Quantitative Precision Second-Order Temporal Transformation-Based Pose Control for Spacecraft Proximity Operations

This article designs a novel 6-degree-of-freedom (6-DOF) relative motion control scheme for spacecraft proximity operations with quantitative precision (QP), which simultaneously focuses on strict convergence time and accuracy constraints. First, a modified dual quaternions based 6-DOF relative motion model for spacecraft proximity operations is proposed, which better keeps validity and clarifies the inheritance relationship with unit quaternions. Then, an original QP second-order temporal transformation (QPST-Trans) is proposed, ensuring the continuity and nonsingularity of system signals and effectively avoiding the chattering and weakening of control inputs. Benefiting from QPST-Trans, a QP controller is designed with an innovative QPST-Trans function and a new robust term, which alleviates the input saturation phenomenon. With numerical simulations, it can be verified that the QP controller can drive spacecraft 6-DOF relative motion error to converge within the given accuracy before the designated convergence time even under input saturation faults.