A redundant manipulator can achieve additional tasks by utilizing the degree of redundancy, in addition to a basic motion task. While some additional tasks can be performed by optimizing a proper objective function, other additional tasks can be performed by satisfying a set of kinematic inequality constraints. In this paper, the redundancy resolution problem with multiple additional tasks is reformulated into a local equality and inequality constrained optimization problem at two different level. One is at the joint value level and the other is joint velocity level. At joint value level, an algorithm to recursively get the optimal solution by using the necessary conditions for the optimal solution has been proposed. At joint velocity level, the transformed optimization problem becomes a convex programming problem. A similar algorithm has been applied to get the optimal solution by using the necessary and sufficient conditions for optimality. The proposed algorithm has been applied to the path planning of a robot for nozzle dam installation/removal.
