稳定步行机器人控制运动综合反动力学方法方程的求解特点

Q3 Mathematics SPIIRAS Proceedings Pub Date : 2019-02-01 DOI:10.15622/SP.18.1.85-122
A. Gorobtsov, A. Andreev, A. Markov, A. Skorikov, P. Tarasov
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引用次数: 21

摘要

研究了用逆动力学方法进行步行机器人控制运动综合的问题。逆动力学方法方程用多体系统动力学方法表示为自由体运动方程和约束方程。引入各种约束方程组来确定机器人的步态,实现机器人的稳定条件,协调机器人的特定环节运动。该公式中的逆动力学方法方程的关键特征是在表示保证机器人保持垂直位置的稳定性条件的约束方程中存在系统坐标的二阶导数。由于拉格朗日乘子初始条件的不确定性,一般情况下这类方程的确定解是不可能的。考虑了不考虑约束方程中决定机器人稳定性的惯性分量的逆动力学近似求解方法。给出了确定机器人各个环节坐标运动的约束方程和基于近似方程的唯一问题求解所需的约束方程。介绍了程序运动合成方法在仿人机器人AR-600控制系统中的实现。对控制运动的理论参数和实验参数进行了比较。结果表明,在机器人连杆跟踪驱动器控制精度达到百分之几的情况下,机器人的绝对运动指标,特别是横摇角、偏航角和俯仰角,与程序的误差相差30-40%。研究结果表明,该方法可以综合机器人在准静态模式下对不同运动类型的控制,如向前移动、侧移、在楼梯上行走、倾斜等。
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Features of solving the inverse dynamic method equations for the synthesis of stable walking robots controlled motion
The problem of walking robots controlled motion synthesis by the inverse dynamic method is considered. The inverse dynamic method equations are represented by the methods of multibody system dynamics as free bodies motion equations and constraint equations. The variety of constraint equations group are introduced to specify the robot gait, to implement the robot stability conditions and to coordinate specified robot links movement. The key feature of the inverse dynamic method equations in this formulation is the presence of the second derivatives of the system coordinates in the constraint equations expressing the stability conditions that ensure the maintenance of the vertical position by the robot. The determined solution of such equations in general case is impossible due to the uncertainty of the initial conditions for the Lagrange multipliers. An approximate method for solving the inverse dynamic without taking into account the inertial components in the constraint equations that determine the stability of the robot is considered. Constraint equations that determine the coordinate movement of individual robot links and required for unique problem solving based on approximate equations are presented. The implementation of program motion synthesis methods in the control system of the humanoid robot AR-600 is presented. The comparison of theoretical and experimental parameters of controlled motion is performed. It has been established that with the achieved high accuracy of the robot links tracking drives control with an error of several percent, the indicators of the robot's absolute movements, in particular, the angles of roll, yaw and pitch, differ from the programmed by 30-40%. It’s shown that proposed method allows to synthesize robot control in quasistatic mode for different movement types such as moving forward, sideways, walking on stairs, inclinations etc.
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来源期刊
SPIIRAS Proceedings
SPIIRAS Proceedings Mathematics-Applied Mathematics
CiteScore
1.90
自引率
0.00%
发文量
0
审稿时长
14 weeks
期刊介绍: The SPIIRAS Proceedings journal publishes scientific, scientific-educational, scientific-popular papers relating to computer science, automation, applied mathematics, interdisciplinary research, as well as information technology, the theoretical foundations of computer science (such as mathematical and related to other scientific disciplines), information security and information protection, decision making and artificial intelligence, mathematical modeling, informatization.
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