Optimal excitation trajectories for mechanical systems identification

Abstract

System identification for multibody mechanical systems such as robots and vehicles is typically formulated as a parameter optimization problem, in which the model parameters are chosen to minimize the difference between measured and predicted trajectories of the system. The problem is made difficult by the large number of parameters of different scales and physical units, and also noisy and incomplete measurements. Even more critically, the choice of reference trajectory has a decisive impact on the accuracy and robustness of the identification procedure. In this paper we propose a set of geometric optimal excitation criteria that can be optimized to generate high-quality reference trajectories. The resulting optimal trajectories are coordinate- and frame-invariant, and can be obtained efficiently and robustly using recursive analytic gradients of the criteria. For high-dimensional systems that can execute only a limited range of feasible trajectories, we also show how our geometrical framework can be used to optimally identify a reduced set of parameters for the given set of trajectories. The improved robustness and accuracy of our geometric approach vis-á-vis existing methods is demonstrated through both numerical and hardware experiments involving robot manipulators and a high-dimensional humanoid robot.