Time dependent control Lyapunov functions and hybrid zero dynamics for stable robotic locomotion
Time dependent control Lyapunov functions and hybrid zero dynamics for stable robotic locomotion
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时间相关控制李雅普诺夫函数和混合零动力学实现稳定的机器人运动
DOI：
10.1109/acc.2016.7525524
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Ames
中科院分区：
文献类型：
--
作者：
Shishir N Y Kolathaya;Ayonga Hereid;A. Ames
在复杂的机器人系统上实现基于状态的参数化周期轨迹，例如，类人机器人，由于动态运动加剧的传感器噪声，可能导致不稳定。作为理解这一现象的一种手段，并受到仿人机器人DURUS现场测试的启发，本文提出了混合周期轨道有界的充分条件（即，步行步态的有界性）的时间依赖控制李雅普诺夫函数。特别是，本文认为虚拟约束，产生混合零动态与期望的输出是一个函数的时间或状态为基础的相位变量。如果相变量和时间之间的差异是有界的，我们建立指数有界的零动态曲面。这些结果被推广到混合动力系统，建立混合周期轨道的指数有界性，即，我们表明，稳定的步行可以通过基于时间的实现基于状态的虚拟约束。这些结果都在仿真和实验中验证的双足人形机器人DURUS;它表明，基于时间的跟踪和基于状态的跟踪之间的紧密匹配可以实现，只要有一个紧密匹配的时间和相位之间的基于期望的输出轨迹。
Implementing state-based parameterized periodic trajectories on complex robotic systems, e.g., humanoid robots, can lead to instability due to sensor noise exacerbated by dynamic movements. As a means of understanding this phenomenon, and motivated by field testing on the humanoid robot DURUS, this paper presents sufficient conditions for the boundedness of hybrid periodic orbits (i.e., boundedness of walking gaits) for time dependent control Lyapunov functions. In particular, this paper considers virtual constraints that yield hybrid zero dynamics with desired outputs that are a function of time or a state-based phase variable. If the difference between the phase variable and time is bounded, we establish exponential boundedness to the zero dynamics surface. These results are extended to hybrid dynamical systems, establishing exponential boundedness of hybrid periodic orbits, i.e., we show that stable walking can be achieved through time-based implementations of state-based virtual constraints. These results are verified on the bipedal humanoid robot DURUS both in simulation and experimentally; it is demonstrated that a close match between time based tracking and state based tracking can be achieved as long as there is a close match between the time and phase based desired output trajectories.