The balancing act of an inverted pendulum with a robotic manipulator is a classical benchmark for testing modern control strategies in conjunction with fast sensor-guided movements. From the control design perspective, it presents a challenging and difficult problem, as the system is open-loop instable and includes nonlinear effects in the actuators, such as friction, backlash, and elasticity. In addition, the necessity of a sensor system that can measure the inclination angles of the pendulum contributes to the complexity of the balancing problem. The pendulum is projected onto the xz and yz planes of the inertial coordinate system. These projections are treated independently from each other and are controlled individually by a state-space controller in the x and y axes, respectively. The nonlinearities of the robot are compensated by using inverse dynamics and inverse kinematics. A specially developed sensor system allows the contactless measurement of the inclination angles of the pendulum. This system consists of a small magnet, placed at the bottom of the pendulum, and Hall-effect sensors placed inside the end effector.
展开▼
