NDLI: Bifurcations of optimal solutions for coordinated robotic systems: Numerical and homotopy methods

Content Provider	IEEE Xplore Digital Library
Author	Baoyang Deng Valenzuela, A.K. Goodwine, B.
Copyright Year	2010
Description	Author affiliation: Faculty of of Aerospace and Mechanical Engineering, University of Notre Dame, IN 46556, USA (Baoyang Deng; Goodwine, B.) \|\| Department of Mechanical Engineering at the Massachusetts Institute of Technology, Cambridge, 02139, USA (Valenzuela, A.K.)
Abstract	This paper presents the relatively rich and interesting bifurcation structure that is present in the nature of optimal solutions to a multi-robot formation control problem. The problem considered is a two point nonlinear boundary-value problem that can only be solved numerically. Since common numerical solution techniques such as the shooting method are local in nature and hence are difficult to use to find multiple solutions, an alternative formulation of the problem is presented that can be solved through homotopy methods for polynomial systems. These methods are guaranteed to find all solutions within the resolution of the system description's discretization. Specifically, this paper studies a group of unicycle-like autonomous mobile robots operating in a 2-dimensional obstacle-free environment. Each robot has a predefined initial state and final state and the problem is to find the optimal path between two states for every robot. The path is optimized with respect to the control effort and the deviation from a desired formation. The bifurcation parameter is the relative weight given to penalizing the deviation from the desired formation versus control effort. It is shown that as this number varies, bifurcations of solutions are obtained. Considering the common use of optimization methods in robotic navigation and coordination problems, understanding the existence and structure of bifurcating and multiple solutions is of great importance in robotics.
Starting Page	4475
Ending Page	4480
File Size	977231
Page Count	6
File Format	PDF
ISBN	9781424450381
ISSN	10504729
DOI	10.1109/ROBOT.2010.5509735
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-05-03
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Bifurcation Robot kinematics Robotics and automation Optimal control Optimization methods Differential equations Eigenvalues and eigenfunctions USA Councils Control systems Polynomials
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Control and Systems Engineering Electrical and Electronic Engineering Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Bifurcations and symmetries of optimal solutions for distributed robotic systems

Visual vein-finding for robotic IV insertion

A family of quadratically-solvable 5-SP̲U parallel robots

Multi-robot pursuit-evasion without maps

Adaptation to robot failures and shape change in decentralized construction

Coordinated motion control of a robot arm and a positioning table with arrangement of multiple goals

From crystals to lattice robots

Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control

Explicit coordinated localization using common visual objects

Bifurcations of optimal solutions for coordinated robotic systems: Numerical and homotopy methods

Similar Documents

Bifurcations and symmetries of optimal solutions for distributed robotic systems

Visual vein-finding for robotic IV insertion

A family of quadratically-solvable 5-SP̲U parallel robots

Multi-robot pursuit-evasion without maps

Adaptation to robot failures and shape change in decentralized construction

Coordinated motion control of a robot arm and a positioning table with arrangement of multiple goals

From crystals to lattice robots

Symmetry-Breaking in Bifurcations of Optimal Solutions for Coordinated Nonholonomic Robotic Control

Explicit coordinated localization using common visual objects

Bifurcations of optimal solutions for coordinated robotic systems: Numerical and homotopy methods