机械臂逆运动学避障最优求解算法

针对多自由度机械臂在障碍物环境下逆运动学求解存在多解性和碰撞问题，提出了一种将碰撞检测算法、最短行程方法与差分进化算法相结合的具有避障能力的机械臂逆运动学最优求解算法。首先，以六自由度机械臂为研究对象，对机械臂和障碍物进行建模，并建立求逆运动学解的目标函数，目标函数由末端执行器位姿误差函数、目标角度与初始角度之间的变化量函数、碰撞检测函数加权求和组成；其次，利用差分进化算法对目标函数进行最优求解，为了减小函数权重对求解速度和精度的影响，设计了一种自适应权重优化算法，使得求解关节角度在优化求解初期快速达到最短行程位姿角度附近，而在优化求解后期具有更高的求解精度，即可求得具有避障能力、行程最短且高精度的最优逆运动学解；最后，以UR5机械臂为例，通过MATLAB软件中的Robotics Toolbox工具箱对所提算法进行仿真验证，验证了所提算法的有效性。

Optimal algorithm for obstacle avoidance of manipulator inverse kinematics

Aiming at the problems of multiple solutions and collisions in the inverse kinematics solution of multi-degree of freedom manipulators in the obstacle environment, an optimal solution algorithm of inverse kinematics of manipulators with obstacle avoidance ability is studied, the method is composed of collision detection algorithm, shortest travel algorithm and differential evolution algorithm. Firstly, taking the six-degree of freedom manipulator as the research object, the models of a six degree of freedom manipulator and obstacles are built. The objective function for inverse kinematics solution is established, the objective function is formed by the weighted summation of the pose error function of end effector, the variation function between target angle and initial angle and the collision detection function. Secondly, the differential evolution algorithm is applied to optimize the objective function. an adaptive weight adaptive algorithm is designed to reduce the influence of the function weight on the solution speed and accuracy. Based on the adaptive algorithm, the joint angle can quickly reach the shortest travel position in the early stage of the optimization solution, and higher solution accuracy can be achieved in the latter stage of the optimization solution. So the optimal inverse kinematics solution with obstacle avoidance ability, shortest travel and high precision can be obtained. Finally, taking the UR5 manipulator as an example, the algorithm is simulated by the Robotics Toolbox in MATLAB software, and the effectiveness of the algorithm is verified.