# Multi-Objective Optimal Control Method for the 6-DOF Robotic Crusher
## 1 Introduction  
A cone crusher is one of the most widely used crushing equipment in crushing operations. In the crushing chamber, the granular material can be crushed into small particles because of the eccentric motion of the mantle. The structure of a traditional cone crusher is shown in Figure 0(a). The working mode is that the main shaft 1 drives the eccentric sleeve 2, which drives the mantle 3 to realize eccentric rotation, so as to realize the function of squeezing and crushing the granular materials in the crushing chamber. The advantages include high  
Figure 1: (**a**) Structure of cone crusher with traditional structure and 6-DOF robotic crusher. Structure of traditional cone crusher: (1) main shaft, (2) eccentric sleeve, (3) mantle, (4) concave. (**b**) Structure of traditional 6-DOF robotic crusher: (1) actuator, (2) mantle, (3) concave. crushing efficiency, large crushing ratio, and uniform particle size of crushing products. However, it also has the disadvantages of complex structure, high energy consumption, and large wear and tear. The advantages of a 6-DOF robotic crusher include high flexibility, simple structure, convenient maintenance, and the ability to realize intellectualization, which is similar to a parallel robot. In order to achieve the best crushing effect, that is, to achieve the goal of energy saving, consumption reduction, and efficiency increase, it is necessary to formulate corresponding crushing strategies for the 6-DOF robotic crusher according to specific materials and crushing chamber. It can provide a reference for the research of optimal control. Previous researchers on the optimization of cone crushers focused on the crushing chamber [1; 2; 3; 4] liner material and wear [5; 6; 7]. The research on the control objectives of cone crushers focused on feeding [8], hopper liquid level [9], and screening [10]. The control methods include the adaptive time-varying state method [8], fuzzy PID method [11], brain emotion learning (BEL) [12] method, etc. Different from the traditional cone crusher, the control and optimization of the 6-DOF platform and crusher need to be considered at the same time. The previous research on the 6-DOF platform focuses on posture. In terms of optimization and control, [PERSON] [13] has proposed a 6-DOF target attitude tracking method, which is robust to severe occlusion. [PERSON] [14] has proposed a multi-stage simplified modeling method for establishing the kinematic static model of a flexible platform with complex configuration. The motion dynamics of the 6-DOF flexible platform have been analyzed, which provides a basis for the design and optimization of flexible mechanisms based on bridge amplifiers. [PERSON] [15] has proposed an improved method for the mechanical manual mechanical model of a 6-DOF robot to improve its motion accuracy. As for the optimal control of the 6-DOF robotic crusher, it is necessary to combine the above research results and take the research content of this paper as the reference of optimal control to achieve the goal of energy conservation, consumption reduction, and efficiency increase. In terms of the specific control method of the 6-DOF robotic crusher, [PERSON] [16; 17] has considered its no-load and full-load conditions, established the corresponding kinematics and dynamics equations, and analyzed and optimized its workspace and singularity. [PERSON] [18] has analyzed the kinematics of the 6-DOF robotic crusher, established the traditional PID and fuzzy PID control models, and simulated them. [PERSON] [19] analyzed the working structure and control strategy of the 6-DOF robotic crusher, established the SimMachanics model of the crusher, and simulated the displacement control of the driving cylinder. As for the optimization algorithm, with the expansion of the application scope of optimization and the deepening of optimization research, the optimization algorithm has been widely researched and applied in many fields.