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Upon solving the inverse kinematics problem of robot manipulators, the inherent singularity problem should always be considered. When a manipulator is approaching a singular configuration, a certain degree of freedom will be lost such that there are no feasible solutions of the manipulator to move into this singular direction. In this paper, the singularities of a 6-DOF PUMA manipulator are analyzed in detail and all the corresponding singular directions in task space are clearly identified. In order to resolve this singularity problem, an approach denoted Singularity Isolation Plus Compact QP (SICQP) method is proposed. The SICQP method decomposes the work space into achievable and unachievable (i.e., singular) directions. Then, the exactness in the singular directions are released such that extra redundancy is provided to the achievable directions. Finally, the Compact QP method is applied to maintain the exactness in the achievable directions, and to minimize the tracking errors in the singular directions under the condition that feasible joint solutions must be obtained. In the end, some simulation results for PUMA manipulator are given to demonstrate the effectiveness of the SICQP method.

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