Dynamic modeling and closed-loop control design for humanoid robotic systems: Gibbs–Appell formulation and SDRE approach

IF 2.6 2区 工程技术 Q2 MECHANICS
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Abstract

Analyzing the walking motion of the bipedal robots that have upper-body parts as well as lower-body legs and exhibit a human-like gait is a challenging task. One of the main objectives of this paper is to present a new and systematic method for designing a desired movement trajectory for a bipedal robot such that it has the greatest conformity with the system dynamics and makes the gait of a bipedal robot similar to the configuration of a human being walking on a sloping surface. To this end, first, the kinematics and the dynamics of a bipedal robot walking down a ramp of shallow slope are investigated. Using the recursive Gibbs–Appell (G-A) methodology and Newton’s kinematic impact law, the governing dynamic equations of this bipedal robot in the two single-support and double-support phases are derived so that we can alter the system’s degrees of freedom without having to perform manual computations. Based on the dynamic equations obtained in the process, an eigenvalue problem is achieved, which can be solved to determine the suitable initial conditions needed for the passive gait of the bipedal robot. Then, having the initial and final conditions (before an impact with the inclined surface), a new method called “passive gait-based trajectory design (PGBTD)” is employed to determine the desired walking trajectory of the robot for one step. Considering the nonlinearity of the examined system, an optimal control method based on the state-dependent Riccati equation (SDRE) is employed to track the desired trajectory obtained. The performed simulations show that by just using a small amount of control energy at the beginning of each step, the steady and continuous gait of the bipedal robot on sloping surfaces can be controlled.

仿人机器人系统的动态建模和闭环控制设计:吉布斯-阿佩尔公式和 SDRE 方法
摘要 分析双足机器人的行走运动是一项具有挑战性的任务,因为双足机器人既有上半身部分,也有下半身腿部,并表现出类似人类的步态。本文的主要目的之一是提出一种新的系统方法,为双足机器人设计理想的运动轨迹,使其与系统动力学达到最大程度的一致,并使双足机器人的步态与人类在斜面上行走时的步态相似。为此,首先研究了双足机器人在浅坡斜面上行走的运动学和动力学。利用递归吉布斯-阿佩尔(G-A)方法和牛顿运动影响定律,推导出该双足机器人在单支撑和双支撑两个阶段的支配动态方程,这样我们就可以改变系统的自由度,而无需进行人工计算。根据在此过程中获得的动态方程,可以求解特征值问题,从而确定双足机器人被动步态所需的合适初始条件。然后,根据初始条件和最终条件(在撞击倾斜表面之前),采用一种名为 "基于被动步态的轨迹设计(PGBTD)"的新方法来确定机器人一步所需的行走轨迹。考虑到被测系统的非线性,采用了一种基于状态相关里卡提方程(SDRE)的优化控制方法来跟踪所获得的理想轨迹。模拟结果表明,只需在每一步开始时使用少量控制能量,就能控制双足机器人在斜面上稳定、持续地行走。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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