Abstract
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable this, we present two novel frameworks for applying principles of constrained optimization to the new variational inference algorithm Stein variational gradient descent. Our general framework supports multiple types of constrained optimizers and can handle arbitrary constraints. We demonstrate on a variety of problems that we are able to learn to approximate distributions without violating constraints. Specifically, we show that we can build distributions of: robot motion plans that exactly avoid collisions, robot arm joint angles on the SE(3) manifold with exact table placement constraints, and object poses from point clouds with table placement constraints.
Abstract (translated)
机器人技术中许多核心问题可以被表述为约束优化问题。通常，在这些问题上，机器人系统存在不确定性，或者识别多个高质量的可行解会更有优势。为了实现这一目标，我们提出了两个新颖的框架，将约束优化原则应用于新的变分推理算法Stein变分梯度下降法中。我们的通用框架支持多种类型的约束优化器，并且可以处理任意类型约束条件。我们在各种问题上展示了能够学习到在不违反约束条件下近似分布的能力。具体来说，我们证明了我们可以构建以下分布： - 精确避免碰撞的机器人运动计划 - 在SE(3)流形上的机械臂关节角度，具有精确的桌面放置约束条件 - 具有桌面放置约束的来自点云的对象姿态 这些框架使得在处理包含复杂约束条件的问题时更加灵活和高效。
URL
https://arxiv.org/abs/2506.00589
