A new inverse kinematics algorithm is developed that may provide singularity avoidance or may be used for quick transition through a singularity with small torque errors. To avoid singularities, angular momentum trajectory of the control moment gyro cluster during the maneuver is to be simulated in advance for the calculation of singularity free gimbal histories. The steering law proposed accurately generates the required torques making it suitable to be used in a feedback system. The desired gimbal trajectories are also closely followed as long as the difference between the planned and requested angular momentum histories are close. A numbers of approaches suitable for the spontaneous response of the spacecraft for singularity avoidance or quick transition through singularities are proposed and presented as well. It is also shown that the computational requirements of the new steering law are comparable to the other commonly used steering laws. (c) 2005 Elsevier SAS. All rights reserved.