基于蒙特卡洛随机采样方法与牛顿-拉夫逊迭代方法的钻锚机器人机械臂逆运动学求解方法

An integrated approach for inverse kinematics of unconventional manipulators using Monte Carlo random sampling method and Newton iterative method

钻锚机器人机械臂逆运动学精确求解是实现煤矿巷道自动支护的关键,针对钻锚机器人机械臂这种非传统结构机械臂逆运动学求解方法存在精度低、实时性差和容易陷入局部最优难以收敛的难题,提出了一种融合蒙特卡洛随机采样方法和牛顿-拉夫逊迭代方法的非传统结构机械臂逆运动学求解方法。首先,根据钻锚机器人机械臂结构构建运动学模型,建立各个关节坐标系,利用坐标系转换关系实现机械臂正运动学求解;其次,基于蒙特卡洛随机采样方法计算机械臂运动空间,设定步长将运动空间轮廓外接立方体分割为若干个小立方体,构建小立方体内空间点的三维坐标和对应关节变量与小立方体的映射关系,根据给定的目标空间点对应的转换矩阵,通过索引函数确定其对应的小立方体,计算立方体内与目标空间点误差最小的点,将它对应的关节变量值作为初始值;最后,引入牛顿-拉夫逊迭代方法,利用多元函数迭代公式确定各关节变量的变化量,循环往复实现非传统结构机械臂逆运动学的求解。仿真实验结果表明,与基于随机初始值的牛顿-拉夫逊迭代方法和粒子群优化算法相比,所提方法计算结果对应的平均角度误差分别降低了64.98%和57.34%,平均耗时分别降低了35.90%和22.33%,求解精度和时效性均有所改善,验证了所提融合蒙特卡洛随机采样方法与牛顿-拉夫逊迭代方法针对非传统结构机械臂逆运动学求解的可行性和有效性。

Accurate determination of the inverse kinematics for the drilling arm of a drilling and anchoring robot is crucial in achieving automatic support in coal mine roadways.Addressing issues such as poor accuracy,limited real-time performance,and susceptibility to local optima,this study presents a novel approach for solving the inverse kinematics problem of an unconventional mechanical arm by combining Monte Carlo random sampling method and Newton iteration method.Initially,a kinematics model is established based on the structure of the drilling arm,and individual coordinate systems are defined for each joint to enable forward kinematics solutions.The Monte Carlo method is employed to determine the motion space of the drill boom.By subdividing the motion space into smaller cubes with a defined step size,a mapping relationship is established between the spatial coordinates of these cubes and the corresponding joint variable values.Using the transformation matrix associated with a given target space point,an index function is employed to identify the relevant small cubes.The points within these cubes,which are closest to the target space point,are calculated,and their corresponding joint variable values are used as initial values.The Newton iteration method is then introduced,utilizing the iterative formula for multivariate functions to determine the variation of each joint variable.The inverse kinematics solution for the unconventional manipulator is obtained through iterative cycles.The simulation results show that,compared with Newton-Raphson iterative method based on random initial values and the particle swarm optimization algorithm,the corresponding average angle error of the calculation results of this method is reduced by 64.98%and 57.34%,and the average time consumption is reduced by 35.90%and 22.33%,respectively,thereby enhancing solution accuracy and realtime performance.The feasibility and effectiveness of the proposed Monte Carlo and Newton iteration method for solving the inverse kinematics problem in unconventional manipulators are verified.Overall,this research provides evidence supporting the practicality and efficiency of the proposed Monte Carlo random sampling method and Newton iteration method for accurate inverse kinematics solutions in unconventional manipulators.