Towards a generalizable simulation framework to study collisions between spacecraft and debris

In recent years, computer simulators of rigid-body systems have been successfully used to improve and expand the field of developing new space robots, becoming a leading tool for the preliminary investigation and evaluation of space robotic missions. However, the impressive progress in performance has not been matched yet by an improvement in modelling capabilities, which remain limited to very basic representations of real systems. We present a new approach to modelling and simulation of collision-inclusive multibody dynamics by leveraging symbolic models generated by a computer algebra system (CAS). While similar investigations into contact dynamics on other domains exploit pre-existing models of common multibody systems (e.g., industrial robot arms, humanoids, and wheeled robots), our focus is on allowing researchers to develop models of novel designs of systems that are not as common or yet to be fabricated: e.g., small spacecraft manipulators. In this paper, we demonstrate the usefulness of our approach to investigate spacecraft-debris collision dynamics.

Leveraging Symbolic Algebra Systems to Simulate Contact Dynamics in Rigid Body Systems

Collision detection plays a key role in the simulation of interacting rigid bodies. However, owing to its computational complexity current methods typically prioritize either maximizing processing speed or fidelity to real-world behaviors. Fast real-time detection is achieved by simulating collisions with simple geometric shapes whereas incorporating more realistic geometries with multiple points of contact requires considerable computing power which slows down collision detection. In this work, we present a new approach to modeling and simulating collision-inclusive multibody dynamics by leveraging computer algebra system (CAS). This approach offers flexibility in modeling a diverse set of multibody systems applications ranging from human biomechanics to space manipulators with docking interfaces, since the geometric relationships between points and rigid bodies are handled in a generalizable manner. We also analyze the performance of integrating this symbolic modeling approach with collision detection formulated either as a traditional overlap test or as a convex optimization problem. We compare these two collision detection methods in different scenarios and collision resolution using a penalty-based method to simulate dynamics. This work demonstrates an effective simplification in solving collision dynamics problems using a symbolic approach, especially for the algorithm based on convex optimization, which is simpler to implement and, in complex collision scenarios, faster than the overlap test.