ICPA-LQR优化的两轮平衡机器人自稳定与轨迹跟踪PID控制器设计

Design of PID controller for self-stability and trajectory tracking of two-wheeled balance robot with ICPA-LQR

摘要:

针对现有两轮平衡机器人线性二次型调节器（LQR）的权重系数需要手动选取的缺陷,提出了一种利用改进的食肉植物算法(ICPA)优化LQR权重系数的方法,实现了两轮平衡机器人的自稳定与高精度轨迹跟踪。首先,利用拉格朗日方程法构建了两轮平衡机器人系统动力学方程,采用LQR优化PID控制策略保证其最优控制力；其次,在食肉植物算法（CPA）成长过程中引入自适应捕捉系数,平衡食肉植物和猎物的成长关系,提升了前期全局探索和后期局部寻优能力；然后,在CPA繁殖过程中设计干扰因子,扩大搜索空间,进一步提升全局寻优能力；最后,基于EA代价函数,利用ICPA 对LQR控制器的权重系数进行寻优,并在MATLAB/Simulink环境中建立两轮平衡机器人控制策略模型。实验结果表明,提出的ICPA-LQR优化的PID控制器,相较于食肉植物算法、麻雀搜索算法、飞蛾扑火算法和改进粒子群算法优化的控制器,动态响应速度更快、抗干扰能力更强、整体性能更好。在扰动情况下,控制两轮平衡机器人跟踪复杂轨迹时,倾角动态偏差小于0.05 rad、横纵坐标的偏差均小于0.2 m、转向角偏差小于0.2 rad、车轮位置角偏差小于3 rad,可以在保持动态平衡的前提下精确跟踪给定的参考轨迹,具有较强的泛化能力。

Abstract:

Aiming at the defects that the weight coefficients of linear quadratic regulator (LQR) of two-wheeled balance robot needs to be manually selected, an improved carnivorous plant algorithm (ICPA) is used to optimize the LQR weight coefficients, which realizes the self-stability and high-precision trajectory tracking of two-wheeled balance robot. Firstly, the dynamic equations of the balance robot system is constructed by Lagrange equation method, and the LQR optimization PID control strategy is used to ensure the optimal control force. Secondly, an adaptive capture coefficient is proposed in the growth process of carnivorous plant algorithm, which balances the growth of carnivorous plants and preys, and improves the ability of global exploration in the early stage and local optimization in the later stage. Then, the interference factor is designed in the reproduction process of carnivorous plant algorithm to expand the search space and further improve the global optimization ability. Finally, based on EA cost function, the weight coefficients of LQR controller is optimized by ICPA, and the control strategy model of two-wheeled balanced robot is established in MATLAB/Simulink environment. The experimental results show that the PID controller optimized by the proposed ICPA-LQR optimized PID controller has faster dynamic response speed, stronger anti-interference ability and better overall performance than the control effect optimized by the carnivorous plant algorithm, sparrow search algorithm, moth fire extinguishing algorithm and improved particle swarm optimization algorithm. Under disturbance, the dynamic deviation of the control two-wheeled balance robot tracking complex trajectory dip angle is less than 0.05 rad, the deviations of the horizontal and vertical coordinates is less than 0.2 m, the deviation of the steering angle is less than 0.2 rad, and the deviation of the wheel position angle is less than 3 rad, which can accurately track the given reference trajectory under the premise of maintaining dynamic balance, behaving strong generalization ability.