This paper investigates the problem of position tracking and attitude synchronization for multiple chaser spacecraft rendezvous and docking with the target spacecraft, in which model uncertainties, unknown external disturbances, path constraints, and collision avoidance are considered. The coupled six-degrees-of-freedom (6DOF) dynamic model is adopted for spacecraft relative motion. By integrating the artificial potential function (APF), a 6DOF robust adaptive controller is designed. In addition, unknown parameters are estimated with a norm-estimation-based adaptive method. The stability of the system is proved by Lyapunov theory and a simulation example is given to verify the theoretical results.