Fast numerical algorithms for optimal robot motion planning

Optimal Motion Planning;Hamilton-Jacobi-Bellman;Numerical methods;Fast Marching Method;Simplicial Discretization;Simplicial Dijkstra Algorithm;Simplicial A* Algorithm;Simplicial Label Correcting Algorithm;Simplicial Value Iteration Algorithm;Simplicial Policy Iteration Algorithm;Mobile Robots;Robotics;Control;Optimal Control;Feedback Control;Obstacles;Shortest Path Problem;Weighted Region Problem;Differential Constraints;Nonholonomic Constraints;Stochastic Control;Stochastic Shortest Path Problem;Nearby Deterministic System;Turing Decidability;Turing Semidecidability;Sampling Metric Spaces;Resolution Completeness

Yershov, Dmytro

关键词: Optimal Motion Planning;    Hamilton-Jacobi-Bellman;    Numerical methods;    Fast Marching Method;    Simplicial Discretization;    Simplicial Dijkstra Algorithm;    Simplicial A* Algorithm;    Simplicial Label Correcting Algorithm;    Simplicial Value Iteration Algorithm;    Simplicial Policy Iteration Algorithm;    Mobile Robots;    Robotics;    Control;    Optimal Control;    Feedback Control;    Obstacles;    Shortest Path Problem;    Weighted Region Problem;    Differential Constraints;    Nonholonomic Constraints;    Stochastic Control;    Stochastic Shortest Path Problem;    Nearby Deterministic System;    Turing Decidability;    Turing Semidecidability;    Sampling Metric Spaces;    Resolution Completeness;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/46659/Dmytro_Yershov.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Optimization of high-level autonomous tasks requires solving the optimal motion planning problem for a mobile robot. For example, to reach the desired destination on time, a self-driving car must quickly navigate streets and avoid hazardous obstacles such as buildings or other cars, as well as provide safety for pedestrians. Our approach to solve the optimal planning problem is to use the optimal control formalism borrowed from the control theory. In this setting, safety constraints for either a robot or its surroundings are defined as obstacles, which are penalized using infinite cost to guarantee that tasks are performed safely. Unlike in control theory, the complexity of real-world tasks in addition with safety constraints prohibit finding an analytic solution to the optimal motion planning problem. Hence, the application of numerical algorithms is necessary. In this thesis, we demonstrate that solutions to a general motion planning problem are computable, which permits the use of numerical algorithms to solve this problem. Moreover, we propose a numerical discretization of a general optimal motion planning problem and prove that this discretization is accurate. Numerical algorithms that use the proposed discretization are applied to several realistic motion planning problems. Using these algorithms, we demonstrate the practicality of the proposed numerical approach. In addition, we extend our consideration beyond the classical deterministic models of motion and apply the proposed numerical algorithms to solve a stochastic optimal motion planning problem.