Kinematic structures are very common in the real world. They range from simple articulated objects to complex mechanical systems. However, despite their relevance, most model-based 3D tracking methods only consider rigid objects. To overcome this limitation, we propose a flexible framework that allows the extension of existing 6DoF algorithms to kinematic structures. Our approach focuses on methods that employ Newton-like optimization techniques, which are widely used in object tracking. The framework considers both tree-like and closed kinematic structures and allows a flexible configuration of joints and constraints. To project equations from individual rigid bodies to a multi-body system, Jacobians are used. For closed kinematic chains, a novel formulation that features Lagrange multipliers is developed. In a detailed mathematical proof, we show that our constraint formulation leads to an exact kinematic solution and converges in a single iteration. Based on the proposed framework, we extend ICG, which is a state-of-the-art rigid object tracking algorithm, to multi-body tracking. For the evaluation, we create a highly-realistic synthetic dataset that features a large number of sequences and various robots. Based on this dataset, we conduct a wide variety of experiments that demonstrate the excellent performance of the developed framework and our multi-body tracker.

翻译：运动学结构在现实世界中非常常见，从简单的关节物体到复杂的机械系统，其应用范围广泛。然而，尽管具有重要性，大多数基于模型的3D跟踪方法仅考虑刚体。为克服这一限制，我们提出了一种灵活的框架，可将现有的6自由度算法扩展至运动学结构。该方法聚焦于采用牛顿类优化技术的跟踪算法，这类技术广泛应用于目标跟踪中。该框架支持树状和闭合运动学结构，并允许关节与约束的灵活配置。为将单个刚体的方程投影至多体系统，我们使用了雅可比矩阵。针对闭合运动链，我们开发了一种引入拉格朗日乘子的新公式。通过详细的数学证明，我们展示了该约束公式能产生精确的运动学解，并可在单次迭代中收敛。基于所提框架，我们将当前最先进的刚体跟踪算法ICG扩展至多体跟踪。为进行评估，我们创建了一个高度逼真的合成数据集，其中包含大量序列和多种机器人。基于该数据集，我们进行了广泛的实验，证明了所开发框架及多体跟踪器的卓越性能。