Collision avoidance control for formation flying of multiple spacecraft using artificial potential field

Abstract

• Trajectory design/control for spacecraft formation flying with obstacle avoidance is presented. • Rotational potential function for obstacle avoidance in 3-dimensional space is newly proposed. • The controller is proven to be asymptotically stable in the sense of Lyapunov and successfully tested. This study presents trajectory design/control for spacecraft formation flying with obstacle avoidance. Based on the artificial potential field (APF), a formation potential is first defined to derive a formation control law for virtual structure, which enables multiple spacecraft to maintain polygonal or tetrahedral formation. As an efficient method to circumvent local minima which often occur in the APF-based approach, a newly proposed rotational potential is derived in a local coordinate frame to add in the APF framework. The synthesized formation and rotational potential function is used to develop a gradient-based control law to design/control the formation flying trajectory while avoiding collision with obstacles. Proven to be asymptotically stable in the sense of Lyapunov, the proposed continuous feedback control law is demonstrated via formation keeping/reconfiguration examples. The proposed approach successfully maintains the trajectory in the desired formation without colliding with obstacles and without falling into local minimum. These results are comparatively analysed with those of other APF-based approaches. The overall analysis shows that the proposed rotational potential, which has been newly derived in this research, enables a group of spacecraft in formation to efficiently avoid collision with obstacles without convergence to a local minimum.