In this paper, an automatic obstacle avoidance trajectory planning strategy is proposed for the simultaneous motion of multi-robots, which perform anthropomorphic skill operations in a large curved preformed three-dimensional (3D) weaving environment with multiple obstacles and limited space, to eliminate tedious manual calibration work of robot path in engineering. Firstly, an Adaptive Goal-guided Rapidly-exploring Random Trees (AGG-RRT) algorithm is proposed, combined with the robot obstacle avoidance strategy, to search the discrete position of the collision-free path of the end-effector gradually from the starting point to the ending point. Then the optimization of the path is completed by bidirectional pruning of redundant nodes and cubic non-uniform rational B-spline (NURBS) curve fitting. And finally, the robot trajectory is interpolated based on S-shaped acceleration/deceleration planning to ensure smooth robot joint motion. The simulation results demonstrate the superiority of the AGG-RRT algorithm over the basic RRT algorithm and related improved algorithms in terms of search time and success rate. The simulated experiments also achieve the smooth trajectory planning of multiple robotic arms with the synchronous obstacle avoidance motion, which shows that the AGG-RRT algorithm is successfully applied and the collision-free trajectory planning strategy is effective.