Dynamic Output Controllers for Exponential Stabilization of Periodic Orbits for Multidomain Hybrid Models of Robotic Locomotion
Dynamic Output Controllers for Exponential Stabilization of Periodic Orbits for Multidomain Hybrid Models of Robotic Locomotion
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DOI：
10.1115/1.4044618
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发表时间：
2019-12-01
影响因子：
1.7
通讯作者：
Gregg, Robert D.
中科院分区：
文献类型：
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作者：
Hamed, Kaveh Akbari;Safaee, Bita;Gregg, Robert D.
本文的主要目标是开发一个分析框架，系统地设计动态输出反馈控制器，指数稳定的多域周期轨道的混合动力学模型的机器人运动。提出了一类参数化动态输出反馈控制器，使得（1）闭环系统诱导出一个多区域周期轨道，（2）该轨道在控制器参数变化时不变.研究了Poincare映射的性质，证明了Poincare映射在不动点附近的雅可比线性化具有三角形形式。这证明了混合周期轨道的非线性分离原理。然后，我们采用一个迭代算法的基础上的一系列优化问题，涉及双线性矩阵不等式调整控制器参数。给出了算法收敛到稳定参数的一组充分条件。研究了动态输出反馈控制下的全状态稳定性和模偏航稳定性。的分析方法的权力，最终证明通过设计一个非线性动态输出反馈控制器的三维（3D）人形机器人的步行与18个状态变量和325个控制器参数。
The primary goal of this paper is to develop an analytical framework to systematically design dynamic output feedback controllers that exponentially stabilize multidomain periodic orbits for hybrid dynamical models of robotic locomotion. We present a class of parameterized dynamic output feedback controllers such that (1) a multidomain periodic orbit is induced for the closed-loop system and (2) the orbit is invariant under the change of the controller parameters. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map around the fixed point takes a triangular form. This demonstrates the nonlinear separation principle for hybrid periodic orbits. We then employ an iterative algorithm based on a sequence of optimization problems involving bilinear matrix inequalities to tune the controller parameters. A set of sufficient conditions for the convergence of the algorithm to stabilizing parameters is presented. Full-state stability and stability modulo yaw under dynamic output feedback control are addressed. The power of the analytical approach is ultimately demonstrated through designing a nonlinear dynamic output feedback controller for walking of a three-dimensional (3D) humanoid robot with 18 state variables and 325 controller parameters.