Dynamical uncontrolled manifolds on manipulators
Robotic manipulator arms are ubiquitous in modern manufacturing industries. Attempts to improve their task - equivalent stability has led robotics engineers to the neuro-biological concept of uncontrolled manifolds (UCMs). However, this concept only extends as far as static poses. This study attempt...
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| Format: | Final Year Project (FYP) |
| Language: | English |
| Published: |
2019
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| Online Access: | http://hdl.handle.net/10356/77125 |
| _version_ | 1826128779748048896 |
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| author | Yeo, Zhan Fei |
| author2 | Andrew James Kricker |
| author_facet | Andrew James Kricker Yeo, Zhan Fei |
| author_sort | Yeo, Zhan Fei |
| collection | NTU |
| description | Robotic manipulator arms are ubiquitous in modern manufacturing industries. Attempts to improve their task - equivalent stability has led robotics engineers to the neuro-biological concept of uncontrolled manifolds (UCMs). However, this concept only extends as far as static poses. This study attempts to generalise the notion of UCMs into their natural dynamical analogues. The structure and dimension of equivalent inputs to a Hamiltonian system for a given outcome was determined. For arbitrary Riemannian manifolds, a generalised version of PCA that works on any inner product space was derived to obtain a local linear estimate of the Hamiltonian system's inputs with simulation. The Sasaki Metric was then independently derived to determine a natural choice for this inner product. The torsionless connection is then studied as a choice to base the Sasaki Metric on. It remains to develop push-forward maps on tangent bundles to pull this Hamiltonian input manifold back into a dynamical UCM on the manipulator configuration tangent bundle. A simulation on the flat space TR3 was conducted to challenge the validity of the first theoretical statement, with favourable results. Additionally, the potential effectiveness of using a dynamical UCM method towards a throwing task was demonstrated. |
| first_indexed | 2024-10-01T07:30:29Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/77125 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:30:29Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | ntu-10356/771252023-02-28T23:17:38Z Dynamical uncontrolled manifolds on manipulators Yeo, Zhan Fei Andrew James Kricker School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Geometry DRNTU::Science::Physics::Descriptive and experimental mechanics Robotic manipulator arms are ubiquitous in modern manufacturing industries. Attempts to improve their task - equivalent stability has led robotics engineers to the neuro-biological concept of uncontrolled manifolds (UCMs). However, this concept only extends as far as static poses. This study attempts to generalise the notion of UCMs into their natural dynamical analogues. The structure and dimension of equivalent inputs to a Hamiltonian system for a given outcome was determined. For arbitrary Riemannian manifolds, a generalised version of PCA that works on any inner product space was derived to obtain a local linear estimate of the Hamiltonian system's inputs with simulation. The Sasaki Metric was then independently derived to determine a natural choice for this inner product. The torsionless connection is then studied as a choice to base the Sasaki Metric on. It remains to develop push-forward maps on tangent bundles to pull this Hamiltonian input manifold back into a dynamical UCM on the manipulator configuration tangent bundle. A simulation on the flat space TR3 was conducted to challenge the validity of the first theoretical statement, with favourable results. Additionally, the potential effectiveness of using a dynamical UCM method towards a throwing task was demonstrated. Bachelor of Science in Physics 2019-05-09T07:17:45Z 2019-05-09T07:17:45Z 2019 Final Year Project (FYP) http://hdl.handle.net/10356/77125 en 112 p. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Geometry DRNTU::Science::Physics::Descriptive and experimental mechanics Yeo, Zhan Fei Dynamical uncontrolled manifolds on manipulators |
| title | Dynamical uncontrolled manifolds on manipulators |
| title_full | Dynamical uncontrolled manifolds on manipulators |
| title_fullStr | Dynamical uncontrolled manifolds on manipulators |
| title_full_unstemmed | Dynamical uncontrolled manifolds on manipulators |
| title_short | Dynamical uncontrolled manifolds on manipulators |
| title_sort | dynamical uncontrolled manifolds on manipulators |
| topic | DRNTU::Science::Mathematics::Geometry DRNTU::Science::Physics::Descriptive and experimental mechanics |
| url | http://hdl.handle.net/10356/77125 |
| work_keys_str_mv | AT yeozhanfei dynamicaluncontrolledmanifoldsonmanipulators |