用几何投影加速机器人实时运动规划，比传统方法更快更高效。
Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization
- 基于欧氏投影和闵可夫斯基和的几何约束优化方法
- 在7轴弗兰卡机器人等平台实测，实时性能显著提升
- 适合需要快速响应的工业机器人与移动平台应用
为与多种形状物体交互的机器人生成运动是一个复杂挑战，尤其受机器人自身几何结构和多重期望行为影响。现有机器人编程工具（如逆运动学、避障、操作规划）常将问题建模为带约束的优化，但多数求解器局限于特定领域或未能有效利用几何约束。本文提出一种高效的一阶方法——增广拉格朗日谱投影梯度下降（ALSPG），通过欧氏投影、闵可夫斯基和及基函数实现几何约束建模。实验表明，仅使用几何约束而非完整约束与梯度，ALSPG显著提升实时性能。相比二阶方法如iLQR，其在无约束情形下仍具竞争力。通过玩具示例与大量仿真验证，并在7轴Franka机器人、6轴P-Rob机器人及1:10比例真实汽车上完成实机测试。源代码、数据与视频见项目主页：https://sites.google.com/view/alspg-oc
原文摘要 · Abstract (English)
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: https://sites.google.com/view/alspg-oc
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