The planetary gear train is often used as the main device for decelerating and increasing the torque of the drive motor of electric vehicles. Considering the lightweight requirement and existing uncertainty in structural design, a multi-objective uncertainty optimization design (MUOD) framework is developed for the planetary gear train of the electric vehicle in this study. The volume and transmission efficiency of the planetary gear train are taken into consideration as optimization objectives. The manufacturing size, material, and load input of the planetary gear train are considered as uncertainties. An approximate direct decoupling model, based on subinterval Taylor expansion, is applied to evaluate the propagation of uncertainties. To improve the convergence ability of the multi-objective evolutionary algorithm, the improved non-dominated sorting genetic algorithm II (NSGA-II) is designed by using chaotic and adaptive strategies. The improved NSGA-II has better convergence efficiency than classical NSGA-II and multi-objective particle swarm optimization (MOPSO). In addition, the multi-criteria decision making (MCDM) method is applied to choose the most satisfactory solution in Pareto sets from the multi-objective evolutionary algorithm. Compared with the multi-objective deterministic optimization design (MDOD), the proposed MUOD framework has better reliability than MDOD under different uncertainty cases. This MUOD method enables further guidance pertaining to the uncertainty optimization design of transportation equipment, containing gear reduction mechanisms, in order to reduce the failure risk.

In order to improve the stability and economy of 4WID-4WIS (four-wheel independent drive—four-wheel independent steering) electric vehicles in trajectory tracking, this paper proposes a trajectory tracking coordinated control strategy considering energy consumption economy. First, a hierarchical chassis coordinated control architecture is designed, which includes target planning layer, and coordinated control layer. Then, the trajectory tracking control is decoupled based on the decentralized control structure. Expert PID and Model Predictive Control (MPC) are employed to realize longitudinal velocity tracking and lateral path tracking, respectively, which calculate generalized forces and moments. In addition, with the objective of optimal overall efficiency, the optimal torque distribution for each wheel is achieved using the Mutant Particle Swarm Optimization (MPSO) algorithm. Additionally, the modified Ackermann theory is used to distribute wheel angles. Finally, the control strategy is simulated and verified using Simulink. Comparing the control results of the average distribution strategy and the wheel load distribution strategy, it can be concluded that the proposed coordinated control not only provides good trajectory tracking but also greatly improves the overall efficiency of the motor operating points, which enhances the energy economy and realizes the multi-objective coordinated control of the chassis.

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<div class="section abstract"><div class="htmlview paragraph">To overcome the shortcoming that vehicles with multiple steering modes need to switch steering modes at parking or very low speeds, a dynamic switch method of steering modes based on MOEA/D (Multi-objective Evolutionary Algorithm Based on Decomposition) was proposed for 4WID-4WIS (Four Wheel Independent Drive-Four Wheel Independent Steering) electric vehicle, considering the smoothness of dynamic switch, the lateral stability of the vehicle and the energy economy of tires. First of all, the vehicle model of 4WID-4WIS was established, and steering modes were introduced and analyzed. Secondly, the conditions for the dynamic switch of steering modes were designed with the goal of stability and safety. According to different constraints, the control strategy was formulated to obtain the target angle of the active wheels. Then aiming at the smoothness of the dynamic switch, the active wheel angle trajectory was constructed based on the B-spline theory. And the MOEA/D algorithm was used to carry out multi-objective optimization of the trajectory to obtain the Pareto optimal solution set. The optimal active wheel angle switch trajectory was decided by TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) decision-making model. Last but not least, in the Simulink-CarSim co-simulation environment, the results of wheel angle, yaw rate, and sideslip angle were compared under different control strategies. The proposed control strategy achieved smoother dynamic switch of steering modes and ensured better handling stability, thus verifying the effectiveness of the strategy.</div></div>