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    % Full thesis title (and subtitle if any)
    {\LARGE\bfseries Bioinspired Agile Robotic Jumping and Balancing\par}

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    % Full name (including all middle names if any)
    {\Large\bfseries Jingcheng Sun\par}

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    {\large Submitted in accordance with the requirements for the degree of\par}
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    {\large Doctor of Philosophy\par}

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    {\large The University of Leeds\par}
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    {\large School of Mechanical Engineering\par}

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    {\large August 2025\par}

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\section*{Intellectual Property and Publication Statements}

\noindent I confirm that the work submitted is my own, except where work which has formed part of jointly authored publications has been included. My contribution and the other authors to this work has been explicitly indicated below. I confirm that appropriate credit has been given within the thesis where reference has been made to the work of others.

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\noindent\textbf{Chapters based on jointly authored publications}

\begin{itemize}
    \item \textbf{Chapter 3} is based on: Sun, Jingcheng, and Chengxu Zhou. ``AeroTail: a bio-inspired aerodynamic tail mechanism for robotic balancing.'' In \textit{2023 28th International Conference on Automation and Computing (ICAC)}, pp.~1--6. IEEE, 2023.
    \item \textbf{Chapter 4} is based on: Sun, Jingcheng, and Chengxu Zhou. ``Optimising aerodynamic drag for enhanced robotic balancing.'' \textit{Engineering Applications of Computational Fluid Mechanics} 18, no.~1 (2024): 2430659.
    \item \textbf{Chapter 5} is based on: Sun, Jingcheng, and Chengxu Zhou. ``Advancing Robotic Jumping with CVT Enhanced SEA.'' In \textit{Annual Conference Towards Autonomous Robotic Systems}, pp.~73--84. Cham: Springer Nature Switzerland, 2024.
\end{itemize}

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\noindent\textbf{Work attributable to me}

\begin{itemize}
    \item Concept development, modelling and derivation, controller design, simulation studies, optimisation, data analysis, figure preparation, manuscript drafting.
\end{itemize}

\vspace{0.75em}

\noindent\textbf{Contributions of other authors}

\begin{itemize}
    \item Supervision, methodological guidance, critical review, editorial feedback.
\end{itemize}

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\noindent This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement.

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\noindent The right of Jingcheng Sun to be identified as Author of this work has been asserted by Jingcheng Sun in accordance with the Copyright, Designs and Patents Act 1988.


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\begin{abstract}

Agile locomotion in legged robots requires the coordinated generation, storage, and regulation of energy under highly nonlinear and hybrid dynamics. Inspired by biological systems that exploit compliant structures and aerodynamic appendages, this thesis presents the design, modelling, and control of a bioinspired monopedal robotic platform capable of agile jumping and balancing through the integration of two key mechanical innovations: a Continuously Variable Transmission–enhanced Series Elastic Actuator (C-SEA) for vertical propulsion, and an AeroTail drag-based balancing mechanism for attitude regulation in flight.

The C-SEA leg incorporates a non-circular gear-based continuously variable transmission within a series elastic architecture to modulate effective mechanical advantage throughout the jump cycle. This enables improved energy transfer, controllable stiffness characteristics, and enhanced jumping performance compared to conventional SEA configurations. The AeroTail introduces a bioinspired drag-inducing appendage that generates aerodynamic torque proportional to rotational velocity, providing passive and actively regulated stabilisation during flight without reliance on high-inertia reaction wheels.

A unified dynamic model of the hybrid flight–stance system is developed, capturing the coupling between aerodynamic torques, compliant leg actuation, and underactuated body dynamics. Control strategies are formulated to regulate attitude and forward velocity through coordinated stance impulse shaping and flight-phase drag modulation. Stability is analysed using both linearised subspace representations and jump-to-jump variability metrics.

Simulation studies demonstrate sustained forward hopping with stable attitude regulation and highlight the importance of coupling between drag magnitude and feedback gain selection. A Monte Carlo sensitivity analysis further reveals that the closed-loop system exhibits a finite yet substantial region of attraction under bounded parameter uncertainty, consistent with the behaviour of nonlinear hybrid systems.

The results establish that combining compliant energy storage with aerodynamic drag-based balancing provides an effective embodied intelligence strategy for agile robotic locomotion. The proposed framework offers a pathway toward energy-efficient, mechanically adaptive jumping robots and contributes to the broader understanding of bioinspired actuation and hybrid dynamic stability.

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\tableofcontents
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\chapter*{Notation and Acronyms} 
\label{chap_not}
\input{Chapters/Notation and Acronyms}


\chapter{Introduction} \label{chap_intro}
\input{Chapters/1.Introduction}


\chapter{Literature Review} \label{chap_lit}
\input{Chapters/2.Literature review}


\chapter{AeroTail: the Utilisation of Aerodynamic Drag in Robotic Balancing} \label{chap_balance}
\input{Chapters/3.Balancing mechanism}


\chapter{Optimisation Study of the Drag-Inducers} \label{chap_di}
\input{Chapters/4.Balancing mechanism optimisation study}


\chapter{CVT enhanced series-elastic jumping} \label{chap_jump}
\input{Chapters/5.Jumping mechanism}


\chapter{AeroTail Enhanced C-SEA Jumping Robot} \label{chap_robot}
\input{Chapters/6.AeroTail enhanced C-SEA jumping robot}

\chapter{Conclusion}
\label{chap_conclusion}
\input{Chapters/7.Conclusion}


\bibliographystyle{ieeetr}
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\appendix

\chapter{Supplementary figures} \label{app_supp}
\input{Chapters/9.Supplementary materials}


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