Abstract
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: this https URL
Abstract (translated)
生成机器人与各种形状物体交互的运动是一个复杂的问题，这个问题进一步因机器人的几何结构和多种期望行为而变得更加困难。当前的机器人编程工具（如逆向动力学、碰撞避免和操作规划）通常将这些问题视为约束优化问题，但许多现有的求解器往往专注于特定领域或无法有效利用几何约束条件。我们提出了一种高效的一阶方法——增广拉格朗日谱投影梯度下降法（ALSPG），该方法通过欧几里得投影、闵可夫斯基和以及基函数来利用几何投影。 研究表明，通过使用几何约束而非全部约束和梯度，ALSPG在实时性能上有了显著的提高。与二次优化方法（如iLQR）相比，在无约束情况下，ALSPG依然具有竞争力。我们通过玩具示例、广泛的仿真验证了我们的方法，并且通过实际实验展示了其在7轴Franka机器人、6轴P-Rob机器人以及1:10比例模型汽车上的有效性。 源代码、实验数据和视频可在项目网页上获得：[此链接](this https URL)。
URL
https://arxiv.org/abs/2506.14865
