Minimization of the total energy consumption for a set of industrial robots can be posed as a Mixed Integer Nonlinear Program (MINLP). A nonlinear cost function describes the energy use while a set of mixed integer linear constraints encode mutual exclusion and preconditions. Much of the problem structure is lost when the mutual exclusions are converted into an integer formulation. We propose integrating MINLP and Constraint Programming (CP) techniques to solve the nonlinear scheduling problem more efficiently. By utilizing CP, infeasibilities caused by the scheduling dynamics may be detected at an earlier stage in the branch and bound tree. Linear and nonlinear programming methods are added to Gecode using a custom constraint. Results from a small case study on a job shop like problem with cubic costs shows some promising results.