Dynamical uncontrolled manifolds on manipulators

• Main Author: Yeo, Zhan Fei
• Other Authors: Andrew James Kricker
• Format: Final Year Project
• Language: English
• Published: 2019
• Subjects: DRNTU::Science::Mathematics::Geometry; DRNTU::Science::Physics::Descriptive and experimental mechanics
• Online Access: http://hdl.handle.net/10356/77125
• Institution: Nanyang Technological University

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.