A double-arm mobile robot (DMR) is an advanced robotic system that integrates a mobile platform and double robotic arms. To address the control issue of the DMR, this paper provides its mathematical model and deduces kinematic equations as preliminaries. On this basis, a physically constrained velocity collaborative control (PCVCC) scheme is proposed for kinematic control of the DMR, which adjusts the mobile platform and robotic arms cooperatively using a designed optimization criterion. To explore the optimal solution of the PCVCC scheme, a gradient descent method assisted by velocity compensation is exploited to design a dynamic neural network (DNN) solver. Subsequently, theoretical analyses confirm the global convergence of the DNN solver. Finally, simulations, experiments, and comparisons demonstrate the feasibility and superiority of the proposed method.