Control barrier function based trajectory generation and tracking control for spacecraft inspection mission under multiple safety constraints

Abstract

In this paper, the safety control problem for spacecraft inspection mission is investigated, which means that there is no position and attitude obstacle collisions between the inspection spacecraft and the defined forbidden zones. We propose a control strategy that ensures safety, utilizing the control barrier function to address multiple safety constraints with logical relationships among them. Firstly, the position and attitude constraints are defined, and the hybrid logical relationship among different attitude constraints is analyzed. To handle complex position and attitude constraints, the Kreisselmeier-Steinhauser function is introduced to approximate the max/min function, thereby expressing them as continuous and differentiable functions. Subsequently, the control barrier function-based quadratic programming (CBF-QP) problems are solved to generate safe velocity and angular velocity. These problems have explicit solutions and do not require extensive computational resources. The safe position and attitude are then obtained by integrating the safe velocity and angular velocity. Notably, the forbidden regions are expanded by a constant in the construction of CBF-QP problems, which acts as a margin for the tracking controller’s performance. Finally, attitude and position tracking controllers based on the control Lyapunov barrier function (CLBF) are designed respectively, taking into account the lumped disturbance in the system, which means that the attitude and position control are computed independently. Numerical simulation results demonstrate that the proposed control strategy effectively handles complex constraints in inspection missions, ensuring system stability and safety, even under severe conditions.