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.

The compact QP method is an effective and efficient algorithm for resolving the manipulator redundancy under inequality constraints. In this paper, a more computationally efficient scheme which will improve the efficiency of the compact QP method-the improved compact BP method-is developed. With the technique of work space decomposition, the redundant inverse kinematics problem can be decomposed into two subproblems. Thus, the size of the redundancy problem can be reduced. For an n degree-of-freedom spatial redundant manipulator, instead of a 6/spl times/n matrix, only a 3/spl times/(n-3) matrix is needed to be manipulated by Gaussian elimination with partial pivoting for selecting the free variables. The simulation results on the CESAR manipulator indicate that the speedup of the compact QP method as compared with the original QP method is about 3.3. Furthermore, the speedup of the improved compact QP method is about 5.6. Therefore, it is believed that the improved compact QP method is one of the most efficient and effective optimization algorithm for resolving the manipulator redundancy under inequality constraints.>

The compact QP method is an effective and efficient algorithm for resolving the manipulator redundancy under inequality constraints. In this paper, a more computationally efficient scheme which will improve the efficiency of the compact QP method-the improved compact QP method -is developed. With the technique of workspace decomposition, the redundant inverse kinematics problem can be decomposed into two subproblems. Thus, the size of the redundancy problem can be reduced. For an n degree-of-freedom spatial redundant manipulator, instead of a 6/spl times/n matrix, only a 3/spl times/(n-3) matrix is needed to be manipulated by Gaussian elimination with partial pivoting for selecting the free variables. The simulation results on the CESAR manipulator indicate that the speedup of the compact QP method as compared with the original QP method is about 4.3. Furthermore, the speedup of the improved compact QP method is about 5.6. Therefore, it is believed that the improved compact QP method is one of the most efficient and effective optimization algorithm for resolving the manipulator redundancy under inequality constraints.>

Due to hardware limitations, physical constraints such as joint rate bounds, joint angle limits, and joint torque constraints always exist. In this paper, these constraints are considered in the general formulation of the redundant inverse kinematic problem. To take these physical constraints into account, the computationally efficient compact quadratic programming (QP) method is formed to resolve the constrained kinematic redundancy problem. In addition, the compact-inverse QP method is also formulated to remedy the inescapable singularity problem with inequality constraints. Two examples are given to demonstrate the generality and superiority of these two methods: to eliminate the drift phenomenon caused by self motion and to remedy saturation-type nonlinearity problems.>

Due to hardware limitations, physical constraints, such as joint rate bounds and joint angle limits, always exist. In the present work, these constraints are included in the general formulation of the redundant inverse kinematic problem. To take into account these physical constraints, the computationally efficient compact QP (quadratic programming) method is derived to resolve the kinematic redundancy problem. In addition, the compact-inverse QP method is developed to remedy the singularity problem. The compact QP (compact and inverse QP) method makes use of the compact formulation to obtain the general solutions and to eliminate the equality constraints. As such, the variables are decomposed into basic and free variables, and the basic variables are expressed by the free variables. Thus, the problem size is reduced and it only requires an optimization algorithm, such as QP, for the free variables subject to pure inequality constraints. This approach will expedite the optimization process and make real-time implementation possible.>

The inverse kinematic problem of redundant manipulators is solved by the compact formulation technique. The compact formulation is derived by applying Gaussian elimination, then the general solutions are still formulated as a particular solution together with homogeneous solutions. The homogeneous solutions are merely functions of free variables. Inverse kinematic solutions derived by the pseudoinverse formulation can always be converted into a compact form. Also, it is proven that the implementation by the compact formulation is computationally more efficient. The inherent singularity problems of inverse kinematics are also considered. In order to obtain continuous and feasible joint-rate solutions even at or in the neighborhood of singular points and to improve the exactness in the achievable directions, the compact-inverse method is introduced. The compact-inverse method applies the compact formulation to constrain the manipulator to move into the achievable directions. It is believed that the compact formulation approach can resolve the inverse kinematic redundancy problem more efficiently and exactly than the traditional pseudoinverse formulation.>