Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers typically produce a single solution only and rely on local search techniques to minimize a highly nonconvex objective function. Recently, 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 shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train a generative graphical inverse kinematics solver (GGIK) that is able to produce a large number of diverse solutions in parallel while also generalizing well -- a single learned model can be used to produce IK solutions for a variety of different robots. The graphical formulation elegantly exposes the symmetry and Euclidean equivariance of the IK problem that stems from the spatial nature of robot manipulators. We exploit this symmetry by encoding it into the architecture of our learned model, yielding a flexible solver that is able to produce sets of IK solutions for multiple robots.

翻译：快速可靠地定位精确逆运动学（IK）解仍是机器人操作中的挑战性问题。现有数值求解器通常仅生成单个解，并依赖局部搜索技术最小化高度非凸的目标函数。近年来，近似完整可行解集的基于学习方法展现出并行生成多个快速精确IK结果的潜力。然而，现有学习技术存在显著缺陷：每台目标机器人需要从头训练的专用模型。为解决这一不足，我们探索了一种新型距离几何机器人表示法，并结合图结构以利用图神经网络（GNNs）的灵活性。基于此方法，我们训练了一个生成式图形逆运动学求解器（GGIK），既能并行生成大量多样化解，又具备强泛化能力——单一学习模型可为多种不同机器人生成IK解。图形化表达优雅地揭示了机器人操作臂空间属性所引发的IK问题的对称性与欧几里得等变性。我们将这一对称性编码到学习模型的架构中，从而得到能够为多台机器人生成IK解集的灵活求解器。