Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for many robot manipulators. Existing numerical solvers are broadly applicable but typically only produce a single solution and rely on local search techniques to minimize nonconvex objective functions. More recent learning-based approaches that approximate the entire feasible set of solutions have shown promise as a means to generate multiple fast and accurate IK results in parallel. However, existing learning-based techniques have a significant drawback: each robot of interest requires a specialized model that must be trained from scratch. To address this key shortcoming, we propose a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the sample efficiency of Euclidean equivariant functions and the generalizability of graph neural networks (GNNs). Our approach is generative graphical inverse kinematics (GGIK), the first learned IK solver able to accurately and efficiently produce a large number of diverse solutions in parallel while also displaying the ability to generalize -- a single learned model can be used to produce IK solutions for a variety of different robots. When compared to several other learned IK methods, GGIK provides more accurate solutions with the same amount of data. GGIK can generalize reasonably well to robot manipulators unseen during training. Additionally, GGIK can learn a constrained distribution that encodes joint limits and scales efficiently to larger robots and a high number of sampled solutions. Finally, GGIK can be used to complement local IK solvers by providing reliable initializations for a local optimization process.

翻译：快速可靠地获取精确的逆运动学（IK）解仍是许多机器人操作臂面临的挑战性问题。现有数值求解器虽然广泛适用，但通常只能生成单一解，并依赖局部搜索技术来最小化非凸目标函数。近期基于学习的方法尝试近似整个可行解集，展现出并行生成多个快速精确IK结果的前景。然而，现有学习方法存在显著缺陷：每类目标机器人均需专门模型且需从头训练。为解决这一关键不足，我们提出一种新颖的距离几何机器人表征方法，并结合图结构以利用等变函数的样本效率与图神经网络（GNNs）的泛化能力。本方法称为生成式图形化逆运动学（GGIK），是首个能够并行准确高效生成大量多样化IK解，同时具备泛化能力的学习型求解器——单一学习模型即可为多种不同机器人产生IK解。与其它学习型IK方法相比，GGIK在同等数据量下能提供更精确的解。其可合理泛化至训练中未见的机器人操作臂。此外，GGIK能学习编码关节限位的约束分布，并高效扩展至更大规模机器人及高采样解数量。最终，GGIK可通过为局部优化过程提供可靠初始化，补充现有局部IK求解器。