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。
Multi-objective Solving Method for Feedback Motion Controller
Zhang Ying kai,Xie Wen Jun,Liu Xiao Ping(School of Computer and Information, Hefei University of Technology)
Objective The physical-based animation synthesis can generate the 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, human physical motion has been one of the hottest topics in the fields of computer graphics and virtual reality in recent years. However, human physical motion is very difficult to generate due to high dimensionality, nonlinearity and strong coupling of joints in human physical model. In addition, especially in the diverse environment or under external forces, feedback controller is often used for controlling human physical motion. During the process of solving the feedback controllers, multiple objective functions are usually designed. Researchers apply optimization methods to solve feedback controller. Multiple objective functions are often converted to single objective function by utilizing the weighted sum method. However, improper weights can easily result in a failure of convergence due to the local traps, the setting of weights is therefore crucial to the direction of optimization, the convergence time and the result. This makes experiment heavy and so often these systems require dedicated technical developers to maintain. In view of the above problem, this paper proposes a multi-objective solving method for feedback motion controller.Method Firstly, we preprocesses motion data and extracts key frames to construct the initial controller. Meanwhile, an improved feedback control mechanism is designed to reduce the difficulty of constraint-solving problem. The parent individuals of population generate children individuals after variation. Nevertheless, there are lots of failure individuals which do not satisfy constraints in the children population. To solve this problem, we utilizes forbidden region pre-filtering strategy which adopts the support vector machine (SVM) with radial basis kernel function (RBF) to remove these failure individuals. In order to supplement these removed individuals, we replenish new children individuals through re-sampling; For the sake of measuring quality of every individual, we set several objective functions, including root cost function, pose cost function, and energy cost function. Then, every individual controller is inputted to the physical simulation system, and multi-objective fitness values are obtained after simulations are finished. In order to select the excellent individuals which show uniform distribution to construct the next generation of parent individuals, the regional density multi-layer optimization algorithm is adopted. At the same time, the SVM with kernel RBF is updated. In order to get more stable controllers which can generate longer physical motion, we prune some individual controllers which merely generate short physical motion. After that, we decides whether to enter the next stage of optimization through multi-stage physical solving algorithm based on pruning. After many iterations, the optimized physical controller is obtained. Finally the optimal controller is applied to generate human physical motion with feedback.Result Based on the proposed method, the experiments are conducted on multiple test functions and physical motions. In the test function experiment, the classical test functions are used for experimental comparison in this paper, including LZ1 function, ZDT2 function, and DTLZ4 function, and we also set several user-defined constraints respectively in order to analyze the methods’ anti-constraints ability. Comparing to the existing methods, the proposed method achieves higher hit ratio of excellent individuals which satisfy user-defined constraints in the children population under the same number of iterations. The final optimal solution set achieves smaller inverted generational distance (IGD) and shows more uniform distribution. In the physical motion experiment, the generation of human physical motion is carried out for walking, running and rolling respectively. Several constraints are appointed, for example, the human physical model is forbidden from falling down and ricocheting off while in the simulation of locomotion. Comparing to the existing methods, the proposed method achieves higher convergence speed and obtains smaller objective function values. The results indicate our generated physical motion has better performance than the others.Conclusion The proposed method can generate a variety of physical human motion controllers, and these controllers not only can generate physical motion, but also can maintain physical model’s balance under external forces. The proposed evolutionary method can solve the problems that it is difficult to set multi-objective weights and conduct long-time optimization; In addition, the proposed method also has a good performance in terms of other multi-objective problems with constraints.