Hybrid model of deep learning and contact theory for predicting distributed contact force in space debris de-tumbling

Abstract

Flexible contact-based de-tumbling serves as a critical prerequisite for space debris removal, requiring precise control of distributed contact force to dissipate angular momentum. However, space debris is non-cooperative targets with no accessible interaction information, in which unknown contact forces may induce uncertain dynamic behaviors, posing significant risks to the safe in-orbit execution of debris removal. To address these challenges, this paper proposes a hybrid model combining deep learning with contact theory (CT) that enables accurate distributed force prediction without surface sensors. The hybrid model employs a Deep Long Short-Term Memory Network (DLSTM) to map end-effector concentrated forces to the Pressure Matrix of Finite Contact Elements (PMFCE) at the contact interface. The standard estimation equations for the characteristic parameters of the distributed contact force were derived from the PMFCE using CT, and solved iteratively via the exponentially weighted least squares (EWRLS) method. Additionally, we proposed a full collision cycle measurement method for ground-equivalent contact force, and developed a corresponding experimental setup to support the model training and validation. Experimental results demonstrated the proposed method’s superior predictive performance in both normal and oblique impact scenarios. Furthermore, statistical analysis using correlation coefficients and probability density functions confirmed the method’s superior accuracy and robustness. The results showed that the confidence level for the relative error within the ±10 % interval exceeded 98 %. This approach enables precise distributed force prediction in various contact-based robotic systems, ensuring safety during orbital debris de-tumbling and capture operations.