Feedback synthesis for underactuated systems using sequential second-order needle variations
Feedback synthesis for underactuated systems using sequential second-order needle variations
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DOI：
10.1177/0278364918776083
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Giorgos Mamakoukas;M. A. MacIver;T. Murphey
中科院分区：
文献类型：
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作者：
Giorgos Mamakoukas;M. A. MacIver;T. Murphey
本文利用最优控制的二阶作用，即最优控制的二阶针形变量，推导出一般控制仿射系统的非线性反馈控制综合，作为选择当前状态的各种控制响应的基础。本文的第二个结果是，该方法通过二阶针形变化对矢量场之间的李括号的显式依赖，可证明地利用了系统的非线性能控性。因此，当系统是一阶李括号非线性可控时，每个控制决策必然降低目标。采用差动驱动小车、三维欠驱动运动学机器人和水下机器人欠驱动动力学模型的仿真结果表明，当一阶分析奇异时，该方法可以得到控制解。最后，即使在速度场存在的情况下，欠驱动动态水下航行器模型也表现出了收敛。
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions, the second-order needle variations of optimal control, as the basis for choosing each control response to the current state. A second result of this paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Finally, the underactuated dynamic underwater vehicle model demonstrates convergence even in the presence of a velocity field.