Energy Optimal Manipulation of an Industrial Robot

The main goal of this contribution is to determine the excitation of an industrial robot, such that the energy consumption becomes a minimum during the manipulation of the tool center point (TCP) from a start position to a given end point within a predefined time. Such tasks can be restated as optimization problems where the functional to be minimized consists of the endpoint error and a measure for the energy. The gradient of this functional can be calculated by solving a linear differential equation, called the adjoint system. On the one hand the minimum of the cost functional can be achieved by the method of steepest descent where a proper step size has to be found or on the other hand by a Quasi-Newton algorithm where the inverse of the Hessian can be appreciated.