\chapter{General Introduction}
\label{c1}

In the multifaceted world of robotics, engineers and researchers face a crucial challenge: 

\vspace{0.6cm}
\begin{center}
\textbf{To develop a robust and efficient locomotion system for humanoid robots, enabling them to seamlessly navigate and adapt to the intricate and ever-evolving nature of complex environments.}
\end{center}
\vspace{0.6cm}
These robots, designed to mimic the human form, strive to replicate our remarkable abilities for movement and adaptability. However, achieving a robotic equivalent of human locomotion is a complex task, requiring advanced technical knowledge, innovative design approaches, and the application of robust mathematical models \parencite{kajita2014introduction,vukobratovic2004zero}.

The ability for a robot to adapt dynamically to a variety of terrains and situations is a critical capability. Just as humans do, humanoid robots need to adjust their locomotion patterns to navigate different ground surfaces and overcome obstacles. This challenge becomes even more significant considering the diverse tasks humanoid robots are assigned to, ranging from assisting the elderly in their homes to aiding in disaster recovery missions or exploring uncharted environments on Earth or even beyond \parencite{Xie_2020}.

At the heart of addressing this challenge lies the understanding and leverage of ground-foot reaction forces, the forces exerted by the ground on the robot's foot during locomotion. As humans, we instinctively adjust our walking pattern based on these forces, enabling us to traverse surfaces such as sand or ice with equal ease. By obtaining a detailed understanding of these forces within the context of humanoid robots, it is possible to design advanced control algorithms that can dynamically adjust the robot's walking pattern in real-time.

In the pursuit of this understanding, machine learning plays a significant role. By employing machine learning algorithms, robots extract meaningful information from sensory data, including visual images, depth maps, and force/torque measurements. This data-driven approach allows robots to perceive and interpret subtle nuances in their environment, enabling them to uncover patterns and correlations that contribute to stable walking patterns. By harnessing this knowledge, it becomes possible to design or refine advanced control algorithms that can dynamically adapt the robot's walking pattern in real-time, utilizing the insights gained from the ground-foot reaction forces.

In the context of the broader challenge, this PhD thesis research undertakes a specific challenge, namely:

\vspace{0.6cm}
\begin{center}
\textbf{Enhancing Bipedal Locomotion on Slippery Environments.}
\end{center}
\vspace{0.6cm}

Navigating and adapting to slippery surfaces present unique difficulties for humanoid robots, requiring specialized control strategies and mechanisms to maintain stability and ensure efficient locomotion. The objective of this research is to explore innovative approaches and techniques that can enhance the ability of humanoid robots to traverse and maneuver on slippery terrains, contributing to advancements in the field of bipedal locomotion. Figure \ref{fig:00001} visually encapsulates the essence of this research objective. It illustrates the challenge faced by the humanoid robot as it struggles to maintain a straight path on increasingly slippery surfaces. Furthermore, this slipperiness poses a significant risk of causing the robot to fall, underscoring the critical importance of addressing this issue.

\begin{figure}[h!]
\includegraphics[width=\textwidth]{tex/contents/fig/c1/test.png}
\vspace*{8pt}
\caption[Illustration depicting a humanoid robot's locomotion on various surfaces with progressively reduced coefficients of friction]{Illustration depicting a humanoid robot's locomotion on various surfaces with progressively reduced coefficients of friction, without slip control and with control. The performance can be assessed by measuring the deviation from the path's mid-line across the four experiments. In the first three without control, noticeable path deviations are evident, while in the fourth, where control is incorporated, deviations are negligible.}
\label{fig:00001}
\end{figure}


\section{Hypotheses and Approach}

To address this challenge, this research proposes three interconnected hypotheses, each posing a specific question:

\begin{itemize}
\item \textbf{Hypothesis 1:} Can we create a wearable, sensor-equipped shoe for humanoid robots that unobtrusively measures \gls{grf}, exhibits universal adaptability across different robot designs, and can be seamlessly integrated without compromising the robot's locomotion?
\item\textbf{Hypothesis 2:} Can we utilize machine learning techniques to effectively distinguish between various types of slippery surfaces, leveraging the normal and tangential \gls{grf} data obtained from the wearable, sensor-equipped shoe proposed in Hypothesis 1?
\item \textbf{Hypothesis 3:} Can we enhance the robot's control system by utilizing the floor-type classification obtained through machine learning techniques, bolstering the walking performance and ensuring the robot adheres to a specified trajectory, regardless of the slipperiness of the ground?
\end{itemize}

Each hypothesis builds upon the previous one, forming a comprehensive research framework (as depicted in Figure \ref{fig:0}) that addresses the intricacies of humanoid locomotion and adaptability on slippery floors. Through the exploration of these hypotheses, this research endeavours to deepen our understanding and equip humanoid robots with the capability to attain stable walking patterns while maximizing efficiency.

\begin{figure}[h!]
\includegraphics[width=\textwidth]{tex/contents/fig/c1/Test_3H.png}
\vspace*{8pt}
\caption{Schematic illustration of the research framework for enhancing humanoid robot locomotion on slippery surfaces.}
\label{fig:0}
\end{figure}

To achieve these objectives, the research will involve a rigorous analysis of scientific papers to identify existing knowledge and gaps in the field. The construction of a wearable system will be undertaken to unobtrusively measure total ground reaction forces and ensure adaptability across different robot designs. Furthermore, machine learning algorithms will be explored to classify various categories of slippery surfaces based on the ground reaction force data captured by the wearable system. Finally, the control system of the robot will be enhanced using the floor-type classification obtained through machine learning techniques to improve walking performance and ensure adherence to a specified trajectory.

By addressing these hypotheses and employing a multidisciplinary approach that combines theoretical analysis, experimental evaluations, and technological advancements, this work aims to unlock new possibilities in humanoid robotics. The outcomes have the potential to significantly contribute to the adaptability of humanoid robots on challenging floors, specifically slippery surfaces, enabling them to navigate such environments with enhanced stability, efficiency, and adaptability.


\section{Fundamental Concepts of Humanoid Stability and Locomotion}

Humanoid stability and locomotion play a foundational role in robotics, driven by several critical factors. First and foremost, stability is of utmost importance to ensure the safety and integrity of humanoid robots, preventing falls and potential damage in complex environments. Efficient locomotion enhances overall performance, enabling robots to conserve energy, increase endurance, and minimize power consumption. Additionally, humanoid stability and locomotion contribute to adaptability, empowering robots to navigate diverse terrains, overcome obstacles, and engage with objects effectively. This is pivotal if we aspire for robots to effectively and safely coexist alongside humans.

At the core of these principles lie key concepts that shape our understanding of humanoid stability and locomotion. The \gls{zmp} is a critical parameter representing the point on the ground where the net moment of inertial and gravity forces is zero, essential for achieving balance control. By carefully controlling the motion of the \gls{zmp} and ensuring it stays within the support polygon, humanoid robots can effectively resist external disturbances and maintain a stable base of support. The support polygon refers to the convex polygon formed by the contact points of the robot's feet with the ground. It defines the region on the ground that provides support to the robot's body. By ensuring that the \gls{zmp} remains within this polygon, the robot can maintain its stability and balance \parencite{vukobratovic2004zero}. The \gls{com} represents the average position of the robot's mass, playing a significant role in locomotion dynamics. The \gls{cop}, on the other hand, represents the distribution of forces exerted by the robot's contact points with the ground. It provides information about the stability and balance of the robot during locomotion and can be used to estimate the \gls{zmp}. \textcite{vukobratovic1969contribution} and \textcite{juricic1972mathematical} introduced the concept of ZMP in their pioneering work on biped gait synthesis and mathematical modeling. Their research laid the foundation for ZMP-based control strategies, shaping the development of stable walking patterns for humanoid robots. The \gls{lipm} simplifies CoM dynamics, providing valuable insights into balance control and facilitating the development of stable locomotion algorithms \parencite{Kajita2001The3L}.

Figure \ref{fig:01} provides a visual representation of a humanoid robot in a single-support phase of its walking cycle. The figure shows the robot balancing on one foot, with the other foot suspended in air. The \gls{lipm} is superimposed on the robot's structure, highlighting how the robot's \gls{com} projects down to the ground, forming the base of the pendulum. In an ideal scenario, the \gls{zmp} aligns with the center of the foot in contact with the ground, effectively serving as the point about which the entire system balances (note that foot slip is not considered). 

\begin{figure}[h!]
\centering
\includegraphics[width=0.7\textwidth]{tex/contents/fig/c1/Test_ZMP_COM_LIPM_1.png}
\caption[Illustration of the linear inverted pendulum model and ideal representation of the \gls{zmp} inside the support polygon]{Illustration of the linear inverted pendulum model and ideal representation of the \gls{zmp} inside the support polygon during a single-support phase of a walking humanoid.}
\label{fig:01}
\end{figure}


Balance control emerges as a critical aspect, requiring continuous adjustments in posture, foot placement, and \gls{com} position to respond to external disturbances. The main objective of the control in a walking humanoid is to guarantee zero moment point and body posture to keep the dynamic balance \parencite{ott2011posture}. The key issue in the matter is to look for a fast algorithm that allows a control even if the robot is subjected to impulsive disturbances caused by external force or unknown ground.

Gait generation focuses on generating coordinated leg movements that optimize efficiency and stability during locomotion. It involves designing algorithms that determine the trajectory and timing of leg movements to achieve stable and efficient locomotion. Gait generation algorithms take into account factors such as step length, step width, walking speed, and terrain conditions to adapt the walking pattern accordingly. These algorithms may be rule-based or employ optimization techniques to find optimal gait parameters \parencite{kramer_review_2010}.

The \gls{wbc} unit coordinates multiple body parts, including arms, legs, and torso, to accomplish tasks while preserving balance and adapting to dynamic environments. Whole-body control algorithms consider the dynamics and kinematics of the robot, along with the desired task objectives and constraints. This field of research aims to develop control strategies that enable humanoid robots to manipulate objects, perform dexterous tasks, interact with humans, and navigate through complex environments. Recent advancements in whole-body control have explored the integration of force and tactile sensing, as well as compliance control, to enhance the robot's ability to interact and collaborate with the surrounding world \parencite{huang2023task}.

Trajectory planning also plays a vital role by generating smooth and feasible motion paths for limbs or the entire body, considering physical limitations, task objectives, and obstacle avoidance.

Advancements in these concepts have fuelled comprehensive research, leading to improved stability, adaptability, and performance of humanoid robots. Researchers and engineers leverage these principles to develop increasingly capable and versatile humanoid systems capable of navigating challenging environments, interacting with objects, and providing assistance in human rehabilitation contexts. By embracing and refining these concepts, the field continues to push the boundaries of humanoid stability and locomotion, opening new possibilities for real-world applications and human-robot interactions.

\section{Instrumented Systems Used in the Field of Humanoid Locomotion}

Much like humans who rely on their senses to adapt while walking, instrumented systems play a central and indispensable role in the field of humanoid locomotion, providing valuable data and insights into the forces and movements involved in walking and maintaining stability. These systems allow to accurately measure and analyse various parameters, contributing to a better understanding and optimization of humanoid locomotion.

One important aspect of instrumented systems used in humanoid locomotion is the measurement of ground reaction forces. These forces result from the interaction between the robot's feet and the supporting surface. \gls{ft} sensors are commonly employed to measure these forces, capturing both their magnitude and direction. By integrating \gls{ft} sensors into the robot's feet or lower limbs, precise real-time measurements can be obtained, facilitating a comprehensive understanding of the interaction between the robot and the ground. On the other hand, flexible force sensors, such as flexiforce sensors, are also used to measure and analyse the ground reaction forces. These thin and flexible sensors not only detect pressure but also provide information on the magnitude and distribution of forces exerted on the robot's feet. By strategically placing flexiforce sensors in various regions of the robot's feet, researchers can gain comprehensive insights into the ground reaction forces during walking, thereby enhancing their understanding of stability and balance control in humanoid locomotion. While \gls{ft} sensors provide comprehensive data, they can often be cost-prohibitive and may pose challenges in terms of integration. In response to these challenges, an alternative approach utilizing strategically positioned flexiforce sensors emerges as a practical solution. As depicted in Fig. \ref{fig:03}, the placement of these sensors at specific angles, such as at 0 degrees for vertical alignment and 45 degrees for horizontal alignment, allows for a measurement of both the vertical and horizontal components of ground reaction forces.

\begin{figure}[h!]
\centering
\includegraphics[width=0.5\textwidth]{tex/contents/fig/c1/test_45.png}
\caption[Schematic representation of strategic placement of FlexiForce sensors]{Schematic representation of strategic placement of FlexiForce sensors at 0 and 45 degrees for measurement of vertical and horizontal components of ground reaction forces.}
\label{fig:03}
\end{figure}

The 0-degree flexiforce sensors allows for the measurement of vertical forces exerted by the robot's feet on the ground. This information proves vital in assessing weight distribution and overall stability during locomotion. On the other hand, the 45-degree flexiforce sensor captures measurements of horizontal forces exerted on the robot's feet. These forces are crucial for evaluating the friction and traction between the robot and the ground, especially in challenging conditions such as slippery surfaces. Precise measurements of horizontal forces enable us to assess the robot's grip and make appropriate adjustments to ensure stable locomotion across a wide range of terrains.

Moreover, flexiforce sensors offer several advantages over \gls{ft} sensors, including cost-effectiveness and ease of integration. These sensors are thin and flexible, allowing for effortless positioning on the robot's feet without requiring significant modifications to the robot's structure. This versatility makes them a practical solution for acquiring force measurements in humanoid locomotion research and applications. Despite their advantages, it is important to note that flexiforce sensors may require more careful use and maintenance compared to \gls{ft} sensors. 

Furthermore, \gls{imu} are employed in instrumented systems to monitor the orientation and movement of humanoid robots. \gls{imu} consist of accelerometers, gyroscopes, and sometimes magnetometers, collectively providing information on the robot's acceleration, angular velocity, and orientation in three-dimensional space. Integrating \gls{imu} into the robot's body allow to track the robot's movements, detect deviations from the desired path, and make necessary adjustments to maintain stable locomotion.

Figure \ref{fig:04} shows an example of a \gls{ft}, flexiforce and \gls{imu} sensor. The amalgamation of \gls{ft} sensors, flexiforce sensors, and \gls{imu} within instrumented systems facilitates comprehensive measurements of ground reaction forces, pressure distribution, and robot orientation.
\begin{figure}[h!]
    \centering
    \begin{subfigure}[b]{0.32\textwidth}
        \includegraphics[width=\textwidth]{tex/contents/fig/c1/FT.png}
        \caption{Force torque sensor.}
        \label{fig:04a}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.32\textwidth}
        \includegraphics[width=\textwidth]{tex/contents/fig/c1/FS.png}
        \caption{Flexiforce sensor.}
        \label{fig:04b}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.32\textwidth}
        \includegraphics[width=\textwidth]{tex/contents/fig/c1/IMU.png}
        \caption{Inertial measurement unit.}
        \label{fig:04c}
    \end{subfigure}
    \caption{Illustration of common sensing systems employed in humanoid locomotion for accurate measurement and control.}
    \label{fig:04}
\end{figure}
The sensors mentioned above are essential for the development of humanoid robots, and they have been used in the development of almost every humanoid robot, including Atlas, iCub, and NAO.

While other sensors, such as cameras and LiDAR, are also important, they are not the focus of this work.


\section{The Significance of Computational Intelligent Techniques in Humanoid Robotics}

Computational intelligent techniques play a central role in extracting valuable insights from data across various domains, and their significance is particularly pronounced in the field of humanoid robotics. These techniques, driven by advanced computational algorithms and models, have the ability to analyse and interpret complex sensor data, enabling humanoid robots to make informed decisions and adapt their locomotion strategies accordingly.

In the realm of humanoid robotics, computational intelligent techniques have transformative applications. They empower robots to process sensory information from multiple sources, such as cameras, force sensors, and \gls{imu} sensors, to gain a comprehensive understanding of their environment. By leveraging this data, humanoid robots can navigate and interact with their surroundings in a more intuitive and adaptive manner. When it comes to locomotion on different types of floors, such as surfaces with varying coefficients of friction, computational intelligent techniques become even more essential. The accurate interpretation of data related to ground reaction forces, \gls{imu} readings, and other relevant parameters becomes crucial for maintaining stability, preventing slips and falls, and optimizing locomotion performance.

By analysing foot contact forces, computational intelligent techniques provide humanoid robots with valuable information about the interaction between their feet and the surface. This data allows them to adjust their gait, joint torques, or control actions to ensure optimal stability and balance on surfaces with different frictional properties. For example, on slippery floors with low coefficients of friction, the robot can adapt its movements to reduce the risk of slipping, while on surfaces with high coefficients of friction, it can optimize its foot placement to maximize traction and efficiency.

Moreover, computational intelligent techniques enable real-time analysis of \gls{imu} data, which provides information about the robot's orientation, acceleration, and angular velocity. By monitoring these parameters, humanoid robots can detect changes in the surface conditions and dynamically adjust their locomotion strategies. For instance, if the coefficient of friction suddenly decreases on a previously stable surface, the robot can react swiftly by modifying its joint torques or adopting a different walking pattern to maintain balance and prevent falls.

\section{Advancements in Humanoid Control}

Humanoid robots, designed to mimic human form and behaviour, require sophisticated control systems to achieve stable and efficient locomotion. The field of humanoid robotics has seen significant advancements in the development of controllers that enable these robots to perform complex tasks, navigate diverse environments, and adapt to changing conditions. Humanoid controllers serve as the underlying framework that orchestrates the robot's movements, ensuring coordination, balance, and responsiveness.

At the core of humanoid controllers is the principle of dynamic stability. Unlike static stability, which focuses on maintaining balance while stationary, dynamic stability refers to the ability of a robot to maintain balance while in motion. Achieving dynamic stability in humanoid locomotion is essential for navigating challenging terrains, performing agile movements, and recovering from external disturbances. Humanoid controllers employ advanced algorithms and control strategies to enable the robot to dynamically adjust its posture, joint angles, and motor torques to maintain stability.

There are various approaches to designing humanoid controllers, each with its own strengths and limitations. One common approach is based on the concept of whole-body control, which considers the robot as a unified system rather than a collection of individual joints and limbs. Whole-body control aims to coordinate the movements of all the robot's body parts to achieve stable and coordinated motion. This approach often incorporates dynamic modelling, optimization techniques, and feedback control to generate desired trajectories and achieve stability \parencite{sentis2006whole}.

Another approach is behaviour-based control, which focuses on organizing the robot's actions into modular behaviours or skills. These behaviours can be designed individually and then combined to generate complex movements and tasks. Behaviour-based controllers provide a flexible and modular framework, allowing for easy adaptation and reconfiguration of the robot's actions based on the task and environment \parencite{katic2003survey}.

Furthermore, humanoid controllers can incorporate machine learning techniques to enhance their adaptability and responsiveness. Machine learning algorithms can be used to learn from sensory data and optimize control policies, enabling the robot to adapt its movements based on real-time feedback and environmental conditions.

Several notable examples highlight the capabilities and advancements in humanoid controllers. One example is the \gls{zmp} controller, which utilizes the concept of the \gls{zmp} to achieve dynamic stability \parencite{sayari2019perfect}. The \gls{zmp} controller calculates the point on the ground where the total moments acting on the robot's body are balanced, ensuring stability during walking and other locomotion tasks.

Another example is the \gls{mpc} approach, which uses dynamic models of the robot and the environment to predict future states and optimize control actions accordingly \parencite{koenemann2015whole}. MPC controllers enable real-time adjustment of control parameters and generate robust and stable locomotion patterns.

Additionally, bio-inspired controllers draw inspiration from biological systems and principles to achieve humanoid locomotion. These controllers aim to replicate the neural and musculoskeletal structures found in humans, allowing for more natural and human-like movements \parencite{colasanto2015bio}.

These examples illustrate the diverse approaches and techniques employed in humanoid controllers to achieve stable and adaptive locomotion. By combining principles of dynamic stability, whole-body control, behaviour-based control, and incorporating machine learning, humanoid controllers continue to advance the capabilities of humanoid robots, enabling them to perform complex tasks, navigate challenging environments, and interact with the world in a more human-like manner.

\section{Humanoid Locomotion in Slippery Environments}

This section offers an in-depth analysis of existing studies concerning humanoid locomotion across unstructured environments, with an emphasis on navigating slippery terrains. The robotic capacity to traverse unregulated or unpredictable environments is vital for their practical utility in real-world contexts \parencite{chen2020robust}. The present review dissects the progress, challenges, and ongoing research covering multiple dimensions of humanoid movement in such conditions. It encompasses aspects like deciphering and manipulating ground reaction forces, harnessing learning techniques to interpret and extract meaningful patterns from such data, and the creation of advanced controllers to refine humanoid mobility.

It's noteworthy that this PhD thesis includes dedicated literature reviews within each chapter, supplementing the comprehension of various factors contributing to the enhancement of humanoid locomotion. These reviews, together, furnish a thorough understanding of the discipline and its developments, offering useful perspectives for the research presented in this thesis.

Over the past decade, impressive improvement have been made in establishing resilient bipedal robot locomotion. This advancement has been steered by the synergistic blend of theoretical modeling and analysis via hybrid systems, application of sophisticated non-linear control methodologies, and meticulous consideration towards mechanical design and hardware implementation \parencite{ma2019dynamic}. 

Bipedal locomotion, as grounded in paradigms like ZMP \parencite{vukobratovic2004zero} and \gls{slip} models \parencite{schwind1998spring}, relies on a fundamental assumption of zero foot slippage. In this framework, the robot foot is regarded as an immovable pivot point, functioning effectively within the controlled environment of a laboratory with adequate floor friction. However, this approach falls short when faced with the complexities of natural outdoor terrains, which often present a medley of surfaces characterized by slipperiness, slight unevenness, or irregularities.

In the context of humanoid robots, the issue of foot slippage is typically treated either as an external disturbance to be preemptively addressed during gait planning \parencite{kajita2004biped} or as a dynamic challenge necessitating real-time detection and recovery through feedback control \parencite{vazquez2013experimental}. 

Enhancing the locomotion of humanoid robots involves a continuous sequence of interactions between the robot's feet and its environment. Within this context, the accurate detection of foot contacts assumes a pivotal role in several aspects of locomotion control \parencite{koolen2016design, herzog2016momentum, neunert2018whole}, including gait planning \parencite{aceituno2018simultaneous, winkler2018gait, hereid2018dynamic}, base state estimation \parencite{bloesch2012state, rotella2014state, raghavan2018study, piperakis2019outlier}, and Center of Mass (CoM) estimation \parencite{rotella2015humanoid, piperakis2016nonlinear, piperakis2018nonlinear}. Consequently, to achieve truly agile and dexterous locomotion, it becomes imperative to achieve precise contact status estimation.

In the realm of contact detection, current methods can be broadly categorized into two primary groups:

\begin{itemize}
\item \textbf{Direct Measurement Approaches} 

These approaches directly utilize measurements of ground reaction wrenches. In the literature, researchers have employed various algorithms for the precise analysis of \gls{grf}. These include the utilization of F/T sensors \parencite{fallon2014drift, kuindersma2016optimization}, contact/pressure sensors \parencite{piperakis2018nonlinear, bloesch2013state}, IMUs sensors \parencite{maravgakis2023probabilistic} or a combination of F/T sensors with IMUs data \parencite{lin2021legged}.

\item \textbf{Kinematics and Dynamics-Based Approaches}

These methods leverage principles of kinematics and dynamics to estimate the GRFs, which are then used to infer the contact status. In the literature, authors estimate the GRFs by capitalizing on the kinematics and dynamics of the robots, each employing different methods for estimation \parencite{ortenzi2016kinematics, hwangbo2016probabilistic, neunert2017trajectory, camurri2017probabilistic, lin2021legged}.
\end{itemize}

Various methodologies are employed to decipher GRFs and estimate the contact between the robot and the floor. These methods encompass a range of techniques, including Schmitt-Trigger \parencite{fallon2014drift,piperakis2018nonlinear,kuindersma2015optimization}, Kalman filtering \parencite{bloesch2012state,bloesch2013state}, clustering using fuzzy c-means algorithms \parencite{rotella2018unsupervised}, probabilistic frameworks incorporating hidden Markov models \parencite{hwangbo2016probabilistic}, deep learning-based approaches \parencite{lin2021legged,piperakis2022robust}, and unsupervised learning frameworks \parencite{rotella2018unsupervised,hoepflinger2013unsupervised}.

In this study, we acknowledge the temporal evolution within the field, particularly the growing trend towards machine learning techniques. Subsequently, we harness the potential of neural networks for performing this classification, as detailed in the following sections of this thesis.

Comprehensive investigations into slip dynamics are relatively limited in the current research landscape. The majority of existing studies pertaining to low-friction foot contact primarily concentrate on preemptive slip avoidance \parencite{ferreira2020humanlike,khadiv2017optimal}. Explicit examinations of slipping dynamics are predominantly oriented towards the domain of human locomotion \parencite{mihalec2022balance,trkov2019bipedal,chen2015robotic}, with a few noteworthy exceptions.

In \textcite{mihalec2023balance}, the authors presented a motion planning methodology that hinges on a two-mass Linear Inverted Pendulum (\gls{tmlip}) model, in conjunction with a frictional Whole-Body Operational Space (FWBOS) full-body recovery control strategy, visually depicted in Figure \ref{fig:05} and Figure \ref{fig:06}. Specifically, Figure \ref{fig:05} illustrates the schematic representation of the \gls{tmlip} model and the utilized full-body model, while Figure \ref{fig:06} offers insight into the control diagram employed. 
\begin{figure}[h!]
\centering
\includegraphics[width=0.75\textwidth]{tex/contents/fig/c1/slip_paper1.png}
\caption[Schematic of the TMLIP model, a bipedal robotic walker and a 5-link full body model.]{Left: schematic of the TMLIP model. Center: bipedal robotic walker. Right: schematic of a 5-link full body model \parencite{mihalec2023balance}.}
\label{fig:05}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[width=0.75\textwidth]{tex/contents/fig/c1/slip_paper2.png}
\caption[Control diagram for walking.]{Control diagram for walking. Slip changes the results of TMLIP and FWBOS calculations  \parencite{mihalec2023balance}.}
\label{fig:06}
\end{figure}
This strategy aimed to calculate joint torques to counteract the effects of slip dynamics during locomotion. Notably, when the robot operated on surfaces with extremely low friction, it encountered challenges in maintaining gait balance. However, the authors asserted that, despite these challenges, their controller exhibited superior performance when compared to conventional controllers. Specifically, it outperformed them in terms of maintaining balance over time and achieving greater walking distances.\\

In \textcite{radosavovic2023learning}, the authors devised a sim-to-real learning based method for enabling real-world humanoid locomotion. The core component of their controller is a causal Transformer, which underwent training through autoregressive prediction of forthcoming actions based on a historical record of observations and actions, as visually illustrated in Figure \ref{fig:07}.
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{tex/contents/fig/c1/slip_paper3.png}
\caption[Humanoid Transformer.]{Causal Transformer model trained by autoregressive prediction of future actions from the history of observations and actions. \parencite{radosavovic2023learning}.}
\label{fig:07}
\end{figure}
This approach underwent reinforcement learning training within a simulation environment and was subsequently deployed without any further adaptation ("zero-shot"). Their model underwent comprehensive evaluation within a high-fidelity simulation environment and showcased remarkable success in deployment across various types of floors. Notably, it faced challenges in the most demanding scenario, characterized by a surface with significantly lower friction, and did not excel in this particular case.

In \textcite{lee2022adaptive}, the authors introduced strategies for stabilizing slippery motion within a Whole-Body Control (WBLC) framework, focusing on known and unknown slip scenarios. They used CoM re-planning based on parameter estimation and online weight adaptation to address unknown slip, improving stability. While effective in simulations, potential challenges include traction loss, parameter estimation inaccuracies, and instability, requiring further investigation. Real-world implementation remains untested, presenting additional hurdles like kinematic singularities and dynamics errors that need to be addressed in future research.

For instance, in \textcite{frizza2022study}, an alternative perspective is offered, wherein the focus shifts towards modifying the robot's feet rather than altering the robot's gait or controller. They conducted experiments utilizing a compliant sole with variable stiffness (Figure \ref{fig:08}), which resulted in notable improvements compared to the robot's flat feet with fixed stiffness.
\begin{figure}[h!]
    \centering
    \begin{subfigure}[b]{0.45\textwidth}
        \includegraphics[width=\textwidth]{tex/contents/fig/c1/slip_paper4.png}
        \caption{Simplified model of the complaint foot.}
        \label{fig:08a}
    \end{subfigure}
    \hfill
    \begin{subfigure}[b]{0.45\textwidth}
        \includegraphics[width=\textwidth]{tex/contents/fig/c1/slip_paper5.png}
        \caption{Deformable foot model used in dynamic simulations.}
        \label{fig:08b}
    \end{subfigure}
    \hfill
    \caption[Variable stiffness feet for humanoid walking.]{Variable stiffness feet for humanoid walking. The plantar arc is composed of ten blocks representing the ten phalanxes, connected between each other by rotational joints with viscoelastic elements. The plantar arch is connected with the frontal and backward arch through rotational passive joints \parencite{frizza2022study}.}
    \label{fig:08}
\end{figure}

Despite the different approaches explored in this context, it is evident that slip dynamics remain a challenging problem with limited research efforts, stressing the need for further attention and exploration.


\section{Brief Research Journey}

My research journey began at the Institute of Electronics and Informatics Engineering of Aveiro (IEETA) and the Laboratory for Automation and Robotics (LAR) housed within the Mechanical Department of Aveiro University. This journey commenced with the creation of an innovative instrumented system, aptly named ITShoe, which was carefully developed for the precise measurement of GRFs experienced by a walking humanoid on a diverse array of surfaces. Notably, our focus lay on those surfaces characterized by low friction coefficients. We are sincerely grateful for the support provided from the Fundação para a Ciência e Tecnologia (FCT) through their funding of the project titled 'Automatic Adaptation of Humanoid Robot Gait to Different Floor-Robot Friction Coefficients,' with the project reference number PTDC/EEI-AUT/5141/2014.

This inaugural phase of my research represented a holistic undertaking, encompassing the entire spectrum of activities involved in the development of the ITShoe, from conceptualization and design to material selection, construction, and the intricacies of setting up electronics. The overarching goal was to ensure the seamless and real-time measurement and transmission of force data. This pioneering phase culminated in the collection of valuable data using the robot+ITShoe architecture. 

Subsequently, I seized the opportunity to further expand my horizons by joining the esteemed Institute Mihailo Pupin in Belgrade, Serbia. Here, I ventured into the field of machine learning, exploring a variety of tools and algorithms, with the objective of finding the most efficient and accurate approach to interpret the force data. My progress was guided and enhanced by the expertise of my dedicated supervisor at the institute. During my three-month stay at the Institute Mihailo Pupin, I actively participated in an ongoing research project focused on the adaptation of the NAO humanoid robot's gait. Moreover, I had the opportunity to contribute to the scientific paper \parencite{gui}, which significantly enriched my research experience.

Upon returning to the LAR, the research journey continued to evolve as various computational intelligence techniques were explored, aiming to refine the data interpretation process. Progressive enhancements were introduced to both data gathering and analysis methodologies. Once the capability to classify different floors in real-time was achieved with the actual robot, a new chapter in the research journey was embarked upon.

I joined the Robotic Laboratory at Carlos III University of Madrid, and for four months, my focus shifted towards advancing the control mechanisms of humanoid robots. Here, collaboration with a different humanoid robot, TEO, provided valuable experience in both simulated and real-world environments.

Ultimately, my path led me back to Aveiro University, where the improved robot control system was integrated with the humanoid robot that had been a constant companion throughout the thesis. I owe a debt of gratitude to ISR for their support and provision of the robot for the duration of my research. By incorporating the controller into a simulated environment, we successfully unified all the work undertaken thus far. Moreover, we developed a controller that dynamically adapted its parameters based on the classification of the walking surface, thus enhancing the humanoid's gait on slippery floors.

\section{Thesis Organization}

This thesis focuses on improving the adaptability of humanoid locomotion on slippery floors. The primary objective is to acquire real-time knowledge of these challenging surfaces in order to enable effective control of humanoid robots and ensure their successful navigation through such obstacles. This goal is achieved by addressing the initial hypotheses presented.

The thesis is structured into several chapters, including a general introduction (Chapter 1), one conference paper and three journal papers (Chapters 2-5), and a comprehensive discussion encompassing concluding remarks and future work (Chapter 6).

This thesis is structured into three interrelated parts that collectively tackle the challenge of enhancing humanoid locomotion adaptability on slippery floors:

\begin{itemize}


\item \textbf{Part I (Chapter 2):} This part is dedicated to the development of a wearable 3D force system known as \gls{itshoes}. The primary objective is to create a robust and versatile instrument that can accurately measure the ground reaction forces experienced by a walking humanoid robot. The ITshoes are designed to seamlessly integrate with various robot designs, although the manufactured units are specifically tailored for the NAO humanoid, while minimizing any disruption to the robot's locomotion. By precisely capturing the ground reaction forces, this system lays the foundation for subsequent analysis and control strategies.

\item \textbf{Part II (Chapters 3-4):} Building upon the data obtained from the ITshoes, this part focuses on the application of machine learning algorithms to address the challenge of classifying different types of slippery floors. The goal is to leverage the ground reaction force data collected by the ITshoes to train and deploy machine learning models capable of accurately identifying and categorizing various slippery surface conditions. This classification system provides valuable real-time information about the ground conditions, empowering the robot to make informed decisions and adapt its locomotion accordingly.

\item \textbf{Part III (Chapter 5):} The emphasis of this part lies in enhancing the humanoid controller by leveraging the real-time knowledge of the floor conditions obtained from Part II. By incorporating the classified floor types into the control system, improvements can be made to optimize the robot's locomotion and ensure its adherence to the specified task. The control system is designed to dynamically adjust the robot's gait, balance, and motion planning based on the identified floor condition. These enhancements aim to maximize walking stability, efficiency, and adaptability, particularly when navigating slippery surfaces.

\end{itemize}

The chapters (Chapters 2-5) in this thesis encompass the research conducted during the PhD program and adhere to a coherent structure. Each chapter of this thesis corresponds to a scientific paper that has already been published, with the exception of chapter 5, which is currently under submission. As a result, every chapter includes an abstract, an introductory section that offers a comprehensive review of the state-of-the-art, details on the methodology employed (which may also be referred to as 'materials and methods'), presentation of the obtained results, discussion of the findings, and concluding remarks. Chapters in Parts I and II are supported by extensive experimental data collected from the physical system, providing a robust foundation for the research. In contrast, Part III, while featuring some physical developments, primarily relies on simulation due to hardware limitations in controlling the actual robot.



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