目的 基于物理模拟的人体运动生成方法由于能够合成符合自然规律的运动片段，可实时响应环境的变化，且生成的物理运动不是机械性的重复，因此是近年来计算机动画和虚拟现实领域中最活跃的研究方向之一。然而人体物理模型具有高维、非线性及关节间强耦合性等特点，求解人体物理运动十分困难。反馈控制器常用于人体物理运动控制，求解时通常需要对多个目标函数加权求和，然而权重的设置需多次试验，烦杂耗时。针对运动控制器求解困难的问题，本文提出了一种面向反馈运动控制器的多目标求解方法。方法 首先，对运动数据进行预处理并提取关键帧求解初始控制器，并设计一种改进的反馈控制机制；在此基础上，种群父代个体变异产生子代，采用禁选区域预筛选策略去除不满足约束的个体，并通过重采样获取新解；然后，通过物理仿真获得多目标适应度值，采用区域密度多层取优选取分布均匀的优秀个体作为下一代父代，并通过基于剪枝的多阶段物理求解算法决定是否进入下一阶段优化；经过多次迭代后获得物理控制器，从而生成具有反馈的人体物理运动。结果 针对提出的方法，本文针对多个测试函数和物理运动分别进行实验：在测试函数实验中，本文分别采用经典的测试函数进行实验对比，在相同的迭代次数下，相比之前算法，本文算法中满足约束的优秀个体命中率更高，反转世距离更小，且最优解集的分布更加均匀；物理运动生成实验中，分别针对走路、跑步和翻滚等运动进行物理运动生成，与之前算法进行对比，本文算法可以更早地完成收敛，同时目标函数值更小，表明生成的运动效果更好。结论 本文提出的进化求解方法可以生成不同运动的控制器，该控制器不仅可以生成物理运动，而且还具备外力干扰下保持平衡的能力，解决了运动控制器求解中多目标权重设置困难、优化时间长的问题；除此之外，本文算法还对具有约束的多目标问题具有较好的求解效果。

Objective A physical-based animation synthesis can generate a human physical motion, which satisfies physical laws. Human physical motion is generated by responding to the environment in real-time and is not mechanically repetitive. Therefore, the human physical motion has been an interesting topic in the computer graphics and virtual reality fields in recent years. However, the human physical motion is difficult to generate given the high dimensionality, nonlinearity, and strong coupling of joints in human physical model. In addition, a feedback controller is frequently used to control human physical motion, especially in the diverse environment or under external forces. Multiple objective functions are typically designed during the process of solving the feedback controllers. Researchers apply optimization methods to solve the feedback controller. Multiple objective functions are frequently converted to a single objective function by utilizing the weighted sum method. However, inaccurate weights can easily result in failure of convergence considering the local traps. Therefore, the setting of weights is crucial to the direction of optimization, convergence time, and result. Thus, experiments become difficult, and these systems require dedicated technical developers. Owing to these problems, a multi-objective solving method is proposed for a feedback motion controller. Method We preprocess motion data and extract key frames to construct the initial controller. Furthermore, an improved feedback control mechanism is designed to reduce the difficulty of the constraint-solving problem. The parents of the population generate children after variation. However, many failure individuals do not satisfy the constraints in the children population. We utilize a forbidden region pre-filtering strategy to solve the abovementioned problem. This strategy adopts the support vector machine (SVM) with a radial basis kernel function (RBF) to remove these failure individuals. We replenish new children by re-sampling to supplement these removed individuals. We set several objective functions, including root, pose, and energy cost functions to measure the quality of every individual. Then, every individual controller is inputted to the physical simulation system, and multi-objective fitness values are obtained after simulations are completed. The regional density multi-layer optimization algorithm is adopted to select the excellent individuals, which show a uniform distribution to construct the next generation of parent individuals. Simultaneously, the SVM with kernel RBF is updated. We prune several individual controllers, which merely generate short physical motion, to obtain stable controllers, which can generate an extensive physical motion. Then, we decide whether to proceed to the next stage of optimization through multi-stage physical solving algorithm based on pruning. The optimized physical controller is obtained after many iterations. Finally, the optimal controller is applied to generate a human physical motion with feedback. Result The experiments are conducted on multiple test functions and physical motions on the basis of the proposed method. In the test function experiment, the classical test functions, including LZ1, ZDT2, and DTLZ4 functions, are used for experimental comparison. We also set several user-defined constraints to analyze the anti-constraint capability of a method. The proposed method achieves higher hit ratio of excellent individuals than the existing methods, thereby satisfying user-defined constraints in the children population under the same number of iterations. The final optimal solution set achieves a small inverted generational distance (IGD) and shows a uniform distribution. In the physical motion experiment, a human physical motion is generated for walking, running, and rolling. Several constraints are appointed; for example, the human physical model is forbidden from falling down and ricocheting off while simulating locomotion. The proposed method achieves a high convergence speed and obtains small objective function values than the existing methods. The results indicate that our generated physical motion has better performance than the other techniques. Conclusion The proposed method can generate various physical human motion controllers, which can not only generate physical motion but also maintain the balance of a physical model under external forces. The proposed evolutionary method can solve the problem of setting multi-objective weights and conducting extensive optimization. In addition, the proposed method has a favorable performance in terms of other multi-objective problems with constraints.