Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL
Bálint Bodor, L. Bencsik
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引用次数: 0

Abstract

Robotics is undergoing dynamic progression with the spread of soft robots and compliant mechanisms. The mechanical models describing these systems are underactuated, having more degrees of freedom than inputs. The trajectory tracking control of underactuated systems is not straightforward. The solution of the inverse dynamics is not stable in all cases, as it only considers the actual state of the system. Therefore employing the advances of optimal control theory is a reasonable choice. However, the real-time application of these is challenging as the solution to the discretized optimization problems is numerically expensive. This paper presents a novel iterative approach to solving nonlinear optimal control problems. The authors first define the iteration formula after which the obtained equations are discretized to prepare the numerical solution, contrarily to the accessible works in the literature having reverse order. The main idea is to approximate the cost functional with a second-order expansion in each iteration step, which is then extremized to get the subsequent approximation of the optimum. In the case of nonlinear optimal control problems, the process leads to a sequence of time-variant LQR problems. The proposed technique was effectively applied to the trajectory tracking control of a flexible RR manipulator. The case study showed that the initialization of the iteration is simple, and the convergence is rapid.
欠驱动机械系统轨迹跟踪控制的变分原理
随着软机器人和柔性机构的普及,机器人技术正经历着动态的发展。描述这些系统的力学模型是欠驱动的,具有比输入更多的自由度。欠驱动系统的轨迹跟踪控制并不简单。逆动力学的解在所有情况下都是不稳定的,因为它只考虑系统的实际状态。因此,采用最优控制理论是一个合理的选择。然而,这些方法的实时应用具有挑战性,因为离散优化问题的求解在数值上是昂贵的。本文提出了一种求解非线性最优控制问题的迭代方法。作者首先定义迭代公式,然后对得到的方程进行离散,得到数值解,这与文献中可获得的逆顺序相反。主要思想是在每个迭代步骤中用二阶展开来近似代价函数,然后对其极值以得到后续的最优逼近。对于非线性最优控制问题,该过程会导致一系列时变LQR问题。将该方法有效地应用于柔性RR机械臂的轨迹跟踪控制。实例分析表明,该方法初始化简单,收敛速度快。
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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