The paper aims to solve problems of the mathematical modeling and realization of a cube robot capable of self-bouncing and self-balancing. First, the dynamic model of the cube robot is derived by using the conservation of the angular momentum and the torque equilibrium theory. Furthermore, the controllability of the cube robot is analyzed and the angle of the cube robot is derived from the attitude and heading reference system (AHRS). Then the parallel proportional–integral–derivative (PID) controller is proposed for the balancing control of the self-designed cube robot. As for the bounce control of the cube robot, a braking system triggered by the servo motor is designed for converting the kinetic energy to the potential energy. Finally, the experimental results are included to demonstrate that the cube robot can complete the actions of self-bouncing and self-balancing with good robustness to external disturbances.

中文翻译：

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立方体机器人的非线性动力学与控制

本文旨在解决具有自弹跳和自平衡功能的立方体机器人的数学建模和实现问题。首先，利用角动量守恒和转矩平衡理论推导了立方机器人的动力学模型。此外，还分析了立方体机器人的可控性，并根据姿态和航向参考系统（AHRS）得出了立方体机器人的角度。然后提出了并行比例-积分-微分（PID）控制器，用于自行设计的立方体机器人的平衡控制。对于立方体机器人的弹跳控制，设计了由伺服电动机触发的制动系统，用于将动能转换为势能。最后，