基于函数空间优化的机器人轨迹规划方法，提升复杂约束下的运动可行性。
FACTO: Function-space Adaptive Constrained Trajectory Optimization for Robotic Manipulators
- 用正交基函数系数直接优化轨迹，提升计算效率
- 在多机械臂场景中实现更高可行性和更优解质量
- 适合对精度和约束满足要求高的工业机器人应用
本文提出一种面向单臂与多臂机器人的轨迹优化算法 FACTO。轨迹以正交基函数的线性组合形式参数化，优化在系数空间中进行。通过有限维目标函数与带截断系数的目标泛函结合，构建约束问题。为处理非线性，采用带指数移动平均的高斯-牛顿近似，得到平滑的二次子问题。全局轨迹约束通过系数空间映射实现，并在活动约束的零空间中使用 Levenberg-Marquardt 算法进行自适应约束更新。与基于优化的规划器（CHOMP、TrajOpt、GPMP2）及采样类规划器（RRT-Connect、RRT*、PRM）相比，FACTO 在受限单臂与多臂场景中表现出更高的解质量和可行性。在 Franka 机器人上的实验验证了其部署可行性。
原文摘要 · Abstract (English)
This paper introduces Function-space Adaptive Constrained Trajectory Optimization (FACTO), a new trajectory optimization algorithm for both single- and multi-arm manipulators. Trajectory representations are parameterized as linear combinations of orthogonal basis functions, and optimization is performed directly in the coefficient space. The constrained problem formulation consists of both an objective functional and a finite-dimensional objective defined over truncated coefficients. To address nonlinearity, FACTO uses a Gauss-Newton approximation with exponential moving averaging, yielding a smoothed quadratic subproblem. Trajectory-wide constraints are addressed using coefficient-space mappings, and an adaptive constrained update using the Levenberg-Marquardt algorithm is performed in the null space of active constraints. Comparisons with optimization-based planners (CHOMP, TrajOpt, GPMP2) and sampling-based planners (RRT-Connect, RRT*, PRM) show the improved solution quality and feasibility, especially in constrained single- and multi-arm scenarios. The experimental evaluation of FACTO on Franka robots verifies the feasibility of deployment.
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