Energy Optimal Control of an Industrial Robot by using the Adjoint Method

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 Hessian can be appreciated. The theory is applied to a six-axis robot and the identification leads to a reduction of 47% of the signal energy.