Abstract: Based on the S-shaped feedrate planning scheme,a fuel minimization control model for parametric curve was presented.The optimality quantitative evaluation for the heuristics of flexible acceleration control was solved in the context of motion control.The velocity,acceleration and jerk constraints were considered simultaneously in the model to realize the optimized smooth feedrate of the control trajectory.Moreover,considering the mechanical inertia,the proposed control model assumed that the acceleration starts from zero-transition and the control trajectory could be made more symmetrical then be given.Due to the structural characteristics of S-shaped trajectory control,the fuel minimization control problem was transformed into a non-linear programming problem.Compared with the existing time minimization model,the fuel minimization model had a broader implication and applicability.Through analyzing the sharp turning points,the entire piecewise curve could be split into a set of S-shaped velocity segment.The optimal S-shaped feedrate planning problem was formulated for both single-axis and multi-axis motion,and the energy consumption was also evaluated for the trajectory control strategy.Numerical simulation results demonstrated the effectiveness of the proposed control method.

Key words: federate planning, optimal fuel control problem, jerk, nonlinear programming

摘要： 基于曲线的路径参数化表示,提出了基于S-型光滑进给速度规划的最小燃料控制模型,解决了运动控制的柔性S-型加减速控制启发式算法的最优性量化与评价问题。通过在规划问题中引入速度、加速度和急动度边界约束,定量描述了轨迹的最优性光滑进给量;考虑机械惯性,假设分段S-型速度轨迹的始终点加速度为零过渡,使得模型对称易于求解;根据S-型速度控制的结构化特点,将最优控制问题转换为求解非线性规划问题。最小燃料模型比一般最短时间模型具有更宽泛的含义和应用可行性。通过曲率极值点的判断,可分段给出参数曲线的S-型速度规划。从单轴到多轴阐述了S-型速度的燃料指标最优规划问题,并引入关联轨迹控制的能耗评价,通过算例说明了所提方法的有效性。

关键词: 进给速度规划, 最小燃料控制模型, 急动度, 非线性规划