Tesi etd-10312025-114245
Link copiato negli appunti
Tipo di tesi
Dottorato
Autore
SETTI, ELISA
URN
etd-10312025-114245
Titolo
Hybrid Kinematic Modeling for Continuum Soft Arms: Combining Analytical and Data-Driven Approaches
Settore scientifico disciplinare
ING-IND/34
Corso di studi
Istituto di Biorobotica - PHD IN BIOROBOTICA
Relatori
relatore Prof. FALOTICO, EGIDIO
Parole chiave
- Hybrid Modeling
- Continuum Soft Arm
- Geometrical model
- Differential Inverse Kinematics
- Bio-inspired robotics
Data inizio appello
15/06/2026;
Disponibilità
parziale
Riassunto analitico
The effective deployment of continuum soft arms in real-world applications fundamentally depends on accurate, computationally efficient, and generalizable models. However, developing such models presents a persistent dilemma: analytical approaches offer interpretability and efficiency but rely on simplifying assumptions that limit accuracy, while data-driven methods capture complex behaviors but lack physical grounding and require extensive training data. This thesis demonstrates that hybrid approaches—synergizing analytical structure with data-driven adaptation—provide a promising path forward for continuum soft arm modeling.
The first contribution addresses forward kinematics through the Piecewise Helix Parametrization (PHP), a geometric model that explicitly incorporates curvature, torsion, and arc length as primitive deformation parameters. Prevalent geometric models, such as PCC neglect torsion entirely, while torsion-aware CRT-based formulations achieve high accuracy at the cost of substantial computational overhead. PHP addresses this gap by treating torsion as a primitive deformation mode within a closed-form geometric framework. Two complementary identification methodologies enable parameter extraction from experimental data: an analytical approach providing closed-form solutions and an optimal method formulating identification as constrained optimization. Systematic validation on a tendon-driven soft robotic platform demonstrates that PHP achieves competitive accuracy compared to state-of-the-art models while using fewer segments and maintaining computational tractability.
The generality of the PHP framework is further validated by its application to biological continuum structures, conducted within the EU Horizon 2020 PROBOSCIS project. This preliminary study applies the PHP model to motion capture data from elephant trunk reaching movements, providing what is, to the best of our knowledge, the first quantitative characterization of three-dimensional trunk kinematics with torsion resolved as a primitive parameter alongside curvature and elongation. The analysis reveals stereotypical coordination principles—including distal-dominant deformation organization, torsion as distributed orientation control, and multi-mode coupling as the default strategy—that validate the model's applicability beyond engineered systems and establish a concrete foundation for future bioinspired soft robot control strategies.
The third contribution develops hybrid differential inverse kinematic methods that leverage the analytical PHP-based Jacobian while incorporating learned corrections from trajectory data collected on the physical robot. Three progressively sophisticated models are introduced: learning a configuration-independent weight matrix for the weighted pseudoinverse, learning configuration-dependent nullspace corrections that exploit kinematic redundancy, and combining both components. The methods are evaluated on real robot data with ground truth configurations extracted via PHP fitting; closed-loop hardware validation remains a direction for future work. Systematic evaluation reveals a fundamental trade-off between end-effector tracking accuracy and configuration parameter accuracy. The combined hybrid approach achieves superior tracking performance compared to the unweighted analytical baseline and the pure data-driven method, while maintaining better interpretability and naturally smooth configuration trajectories. The results establish that proper parameter scaling is essential—identity weighting produces catastrophic failure—and that hybrid approaches combining analytical structure with learned corrections outperform purely data-driven methods in task-space tracking while retaining physical interpretability.
Together, these contributions establish that hybrid modeling offers systematic advantages for continuum soft arm kinematics, providing a foundation for advanced control architectures that balance accuracy, interpretability, and computational efficiency.
The first contribution addresses forward kinematics through the Piecewise Helix Parametrization (PHP), a geometric model that explicitly incorporates curvature, torsion, and arc length as primitive deformation parameters. Prevalent geometric models, such as PCC neglect torsion entirely, while torsion-aware CRT-based formulations achieve high accuracy at the cost of substantial computational overhead. PHP addresses this gap by treating torsion as a primitive deformation mode within a closed-form geometric framework. Two complementary identification methodologies enable parameter extraction from experimental data: an analytical approach providing closed-form solutions and an optimal method formulating identification as constrained optimization. Systematic validation on a tendon-driven soft robotic platform demonstrates that PHP achieves competitive accuracy compared to state-of-the-art models while using fewer segments and maintaining computational tractability.
The generality of the PHP framework is further validated by its application to biological continuum structures, conducted within the EU Horizon 2020 PROBOSCIS project. This preliminary study applies the PHP model to motion capture data from elephant trunk reaching movements, providing what is, to the best of our knowledge, the first quantitative characterization of three-dimensional trunk kinematics with torsion resolved as a primitive parameter alongside curvature and elongation. The analysis reveals stereotypical coordination principles—including distal-dominant deformation organization, torsion as distributed orientation control, and multi-mode coupling as the default strategy—that validate the model's applicability beyond engineered systems and establish a concrete foundation for future bioinspired soft robot control strategies.
The third contribution develops hybrid differential inverse kinematic methods that leverage the analytical PHP-based Jacobian while incorporating learned corrections from trajectory data collected on the physical robot. Three progressively sophisticated models are introduced: learning a configuration-independent weight matrix for the weighted pseudoinverse, learning configuration-dependent nullspace corrections that exploit kinematic redundancy, and combining both components. The methods are evaluated on real robot data with ground truth configurations extracted via PHP fitting; closed-loop hardware validation remains a direction for future work. Systematic evaluation reveals a fundamental trade-off between end-effector tracking accuracy and configuration parameter accuracy. The combined hybrid approach achieves superior tracking performance compared to the unweighted analytical baseline and the pure data-driven method, while maintaining better interpretability and naturally smooth configuration trajectories. The results establish that proper parameter scaling is essential—identity weighting produces catastrophic failure—and that hybrid approaches combining analytical structure with learned corrections outperform purely data-driven methods in task-space tracking while retaining physical interpretability.
Together, these contributions establish that hybrid modeling offers systematic advantages for continuum soft arm kinematics, providing a foundation for advanced control architectures that balance accuracy, interpretability, and computational efficiency.
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