טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKhmelniker Polina
SubjectInvestigation of Mobile Robot Time Optimal Trajectories
Under State Dependent Constraints
DepartmentDepartment of Aerospace Engineering
Supervisors Professor Yoseph Ben-Asher
Professor Elon Rimon


Abstract

This thesis studies a time optimization problem of an autonomous mobile robot moving in a planar environment containing a single polygonal obstacle. The robot is subjected to state-dependent constraints and should strive to prevent an inevitable collusion with the obstacle. That is, a safety constraint. Moreover, the mobile robot is subject to a constraint on its minimal turning radius.  While being subjected to these constraints, the robot's goal is to navigate along a minimum time path from a given start point with a specific initial heading angle to a target point, which can be of two types. The thesis is divided into two problems according to the target type: the docking problem where the target is placed on the edge of the obstacle (main consideration of this thesis), and the non-docking problem where the target is arbitrary placed with a given heading direction (secondary problem of this thesis).


The research process dealt with mapping the environment of the mobile robot into heading dependent regions that describe different influence areas of the obstacle (wall or corner subjected regions), or areas outside the influence of the obstacle. For every region, the proper safety distances is being constructed and computed, and the Euler-Lagrange equation which captures the time optimal path is examined. Moreover, known terms from the robot navigation literature as the Voronoi curve are adapted and extended in order to serve the purpose of this work.


The unique form of the safety distance defined in this work allows a greater braking distance in relation to a previous work regarding a uniform safety constraint. Hence, allowing a faster movement of the mobile robot, this contributes to shorten the overall travel time under safety constraints. The whole problem is solved by establishing two search algorithms (for the docking and the non-docking problems), which are tested on simulation examples. This thesis establishes analytical and numerical analysis of the optimization process through examples and simulation results.