基于NURBS的挖掘机器人时间最优轨迹规划

NURBS-based time-optimal trajectory planning on robotic excavators

为提高挖掘机器人的工作效率,保证其运行轨迹平滑,提出了一种基于NURBS曲线的轨迹规划方法。利用5次NURBS曲线插值挖掘机器人关节位置,引入矢值函数,通过莱布尼茨公式求解NURBS曲线的高阶导矢,设定启停速度和加速度,得到经过指定关节位置加加速度连续的轨迹曲线。分析了NURBS曲线权因子在挖掘轨迹局部规划中的作用。采用序列二次规划方法求解约束条件下的非线性最小化问题,规划出时间最优轨迹曲线。仿真和试验表明:提出的轨迹规划方法能够得到满足物理约束的时间最优关节轨迹,且可进行轨迹局部优化。

In order to improve the efficiency of the robotic excavator meanwhile to obtain its smooth running trajectory,a new trajectory planning method based on Non-uniform Rational Basis Spline（NURBS）was proposed.A quintic NURBS curve was employed to interpolate joint positions of the robotic excavator.Using the vector-valued function,by Leibniz formula,higher order derivative vector of NURBS curve was obtained to set the start and stop speeds and accelerations;and to make up the trajectory curves with continuous jerk,which passes specified joint positions.The effect of NURBS weight factor in sectional trajectory planning was analyzed.Nonlinear minimization problems under constraints were solved using sequential quadratic programming;then time-optimal trajectories were planned.Simulation and experiment results show that the proposed trajectory planning method can provide time-optimal trajectories,which satisfy kinematic constraints and the sectional trajectory optimization is effective.