基于MPC的球形机器人轨迹跟踪方法研究

Research on trajectory tracking method of spherical robot based on MPC

单摆驱动式球形机器人运动存在欠驱动和非线性特性,导致轨迹跟踪难度较大。为此,提出了一种基于模型预测控制(MPC)的球形机器人轨迹跟踪控制方法。该方法首先利用拉格朗日动力学模型和参考运动轨迹,结合泰勒线性展开和时域离散处理,得到球形机器人运动状态偏差的预测模型。随后,以未来特定时段内轨迹跟踪误差最小为目标,在满足控制量和控制增量约束的条件下,利用二次规划对球形机器人长轴和短轴电机转矩进行滚动优化,同时在特定控制步长下不断根据优化结果进行电机转矩控制,最终实现对机器人参考轨迹的跟踪。仿真结果表明,与传统PID控制方法相比,所提MPC方法横向跟踪最大误差减少了0.664 4 m,纵向跟踪最大误差减少了0.112 1 m,跟踪误差曲线基本在0附近波动,具有明显的轨迹跟踪精度与稳定性优势。

The trajectory tracking control of a spherical robot driven by a pendulum suffers from underactuation and nonlinearity,making it difficult to accurately follow desired trajectories.To address this,a Model Predictive Control(MPC)based trajectory tracking control method is proposed.This method utilizes the Lagrangian dynamics model and reference motion trajectory to derive a predictive model for the state deviation of the spherical robot,incorporating Taylor linearization and temporal discretization.Subsequently,with the objective of minimizing trajectory tracking errors within a future time horizon,subject to constraints on control inputs and control increment,a quadratic programming problem is formulated to optimize the rolling torques of the long and short axis motors of the spherical robot.The optimization results are used for torque control of the motors at specific control steps,enabling the robot to track the desired reference trajectory.Simulation results demonstrate that compared to the traditional PID control method,the proposed MPC method reduces the maximum lateral tracking error by 0.6644 m and the maximum longitudinal tracking error by 0.1121 m.The tracking error curve remains close to zero,indicating significant advantages in terms of trajectory tracking accuracy and stability.