双足机器人具有仿人的身体结构和外观，可以很好的适应人类的生活环境，是替代人类工作的理想机器人。近50年来，科研人员在双足机器人的样机制作及控制理论进行了许多研究，并取得显著的进展。双足行走是双足机器人运动研究领域最重要、最基础的问题。按照研究思想的不同，提出的双足行走方法可分为基于简化机器人动力学模型的方法和参照人类运动方式的仿生学方法。由于目前的机器人结构与人类相比尚有较大差异，更多的科研人员倾向于研究中采用简化模型的方法。本文从机器人多质心简化模型出发，对节能行走优化算法的关键技术进行研究。

建立数学模型是设计双足机器人运动控制算法的基础。本文依据双足机器人的结构特征，将世界坐标系与浮动坐标系结合，构建机器人模型的广义坐标表示方法，分析双足机器人行走过程中关节角度、角速度与关节-连杆的位姿及其在三维空间的运动速度的变换关系，建立双足机器人正运动学模型。基于双足机器人步态控制算法优化中大规模逆运动学计算的要求，遵循运动过程中腿部各关节的几何关系，建立双足机器人逆运动学解算模型，该方法适于快速、并行计算机器人的运动参数。依照双足机器人运动过程中存在的多种脚、地接触状态，建立单足相、双足相和碰撞相等多形态机器人动力学模型。

完整的动力学模型可精确的评估机器人行走的运动状态，但模型运算产生的计算量过大，在需要大量运算的机器人参数优化算法中难以实现。本文提出依据步态周期内双足机器人行走的质量分布统计信息，建立双足机器人行走的多质心简化模型。如何在双足机器人运动中保持稳定、避免摔倒，是机器人运动控制算法应考虑的重要问题。按照算法需求，本文选择庞加莱映射判据与可变零力矩点区域结合的稳定性描述方法。高能耗问题是阻碍双足机器人应用和发展的重要因素之一，而不同的步态控制算法在机器人运动能耗方面存在很大差异。本文在机器人优化算法的能耗评价中，提出依据双足机器人质心重力作用下各关节负荷力矩及角速度，建立双足机器人运动能耗函数，以在控制算法优化中快速计算机器人的运动能耗。

如何在满足行走稳定性要求的前提下，获取双足机器人行走最小能耗的步态参数是本文算法的核心问题之一。本文提出以描述参数表征双足机器人运动中身体的限定空间，通过建立描述参数与机器人行走步态、能耗之间的映射关系，探索以数学方程表征具有高度非线性特征的机器人步态优化问题。提出的算法通过参数空间采样及步态参数计算，按照稳定裕度对样本分类，利用设计的三维单纯形种子抽取算法及方向加速梯度优化算法，实现在大范围的参数空间获取的能耗最低点的步态参数即为目标映射函数。

双足机器人行走是一个高度非线性的控制问题，在存在干扰的环境中实现双足机器人行走的最小能耗控制是本文研究的另一个核心问题。本文提出以建立步态数据库作为机器人行走认知的知识储备，探索以近似线性的控制方法实现双足机器人行走的步态控制。提出的算法利用步态类型、稳定裕度等属性的数据库检索，实现给定运动目标的最小能耗步态轨迹的动态规划，并通过实时零力矩点反馈及稳定裕度差值的线性校正，调整适配稳定裕度的步态数据项，实现双足机器人节能行走的步态控制。

为验证本文设计的双足机器人行走控制算法，分别在Matlab环境和Webots环境构造3D仿真模型。其中，在Matlab环境中，利用仿真模型对算法的各个计算过程，进行验证评估，并按照机器人行走要求精度，建立行走步态数据库。在Webots环境中，利用虚拟现实的动力学仿真模型，对步态参数优化的数据进行检验评估。机器人仿真所获的结果数据，均在实物机器人的实时行走中进行验证。仿真和实验结果表明，本文算法在机器人行走过程中具有明显的节能效果。

Biped robots have human-like structures and appearances, which can adapt to human environment, and are ideal robots to replace human work. In the past 50 years, researchers have carried out researches on the prototype manufacturing and control theory of biped robots, and have achieved remarkable progress. Bipedal walking is the most important and basic problem in research on biped robot motion. According to different research ideas, the proposed biped walking methods can be divided into two approaches, which are methods based on simplified robot dynamic models and bionic methods referring to human motion modes. Because there are still great differences between existing robot structures and human beings, researchers prefer to adopt the method of simplifying biped models. Starting from a simplified multimass robot model, the key technology of an energy-saving walking optimization algorithm is studied.

The establishment of a mathematical model is the basis of designing a biped robot motion control algorithm. According to the structural characteristics of a biped robot, the robot motion space combines the global coordinate system with the floating coordinate system to construct a generalized coordinate representation, analyzes the transformation relationship among the joint angle, angular velocity and the position and attitude of the joint connecting rod and its motion velocity in three-dimensional space, and establishes a forward kinematics model of the biped robot. To address the large-scale calculation requirements in the optimization of the biped robot gait control algorithm, based on the geometric relationship of the leg joints in the movement process, this research established an inverse kinematics solution model of the biped robot. The method is suitable for parallel operation to quickly calculate the motion parameters of the robot. According to the various states in the movement process of the biped robot, the contact state between the foot and ground is distinguished, and the multimodal dynamic models of the monopedal phase, bipedal phase and collision are established.

The complete dynamic model can accurately evaluate the motion state of robot walking, but the amount of calculation generated by model operation is too large to be realized in the robot parameter optimization algorithm, which requires many operations. A simplified multimass walking model is proposed on the basis of the statistical information of the biped robot walking mass distribution in the gait cycle. How to avoid falls in biped robot motion is an important problem that should be considered in robot motion control algorithms. According to the requirements of the algorithm, a stability description method combining the Poincaré mapping criterion and allowable zero-moment point region is selected. High energy consumption is one of the important factors hindering the application and development of biped robots, and different gait control algorithms have large differences in robot motion energy consumption. In the energy consumption evaluation, a method is proposed to establish the motion energy consumption function of the biped robot according to the load torque and angular velocity of each joint under the gravity of the biped robot's centroid to quickly calculate the motion energy consumption of the robot in the optimization of the control algorithm.

Obtaining the gait parameters of a biped robot with minimum energy consumption on the premise to meeting the requirements of walking stability is one of the core problems of this algorithm. In the gait parameter algorighm optimization, the limited space of the body in the movement of the biped robot is proposed, and a representation method of the robot trajectory expressed using finite term description parameters is established. Then, a method of extracting the seed set according to the sample ZMP trajectory and energy consumption function is proposed through parameter space sampling and inverse kinematics calculation. To address optimizing the minimum-energy consumption gait in the seed field, the gradient direction of the energy consumption function is determined using spacing search, and a multistep gradient optimization algorithm based on direction acceleration is employed. The gait parameters at the lowest energy consumption are obtained as the objective mapping function.

Biped robot walking is a highly nonlinear control problem. Realizing energy-saving and stable walking of biped robots in an environment with interference is another core problem studied in this paper. In the design of the control system, based on the results of the gait parameter optimization calculation, this research classified the walking gait according to step size, gait type and stability margin, and a walking gait database of the biped robot with the minimum energy consumption index is established. To address the given walking target of a biped robot, with the usage of the robot walking gait database, an algorithm planning the gait trajectory with minimum energy consumption of biped walking is proposed, and the energy-saving walking gait control of a biped robot is realized through the stability margin correction method of real-time ZMP feedback.

To verify the walking control algorithm of the biped robot designed in this paper, 3D simulation models are constructed in the MATLAB and Webots environments. In the MATLAB environment, the simulation model is used to verify and evaluate each calculation process of the algorithm, and the walking gait database is constructed according to the required accuracy of robot walking. In the Webots environment, a virtual reality dynamic simulation model is used to test and evaluate the gait parameter optimization data. The resulting data obtained from the robot simulation are verified in the real-time walking of a physical robot. Simulation and experimental results show that the proposed algorithm meets the design expectation and has an obvious energy-saving effect in the robot walking process.

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