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UBC Theses and Dissertations
Determination of robot trajectories satisfying joint limit and interference constraints using an optimization method Buchal, Ralph Oliver
Abstract
An important problem in robotics research is the automatic off-line planning of optimal robot trajectories to perform specified tasks while satisfying physical constraints. This thesis proposes a method for finding an optimal geometric robot trajectory subject to the constraints of joint displacement limits and interference avoidance. A geometric method for calculating the distance between convex polyhedra is presented, and the method is implemented in two dimensions for the calculation of interference. Point-to-point trajectory planning is posed as a two-point boundary value problem in the calculus of variations. The kinematic constraints are formulated as exterior penalty functions and are combined with other optimization criteria to form a cost functional. The problem is solved by discretizing the problem and numerically minimizing the cost functional by using a steepest-descent approach to iteratively modify the trajectory. Any starting trajectory which satisfies the boundary conditions is acceptable, but different starting trajectories may converge to different locally optimal final trajectories. The method has been implemented for the two-dimensional case by an interactive FORTRAN program running on a VAX 11/750 computer. Successful results were obtained for a number of test cases, and further work has been identified to allow application of the method to a wide range of problems.
Item Metadata
Title |
Determination of robot trajectories satisfying joint limit and interference constraints using an optimization method
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1987
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Description |
An important problem in robotics research is the automatic off-line planning of optimal robot trajectories to perform specified tasks while satisfying physical constraints.
This thesis proposes a method for finding an optimal geometric robot trajectory subject to the constraints of joint displacement limits and interference avoidance. A geometric method for calculating the distance between convex polyhedra is presented, and the method is implemented in two dimensions for the calculation of interference. Point-to-point trajectory planning is posed as a two-point boundary value problem in the calculus of variations. The kinematic constraints are formulated as exterior penalty functions and are combined with other optimization criteria to form a cost functional. The problem is solved by discretizing the problem and numerically minimizing the cost functional by using a steepest-descent approach to iteratively modify the trajectory. Any starting trajectory which satisfies the boundary conditions is acceptable, but different starting trajectories may converge to different locally optimal final trajectories.
The method has been implemented for the two-dimensional case by an interactive FORTRAN program running on a VAX 11/750 computer. Successful results were obtained for a number of test cases, and further work has been identified to allow application of the method to a wide range of problems.
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Language |
eng
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Date Available |
2010-07-27
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0097137
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Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.