The article develops a generic framework for the control of a dual-manipulator mobile robotic system for nuclear decommissioning, with a particular focus on the inverse kinematics and trajectory planning. A six Degrees-Of-Freedom (DOF) kinematic model for each manipulator is described, including the rotation of the end-effector. On this basis, the forward kinematic equations are relatively straightforward to determine. However, the redundant nature of the manipulator and its particular geometry exclude the possibility of a closed-form analytic solution to the inverse kinematics. Hence, previous studies into advanced automatic control using the device have locked off selected control valves. For example, recent research into nonlinear, state-dependent control systems for the hydraulic actuators have been limited to just three DOF. By contrast, this new study considers all the joints of each manipulator, basing the resolution of the inverse kinematics on the iterative Jacobian transpose method. Preliminary experimental and simulation results highlight the potential utility of the system by performing standard tasks such as pick and place operations.