基于模糊MPC算法的双轮足机器人运动控制研究

Research on Motion Control of Bipedal Wheel-Legged Robots Based on the Fuzzy MPC Algorithm

摘要: 针对双轮足机器人在外部干扰下易姿态发散、对精确模型敏感且在线求解压力大的问题，本文提出一种模糊调度——模型预测控制(Fuzzy-MPC)一体化方案。方法以倒立摆模型近似为预测模型，在不改变凸QP结构的前提下：1) 依据IMU的姿态误差与变化率构造风险度量，将其连续映射到“采样步长/预测域”以实现自适应预测时域；2) 设计两路Mamdani模糊器(位移–速度、俯仰角–角速度)生成误差补偿系数，按指数衰减注入到滚动预测轨迹，抵消模型失配与数值滞后的影响。以MATLAB平台进行对比显示：在15˚与30˚初始倾角两种场景下，相较于PD与标准MPC，Fuzzy-MPC可在更短稳定时间与更小位移漂移的同时，显著降低约束违背与执行器持续饱和的风险，体现出更好的鲁棒性与能耗友好性。

Abstract: To address the issues that bipedal wheel-legged robots are prone to posture divergence under external disturbances, are sensitive to accurate models, and face heavy online computation demands, this paper proposes an integrated Fuzzy-MPC (Fuzzy Scheduling-Model Predictive Control) scheme. The method uses an inverted pendulum model as an approximate prediction model, and without changing the convex QP structure: 1) it constructs a risk metric based on the IMU’s attitude error and its rate of change, continuously mapping it to the “sampling step/prediction horizon” to achieve an adaptive prediction horizon; 2) it designs two Mamdani fuzzy controllers (displacement-velocity and pitch angle-angular velocity) to generate error compensation coefficients, which are injected into the rolling prediction trajectory with exponential decay to counteract model mismatch and numerical lag. Comparative results on the MATLAB platform show that in scenarios with initial tilt angles of 15˚ and 30˚, compared with PD and standard MPC, Fuzzy-MPC achieves shorter stabilization times and smaller displacement drift while significantly reducing the risks of constraint violations and continuous actuator saturation, demonstrating better robustness and energy efficiency.