in orbit. The rapid growth of orbital debris and the increasing number of uncooperative satellites require robust algorithms enabling servicer spacecraft to safely interact with tumbling targets whose orientation and inertia properties are uncertain. A key safety challenge in such scenarios is predicting all possible future rotational states of a tumbling rigid body under uncertainty. Reachability analysis provides mathematically guaranteed over-approximations of these future states. However, classical conservative reachability techniques often suffer from excessive bound growth when applied to nonlinear attitude dynamics. On compact spaces such as SO(3), the resulting over-approximations may rapidly cover the entire manifold even over short time horizons, significantly reducing their usefulness for practical analysis. Recent work has proposed a reachability framework based on numerical estimation of Lipschitz constants derived from sensitivity equations of the rigid-body dynamics. This method constructs conservative convex hull over-approximations of reachable orientations while avoiding the rapid bound inflation typical of classical approaches. The framework is particularly well-suited for parallel evaluation and therefore benefits significantly from GPU acceleration.