This paper presents a method to develop minimum energy trajectories for redundant/hyper-redundant manipulators with pre-defined kinematic and dynamic constraints. The optimal trajectory planning uses fifth order B-spline functions to represent the Cartesian coordinates of the end-effector and angles of the redundant links. The actuator torques are considered for the formulation of the cost function. Calculation of the cost function is carried out by using an inverse dynamic analysis. The system constraints are handled within the cost function to avoid running the inverse dynamics when the constraints are not satisfied. A novel virtual link concept is introduced to replace all the redundant links to eliminate physicaly impossible configurations before running the inverse dynamic model. The process is applicable to hyper redundant manipulators with large number of links. The proposed scheme is verified with computer simulations based on a 5-link planar redundant manipulator.

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