计算机数控系统光滑时间最优轨迹规划

基于控制向量参数化(CVP)方法, 研究了计算机数控(CNC)系统光滑时间最优轨迹规划方法. 通过在规划问题中引入加加速度约束, 实现轨迹的光滑给进. 引入时间归一化因子, 将加加速度约束的时间最优轨迹规划问题转化为固定时间的一般性最优控制问题. 以路径参数对时间的三阶导数(伪加加速度)和终端时刻为优化变量, 并采用分段常数近似伪加加速度, 将最优控制问题转化为一般的非线性规划(NLP)问题进行求解. 针对加加速度、加速度等过程不等式约束, 引入约束凝聚函数, 将过程约束转化为终端时刻约束, 从而显著减少约束计算. 构造目标和约束函数的Hamiltonian函数, 利用伴随方法获得求解NLP问题所需的梯度.

Smooth and time-optimal trajectory planning for computer numerical control systems

On the basis of the control vector parameterization (CVP) method, we investigate the numerical approach for solving the smooth and time-optimal trajectory planning problem of computer numerical control (CNC) systems. The jerk constraints are considered in the problem to realize the smooth feeding-rate of the trajectory. By using a time normalization factor, we reformulate the original jerk constrained time-optimal trajectory planning problem as a time-independent optimal control problem. The third derivative of the path parameter with respect to time, also known as pseudo-jerk, and the terminal time are taken as optimization variables. The piece-wise constant approximation method is used to approach the pseudojerk, and the optimal control problem is converted into a general nonlinear programming (NLP) problem. Constraint aggregation functions are introduced to approximate the process constraints (i.e., jerk and acceleration constraints) as final time onstraints, and the computation load of constraints can be reduced significantly. By constructing the Hamiltonian functions of objective and constraint functions, and employing the adjoint approach, we obtain the gradients which are required in the process of NLP solution.