基于坐标变换下的球形机器人稳定平台控制

Stabilized Platform Control in the Spherical Robot Based on Coordinate Transformation

由于球形机器人内部构件相对于壳体需要保证全方位的运动,所以机器人内部的传感器以及探测设备常因缺乏稳定支撑而无法正常工作。基于此,探讨通过控制的方法使机器人内部形成稳定平台。利用基于能量耗散形式下的拉格朗日方程建立球形机器人前向滚动状态下的动力学模型,并根据实际运动情况对所推导的动力学方程进行线性化处理,接着通过坐标变换的方法,使方程在新的平衡点处转化为线性定常的状态空间形式。在整个变换过程中引入平衡摆角和平衡速度两个重要概念,为进一步分析机器人运动特征奠定基础。对于动力学方程中出现的循环坐标,采用减少状态变量的方式来保证系统的可控、可观性。针对机器人运动中所需要达到的具体性能指标要求,设计机器人的全状态反馈控制器,可对系统的极点进行任意配置。仿真结果表明了所设计的控制器的有效性。

Because the inner components of the spherical robot should have ornni-directional characteristics with respect to sphere shell, the sensors and the detection equipment applied by the robot cannot work normally without a relative stable platform. A stable platform is provided for the spherical robot by using control techniques. The dynamic model of rolling forward is derived by applying Lagrangian function based on energy dissipation, and then, the proposed function is linearized according to the actual movement situation. The system is transformed into linear and fixed-length state-space form effectively around the new balance points via coordinate transformation. The two importance concepts, balance pendulum angle and balance rolling velocity, are introduced in the process of this transformation, which lay foundation for further analyzing robot motion property. The cyclic coordinates in the dynamic model, as a state variable, are removed in order to assure controllability and observability of the robot system. A state feedback controller, which can realize arbitrarily pole assignment, is designed to get the expected performance index, and corresponding simulation result verifies the effectiveness of the proposed controller.