The paper proposes an off-line robot motion planning approach, aimed at the reduction of the energy consumption, for any trajectory defined on a set of target points including some "fly" ones, i.e., points that must not be exactly reached by the robot. The proposed solution is based on the search for alternative paths close to the fly target points originally defined by the operator, and on the computation of the mechanical and total energy associated to each single possible motion defined for the generated alternative paths. A branch and bound algorithm is employed to scan all the possible motions and find the complete trajectory that corresponds to the minimum energy consumption. The approach has been implemented in a software architecture that exploits some COMAU software modules, but it could be easily adapted to generic, similar modules. The results that have been experimentally obtained for two typical industrial cycles, performed by a COMAU Racer robot, can be considered as very satisfying.