针对双足机器人在三维空间内的稳定行走问题,首先采用3次样条插值法规划出机器人三维行走所需的髋关节、踝关节轨迹,继而提出正、逆向位置解析模型并进行参数求解,基于此实现了机器人三维行走过程中足底零力矩点(zero moment point,ZMP)轨迹的精确数值求解.为确保机器人三维行走的稳定性,提出了实现机器人髋关节侧向偏移量最优粒子群(particle swarm optimization,PSO)算法,求得确保机器人稳定行走的髋关节侧向最优轨迹.虚拟仿真实验结果表明,提出的先规划髋/踝关节轨迹、再求解位置模型参数和ZMP轨迹、继而优化髋关节侧向轨迹的思路,不仅合理可行、计算简便,而且能够可靠确保机器人的三维稳定行走.该研究方法及结论可望为人形机器人的运动规划及控制奠定必要的基础.
To address the stable walking issue of biped robots in three-dimensional space, this paper first employed the cubic spline interpolation method to plan the hip and ankle joint trajectories required for the three-dimensional walking of the robot. Subsequently, forward and inverse position analysis models were proposed, and their parameters were solved. Based on this, an accurate numerical calculation of the foot zero moment point (ZMP) trajectory during the three-dimensional walking process of the robot was achieved. To ensure the stability of the robot’s three-dimensional walking, this paper proposed a particle swarm optimization (PSO) algorithm for optimizing the lateral offset of the robot’s hip joint and obtained the optimal lateral trajectory of the hip joint that guarantees the robot’s stable walking. The results of the subsequent virtual simulation experiments show that the approach proposed in this paper, first planning the hip and ankle joint trajectories, then solving the position model parameters and ZMP trajectory, and finally optimizing the lateral trajectory of the hip joint, is not only reasonable, feasible, and easy to calculate but also reliably ensures the stable three-dimensional walking of the robot. The research methods and conclusions of this paper are expected to lay a necessary foundation for the motion planning and control of humanoid robots.
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