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

利用凸优化直接计算李雅普诺夫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区域成为可能。 这些工具可以与随机运动规划算法相结合，以获得新的反馈运动规划算法，其概率覆盖有界可达状态空间与验证区域的稳定性，有效地构建一个全球反馈控制器的许多本地有效的控制器。如果成功的话，所提出的工作将产生一类算法，能够计算覆盖的非线性系统的反馈策略的维数超过动态规划。 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的陷阱的影响。 通过在规划过程中考虑反馈，所得到的计划是强大的干扰和实施真实的robots.Through这些算法的理论和实验验证，这项工作的目的是有广泛的影响，实验控制的非线性和欠驱动系统，包括步行机器人，飞行器和机器人的把握和操纵环境。 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进行传播。

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.