A 6-DOF vibration isolation system with magneto-rheological damper (MRD) based on Stewart mechanism was designed to reduce the mechanical vibration more effectively. To make the isolation system perform well, an effective control method was also proposed. Using the linear multibody systems transfer matrix method (MSTMM), the dynamic model of the MRD 6-DOF vibration isolation system was established to obtain the dynamic characteristics. Firstly, based on the test mechanical property of magnetorheological damper, the electromagnetic coupling model of magnetorheological damper was established. Secondly, the transfer equation of 6-DOF vibration isolation system was established by linear MSTMM. And the state space equation was derived using the modal superposition method, which was based on the augmented eigenvector and body dynamics equation. Thirdly, the linear quadratic Gaussian control method of MRD 6-DOF vibration isolation system was designed. Finally, the numerical simulation was carried out. The results showed that MRD 6-DOF vibration isolation system with optimal control improved the dynamic performance of mechanical equipment effectively. Compared with passive vibration isolation system, the translation of the vibration isolation system in the X, Y, and Z directions, as well as the rotation around the X axis, Y axis and Z axis were reduced by 51.85%, 58.71%, 64.43%, 75.43%, 66.45% and 52.87%, respectively. Similarly, the percentage drops were 50.00%, 56.16%, 34.94%, 53.09%, 38.14% and 46.76% compared to the PID control based vibration isolation system, respectively. The established dynamic model and control strategy provided theoretical basis for relevant vibration isolation tests.

To overcome the shortcomings of the Bouc–Wen model, such as too many parameters, complex identification process, and long time consuming, the sensitivity of parameters was analyzed. A Bouc–Wen optimum model with sensitive parameters to guarantee calculating accuracy was established. First, according to the results of the magnetorheological damper’s mechanical property test, the sensitivity of Bouc–Wen model’s parameters was analyzed by the one-at-a-time method. Optimization of the Bouc–Wen model was completed. Second, the parameters of the Bouc–Wen optimum model were identified under three harmonic excitations. Compared with the original Bouc–Wen model, the differences of calculation accuracy were 0.0055, 0.0007, and 0.0070 respectively. And the convergence rate of the fitness function for parameter identification increased by 67.89%, 49.94%, and 67.24%, respectively. And the iteration time of 1000 iterations was shortened by 36.52%, 25.95%, and 64.11%, respectively. It indicates that the Bouc–Wen optimum model had higher efficiency and certain accuracy in parameter identification process. Then, the calculation accuracy of Bouc–Wen optimum model with independent and coupled mean parameters were analyzed respectively. Finally, the parameters of the Bouc–Wen optimum model and current were fitted by the least square method. The results showed that the Bouc–Wen optimum model can accurately and efficiently simulate the dynamic characteristics of magnetorheological dampers.

The aim of this study is to propose a damper based on magnetorheological (MR) fluid and elastomer for application in vehicle engine mounting systems to dissipate the vibration energy transferred from the engine to the vehicle body. The magnetic circuit structure of the damper has been precisely designed, and its reasonableness has been verified by static magnetic field simulation. After the principle prototype’s completion, the damper’s mechanical properties are tested by an electro–hydraulic servo fatigue machine. The results show that with the current increase, the damper’s in-phase stiffness increases by 20.6%. The equivalent damping improves by 81.6%, which indicates that the damper has a good MR effect. A new phenomenological model is proposed, and a genetic algorithm is used to identify the parameters of the model. Finally, a 1/4 vehicle engine vibration damping system model is established and a dynamics simulation is carried out. The simulation results show that the damper effectively reduces the vibration transmitted from the engine to the body, and the vibration-damping effect is even more obvious through sky-hook control. This proves that the damper proposed in this study has good vibration-damping performance.

An improved butterfly optimization algorithm (IBOA) is proposed to overcome the disadvantages, including slow convergence, generation of local optimum solutions, and deadlock phenomenon, of the optimization algorithm in the path planning of mobile robots. A path-planning grid model is established based on an improved obstacle model. First, the population diversity is improved by introducing kent mapping during population position renewal in the normal butterfly optimization algorithm (BOA) to enhance the global search ability of the butterfly population. Second, an adaptive weight coefficient is introduced in the renewal process of each generation to increase the convergence speed and accuracy. An opposition-based learning strategy based on convex lens imaging is introduced to help the butterfly population jump out of the local optimum. Finally, a mutation strategy is introduced to solve the path planning problem. On this basis, two path simplification strategies are proposed to make up for the shortcomings of planning paths in grid maps. The shortest path lengths solved by IBOA, BOA, and GA in the 20 × 20 map are 30.97, 31.799, and 31.799, respectively. The numbers of iterations for the shortest paths searched by IBOA, BOA, and GA are 14, 24, and 38 in that order. The shortest path lengths solved by IBOA, BOA and GA in the 40 × 40 map are 63.84, 65.60, and 65.84, respectively. The number of iterations for the shortest paths searched by IBOA, BOA and GA are 32, 40, and 46, respectively. Simulation results show that IBOA has a strong ability to solve robot path planning problems and that the proposed path simplification strategy can effectively reduce the length of the optimal path in the grid map to solve the path planning problem of mobile robots. The shortest paths solved by IBOA in 20 × 20 and 40 × 40 maps are simplified to lengths of 30.2914 and 61.03, respectively.

Magnetorheological dampers (MRDs) are of great interest in engineering due to their continuously adjustable damping characteristics. Accurate models are essential for optimizing MRDs and analyzing system dynamics. However, conventional methods widely overlook the impact of excitation frequency and amplitude. To address this issue, this work proposes a modified Bouc–Wen model that can be adapted to various excitation conditions. The model’s parameters depend on the current, excitation frequency, and amplitude. The mechanical characteristics of the MRD were analyzed by the tests. The parameters in the Bouc–Wen model were identified by combining the harmonic balance method and the genetic algorithm. The modified Bouc–Wen model was established by analyzing the variation of each parameter with current, excitation frequency, and amplitude. Finally, the agreement between the modified prediction model and the test results was verified under sinusoidal excitation of 80 mm and 1 Hz. The average relative errors were 3.87%, 2.82%, 2.45%, 2.19%, and 3.27% for current excitations of 0 A, 0.5 A, 1 A, 1.5 A, and 2.0 A, respectively. Since the MRD in this paper operates from 0.5 Hz to 2 Hz, the modified model was validated in the same range. Experiments demonstrate that the modified Bouc–Wen model efficiently and accurately describes the mechanical properties of the MRD under various excitation conditions.