Investigations on Local Minimum Problem for Dual‐Quaternion‐Based Sliding Mode Control With Artificial Potential Functions

ABSTRACT This paper investigates a sliding mode control law based on dual quaternions for six‐degree‐of‐freedom (six‐DOF) proximity operations between a chaser and a target spacecraft. Dual quaternions, which can simultaneously represent both the rotation and translation of rigid bodies, effectively model the coupled relative motion during these operations. The sliding surface design incorporates artificial potential functions, enabling the consideration of motion constraints including field‐of‐view restrictions, approach path constraints, and collision avoidance. However, these functions are prone to local minima, where attractive and repulsive forces balance each other out, leading to undesired convergence. This paper presents a comprehensive mathematical analysis of the local minimum problem, elucidating the impact of individual and combined constraints on the chaser behavior. To address the local minimum issue, an active escape mechanism is proposed to apply additional corrective forces to help the chaser overcome these traps and achieve reliable control. Numerical simulation evaluates the proposed solution, confirming its effectiveness in resolving local minima challenges and enhancing mission reliability.