Cooperative robotic system for automated fiber placement (AFP) is a promising solution to fulfill the requirement of manufacturing fiber composites on intricate structures. This project works on the trajectory planning and control of a 13-degree-of-freedom (13-DOF) AFP system. A 1-DOF rotary stage is attached to the end-effector of a 6-Revolute-Spherical-Spherical (6-RSS) parallel robot to hold a Y-shape mandrel, while an AFP head is attached to the end-effector of a 6-DOF serial robot to place fiber with the desired degree. A photogrammetry sensor C-Track 780 can measure the real-time end-effector pose of the robots. To ensure the desired cooperation performance and limit the communication cost, a distributed control structure with an event-triggered network is developed, based on the measured end-effector pose of the serial robot. An adaptive Kalman filter (AKF) is employed to address uncertain noises in pose estimation. A leader-follower trajectory planning strategy is proposed with the serial robot as the leader and the parallel robot as the follower. A time-jerk optimal trajectory planning scheme is designed for the serial robot considering the kinematic and dynamic constraints. To compensate the serial robot motion and satisfy the AFP geometric constraints, a vision-based trajectory generation approach is developed for the parallel robot. A position-based visual servoing (PBVS) strategy is proposed for the parallel robot in Cartesian space. To enable the robot to effectively track different trajectories under time-varying conditions, an adaptive sliding mode control method using radial basis function (RBF) neural network is developed to guarantee system robustness and realize the self-tuning of the control gains. In the presence of dynamic uncertainties and external disturbances, a distributed control approach based on adaptive sliding mode controller (ASMC) is developed for the two robots. A deep recurrent neural network (DRNN) is employed to estimate the lumped system uncertainties. The DRNN demonstrates superior learning capability and dynamic adaptability compared to shallow feedforward neural networks. Based on Lyapunov theorem, the stability analyses of the controllers have been done. The effectiveness and superiority of the proposed algorithms have been validated by simulation and experiment, and comparisons are made with the previous published work.