Robotic assisted technologies benefit surgeon for less workload via dexterous manipulation in minimally invasive surgeries (MIS). Redundant manipulator can provide sufficient dexterity and is potential to use in a confined and narrow workspace. We had designed a master-slave paediatric surgical assist robot, which consists of two symmetric slave arms with nine DOFs each for dexterous manipulation. This paper presents the kinematics computation of the redundant manipulator based on its geometrical structure, and then, a shape optimization algorithm is constructed to calculate the posture configuration along the redundant manipulator, subsequently, a collision avoidance algorithm is constructed to perform motion planning in a narrow workspace. The experiments were executed to validate the correctness of the derived inverse kinematics algorithm and the results demonstrated that the redundant manipulator is capable of performing dexterous manipulation with a positioning accuracy within 1.5 mm in a narrow surgical workspace.