Vibration-polynomial-based optimal trajectory planning for mobile concrete pumping equipment with state constraints

To improve the operating stabilities of the flexible hydraulic manipulator in concrete pumping equipment, a trajectory planning method based on optimal vibration energy is presented. First, predefined trajectories are generated by the quintic polynomial method, and kinematic inversions are established by unifying the velocity and angle constraints into the velocity level. Then, relationships between the boom vibration and the vibration energy are solved in modal space. Specifically, hydraulic actuators are regarded as spring-damping systems to calculate generalized forces into the vibration equation. The vibration equation can solve the modal coordinate and vibration model function, such that the elastic potential energy to cause vibration is completely described. Next, floating values are captured by a genetic algorithm to minimize vibration energy, and then introduced to the predefined trajectory to weaken the boom vibration. Last, the proposed trajectory planning method is verified by a concrete pumping spreader with a 13 m hydraulic manipulator.