Robot motion planning via curve shortening flows

Fan, Yinai

Permalink

https://hdl.handle.net/2142/113836 Copy

Description

Title

Robot motion planning via curve shortening flows

Author(s)

Fan, Yinai

Issue Date

2021-11-16

Director of Research (if dissertation) or Advisor (if thesis)

Belabbas, Mohamed-Ali

Doctoral Committee Chair(s)

Mehta, Prashant

Committee Member(s)

• Dullerud, Geir Eirik
• Liberzon, Daniel

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• motion planning
• optimal control
• trajectory optimization
• nonlinear dynamical systems
• geometric control
• nonholonomic constraints

Abstract

This work will present a series of developments of geometric heat flow method in robot motion planning and estimation. The key of geometric heat flow is to formulate the motion planning problem into a curve shortening problem. By solving the geometric heat flow, an arbitrary initial curve can be deformed to a curve of minimal length, which corresponds to a feasible motion. Preliminary theories and algorithms for motion planning based on geometric heat flow have been developed for driftless control affine systems. The main contribution of this research is to extend the algorithm to robotic systems, which are dynamic systems with drifts and different types of constraint. Early stages of the research focus on adapting the algorithm to solve motion planning problems for systems with drift. To tackle systems with drift, actuated curve length and affine geometric heat flow is proposed. The method is then enriched to solve robot gymnastics motion planning, in which the effect of state constraints is encoded into curve length. Free boundary conditions are also studied to enforce the conservation of the robot's momentum. The second stage of the research focus on the construction of the geometric heat flow framework for robot locomotion planning, which involves hybrid dynamics due to contact. The activation and deactivation of phase-dependent constraints are controlled by activation functions. Lastly, to solve 3D problems in robotics, planning and estimation in SO(3) space is formulated using the geometric heat flow method.

Graduation Semester

2021-12

Type of Resource

Thesis

Permalink

http://hdl.handle.net/2142/113836

Copyright and License Information

Copyright 2021 Yinai Fan

Owning Collections