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.

机器人和车辆等多体机械系统的系统识别通常被表述为参数优化问题，其中选择模型参数以最小化系统的测量轨迹和预测轨迹之间的差异。不同尺度和物理单位的大量参数以及嘈杂和不完整的测量使问题变得困难。更关键的是，参考轨迹的选择对识别程序的准确性和稳健性具有决定性影响。在本文中，我们提出了一组几何最优激励标准，可以对其进行优化以生成高质量的参考轨迹。由此产生的最佳轨迹是坐标和框架不变的，并且可以使用标准的递归分析梯度有效和稳健地获得。对于只能执行有限范围可行轨迹的高维系统，我们还展示了如何使用我们的几何框架来优化识别给定轨迹集的缩减参数集。我们的几何方法相对于现有方法的改进的鲁棒性和准确性通过涉及机器人操纵器和高维的数值和硬件实验得到证明人形机器人。