提出线性参数化方法，高效生成机械臂平滑最优路径
A Parameter-Linear Formulation of the Optimal Path Following Problem for Robotic Manipulator
- 用路径速度最大化替代时间最小化，避免速度为零时奇点
- 离散化后优化变量呈线性关系，计算效率显著提升
- 适合对实时性要求高的机器人轨迹规划场景
本文针对时间最优路径跟踪的计算挑战提出新方法。传统方法以最小化行程时间为目标，但转化为路径参数形式时会在路径速度为零处出现奇点，导致轨迹生成困难且计算复杂。为此，本文提出一种新思路：在给定路径上最大化路径速度。该方法能高效生成平滑轨迹，且其离散化后的优化问题在变量上为线性，具有较低的计算开销。
原文摘要 · Abstract (English)
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization problem in terms of a path parameter. Thus, smooth trajectory generation while maintaining a low computational effort is quite challenging, since the singularities have to be taken into account. To this end, a different approach is presented in this paper. This approach is based on maximizing the path speed along a prescribed path. Furthermore, the approach is capable of planning smooth trajectories numerically efficient. Moreover, the discrete reformulation of the underlying problem is linear in optimization variables.
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