Trajectory planning is a crucial precondition for mechatronic systems to achieve precise and energy-saving working activities. However, conventional trajectory planning methods are restrained by curve types, which may not obtain the optimal trajectory adequately and explicitly. To address these challenges, a surrogate based trajectory planning (STP) method is developed in this study. Firstly, the time dependent variables of the optimal control problem are discretized using appropriate design of experiment (DoE) method. All the obtained training points for establishing the trajectory/speed surrogate model serve as the design variables. Thus, updating of the training points set is equal to updating the full-time trajectory/speed curve at every optimization iteration. By setting indispensable system dynamic constraints, the optimizer can gradually find the optimal trajectory. The proposed STP method is illustrated using an unmanned electric shovel (ES) example, which builds on the excavating trajectory planning problem by incorporating the excavating efficiency and energy consumption as the objectives. Numerical results show that the STP method can achieve a better excavating performance than other conventional trajectory planning methods. Besides, the high flexibility of STP is also demonstrated across different working conditions, including variable pile angles and complex pile surfaces.

轨迹规划是机电系统实现精确节能工作的关键先决条件。然而，传统的轨迹规划方法受到曲线类型的限制，曲线类型可能无法充分，明确地获得最佳轨迹。为了解决这些挑战，本研究开发了一种基于代理的轨迹规划（STP）方法。首先，使用适当的实验设计方法将最优控制问题的时间相关变量离散化。所有获得的用于建立轨迹/速度替代模型的训练点都用作设计变量。因此，训练点集的更新等于在每次优化迭代时更新全时轨迹/速度曲线。通过设置必不可少的系统动态约束，优化器可以逐渐找到最佳轨迹。以无人驾驶电铲为例说明了所提出的STP方法，该方法以挖掘效率和能耗为目标，以挖掘轨迹规划问题为基础。数值结果表明，与其他常规轨迹规划方法相比，STP方法具有更好的开挖性能。此外，STP的高灵活性也体现在不同的工作条件下，包括可变的桩角和复杂的桩面。数值结果表明，与其他常规轨迹规划方法相比，STP方法具有更好的开挖性能。此外，STP的高灵活性也体现在不同的工作条件下，包括可变的桩角和复杂的桩面。数值结果表明，与其他常规轨迹规划方法相比，STP方法具有更好的开挖性能。此外，STP的高灵活性也体现在不同的工作条件下，包括可变的桩角和复杂的桩面。