Collision will result in mission failure or even damage to the robot. To address the mutual collision between redundant dual manipulators (RDMs), a novel double barrier function (DBF)-based mutual collision avoidance (MCA) scheme is proposed and investigated which can be formulated into a quadratic programming (QP)-based problem. Firstly, a novel safe barrier function (SBF)-based MCA inequality constraint is designed and derived which maximises the feasible region of collision avoidance and maintains the maximum safe distance between the RDMs under the same trajectory tracking task constraint. Secondly, a novel barrier varying-parameter recurrent neural network (BVRNN)-based QP solver with newly designed varying-parameter and activation function is proposed with faster convergence rate and higher error accuracy compared to the traditional varying-parameter neural network. Through the iteration and online-learning of the BVRNN-based QP solver, the RDMs can obtain the ability of MCA. Finally, Simulation experiments are presented to verify the effectiveness and superiority of the proposed DBF-based MCA scheme, i.e., ensuring that the RDMs are always at a set safe distance while performing a perfect end-effectors trajectory tracking task (error less than \(10^{-7}\) ) during the collaborative operation process.