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

利用凸优化直接计算Lyapunov函数的最新进展使得有效地评估光滑非线性系统的局部稳定性成为可能。这些工具可以与随机运动规划算法相结合，获得新的反馈运动规划算法，该算法在概率上覆盖有界可达状态空间，并具有经过验证的稳定区域；从许多局部有效的控制器中高效地构造一个全局反馈控制器。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反馈策略的算法，其维数超过动态规划。此外，该算法直接在连续状态和动作空间上运行，因此不会受到离散化的陷阱的影响。通过在规划过程中考虑反馈，得到的规划对干扰具有鲁棒性，非常适合在真实机器人上实现。通过对这些算法的理论和实验验证，本工作旨在对非线性和欠驱动系统的实验控制产生广泛的影响，包括步行机器人、飞行器和掌握和操纵环境的机器人。算法和机器人实验将被整合到PI的研究生机器人课程和推广活动中，算法将通过软件分发。

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.