Time-jerk optimal trajectory planning is crucial in advancing robotic arms'
performance in dynamic tasks. Traditional methods rely on solving complex
nonlinear programming problems, bringing significant delays in generating
optimized trajectories. In this paper, we propose a two-stage approach to
accelerate time-jerk optimal trajectory planning. Firstly, we introduce a
dual-encoder based transformer model to establish a good preliminary
trajectory. This trajectory is subsequently refined through sequential
quadratic programming to improve its optimality and robustness. Our approach
outperforms the state-of-the-art by up to 79.72\% in reducing trajectory
planning time. Compared with existing methods, our method shrinks the
optimality gap with the objective function value decreasing by up to 29.9\%.

我们提出了一种双编码器基于转换器模型的两阶段方法，以加速时间 - 抖动最优轨迹规划。通过顺序二次规划对初步轨迹进行改进，以提高其最优性和鲁棒性。与现有方法相比，我们的方法在减少轨迹规划时间方面超过了最先进方法 79.72％，并且优化目标函数值减少了最多 29.9％。

双编码器多目标轨迹规划

Multi-Objective Trajectory Planning with Dual-Encoder

This paper exploits a basic connection between sequential quadratic
programming and Riemannian gradient optimization to address the general
question of selecting a metric in Riemannian optimization, in particular when
the Riemannian structure is sought on a quotient manifold. The proposed method
is shown to be particularly insightful and efficient in quadratic optimization
with orthogonality and/or rank constraints, which covers most current
applications of Riemannian optimization in matrix manifolds.

本文通过串行二次规划和黎曼梯度优化的基本联系，解决了在黎曼优化中选择度量的一般问题，特别是在商流形上寻求黎曼结构的情况下。所提出的方法在具有正交和 / 或秩约束的二次规划中表现得特别明晰高效，覆盖了矩阵流形中当前大多数黎曼优化的应用。