Geometric Recursive Dynamic Modelling and Simulation of Soft Robotic Systems
Bibliographic record
Abstract
This thesis studies the dynamics of soft robotic systems modelled as rigid-flexible multi-body systems.A numerical framework is developed to capture finite deformations including extension, shear, bending and torsion of a dynamic 1-Dimensional (1D) flexible body on the Special Euclidean group SE(3) based on Cosserat rod theory.The governing parameterization-free equations are expressed as a set of Partial Differential Equations (PDEs) on the SE( 3).An implicit differentiation method semidiscretizes the time derivatives on the Lie algebra of SE(3) to convert the PDEs to a set of Ordinary Differential Equations (ODEs) in the arc-length of the continuum.The novelty of this work is the implementation of a finite difference solution on SE(3) along with a higher-order Runge-Kutta-Munthe-Kaas geometric integrator employed to spatially propagate the configuration of the rod.The resulting solution is a dynamic model of the flexible body that is parameterization-free, computationally inexpensive and can be used in real-time applications.A recursive parameterization-free formulation for the forward and inverse dynamics of multi-body systems is expressed on the SE(3), using the previously developed model for flexible bodies.The system is composed of bodies serially connected with single degree of freedom actuated joints from a fixed base.The Newton-Euler equation of motion for a rigid body and a set of PDEs for a dynamic Cosserat rod are coupled to recursively formulate the dynamics of multi-body systems.The joint kinematics is captured through the exponential map of the SE(3).The inverse dynamics algorithm recursively determines the system response and the joint torques needed to follow a given joint space trajectory, while the forward dynamics algorithm determines the system's motion given joint torques.A shooting-method-based Boundary Condition (BC) solver is developed to solve for the BCs in the set of PDEs and implement a finite difference solution.This study can be implemented to develop joint-space computed-torque control strategies.Recent geometric methods for rigid-flexible multi-body dynamics often use shape This thesis is submitted under only my name but the hardest part of this endeavor, keeping me motivated, was done by everyone but me.Any progress that I have made, and more that I will, is from the guidance of my professors with a special gratitude for Prof. Chhabra, Benavides, Gerrick and Hill.As with solving any problem, running into challenges was inevitable; and in such times working on this thesis, I have relied on my friends Dana, Paige, Wissam, Marana, Harry and Zach to remind me what it means to love learning.More often than not, I have sustained an unhealthy fixation on my studies.So I am grateful to my colleagues Reza, Vaughn, Aman, Ini, Kamala and Sara for taking better care of me than I did of myself and my homies Elias, Hassan and Arafain for telling me when it's time to go home.But no night could end nor sleep subsist without my ma or sisters wishing me goodnight.With the support from these people, and many more, I only had to worry about the easy parts of this endeavor; solving some problems and writing about it.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".