基于滑模控制的改进差分进化算法

针对机器人轨迹规划问题，提出了一种基于滑模控制的改进差分进化（IDE）算法.以运行时间和能量损耗为目标函数.利用种群中最好个体和平均水平个体的差分引导变异方向，利用种群中最好个体替换最差个体，加快收敛速度.取消变异因子和交叉因子，降低人工干预，增强了模型稳定性.利用保形分段三次Hermite插值代替三次样条插值，防止拟合过冲，降低了抖振.基于给出的状态空间方程，设计了滑模控制律，通过李亚普诺夫函数方法证明了系统的稳定性.仿真实验和结果分析表明，改进的算法有较强的搜索能力，加快了收敛速度，降低了运动轨迹的抖振.

Improved Method of Difference Evolution Algorithm Based on Sliding Mode Control

For the robot trajectory planning problem, an improved Differential Evolution(DE) algorithm based on sliding mode control is proposed. The operation time and energy consumption is taken as the objective function. The direction of variation is guided by the difference between the best individuals and the average individuals in the population. Using the best individuals to replace the worst individuals in the population, the rate of convergence is accelerated. Removal of mutation factor and cross factor reduces manual intervention and enhances the stability of the model. Using piecewise Hermite interpolation of order 3 instead of spline interpolation of order 3 to prevent fitting overshoot and reduce chattering. Based on the system state space equation, a sliding mode control law was designed and stability is proved by using a Lyapunov function. Simulation experiments and the analysis of results are demonstrated that the improved algorithm not only has strong search ability but also accelerate the convergence rate and reduce the chattering effect in the trajectory planning of the system states.