RI: Small: Randomized Feedback Motion Planning with Computational Lyapunov Certificates

利用凸优化方法直接计算Lyapunov函数的最新进展使得有效地估计光滑非线性系统的局部稳定区域成为可能。这些工具可以与随机化的运动规划算法相结合，获得新的反馈运动规划算法，该算法概率地覆盖具有验证稳定区域的有界可达状态空间；有效地从许多局部有效控制器中构造全局反馈控制器。如果成功，所提出的工作将产生一类能够计算非线性系统的覆盖反馈策略的算法，其维度超过了动态规划的维度。此外，算法直接在连续的状态和动作空间上操作，因此不会受到离散化陷阱的影响。通过对这些算法的理论和实验验证，本工作旨在对包括步行机器人、飞行器和抓取和操纵环境的机器人在内的非线性和欠驱动系统的实验控制产生广泛的影响。算法和机器人实验将被整合到PI的机器人研究生课程和推广活动中，并将通过软件分发来传播算法。

Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate local regions of stability for smooth nonlinear systems. These tools can be combined with randomized motion planning algorithms to obtain new feedback motion planning algorithms which probabilistically cover a bounded reachable state-space with verified regions of stability; efficiently constructing a global feedback controller out of many locally valid controllers. If successful, the proposed work will generate a class of algorithms capable of computing covering feedback policies for nonlinear systems with dimensionality beyond that of dynamic programming. In addition, the algorithms operate directly on the continuous state and action spaces, and thus are not subject to the pitfalls of discretization. By considering feedback during the planning process, the resulting plans are robust to disturbances and quite suitable for implementation on real robots.Through both theoretical and experimental validation of these algorithms, this work aims to have broad impact on the experimental control of nonlinear and underactuated systems, including walking robots, aerial vehicles, and robots which grasp and manipulate the environment. The algorithms and robotic experiments will be integrated in the PI's graduate robotics curriculum and outreach activities, and the algorithms will be disseminated through a software distribution.