<p>Successful navigation requires an accurate mental spatial representation of the environment that can be updated during movement. Experiments with animals and humans have demonstrated the existence of two forms of spatial representation: egocentric (observer-centered) and allocentric (environment-centered). Unfortunately, specifically how humans use these two systems is not well understood. The current dissertation was focused on providing evidence differentiating human use of egocentric and allocentric spatial reference frames, specifically examining the characteristics and contributions from body-based sources. Two empirical chapters are presented that include experiments involving two common spatial tasks. In Chapter 2, updating of feature relations within a room-sized environment was examined by having observers provide directional judgments to learned features with respect to an imagined orientation that was either congruent or incongruent with their physical orientation. The information available for updating the physical orientation was manipulated across experiments. Performance differences between congruent and incongruent conditions demonstrated the reliance on egocentric representations for updating, and differentiated body- and knowledge-based components of the egocentric updating process. The specificity of the body-based component was examined in Chapter 3 by having observers detect changes made to a tabletop spatial scene following a viewpoint shift resulting from their movement, scene rotation or both. The relation between the extent of observer movement and the magnitude of the experienced viewpoint shift was manipulated. Change detection performance was best when the extent of observer movement most closely matched the viewpoint shift, and declined as the match declined. Thus, body-based cues contributed specific information for updating self-to-feature relations that facilitated scene recognition. Throughout the course of the research program it has become clear that humans rely on egocentric representations to complete these tasks, and sensory and motor modalities involved in self-motion are integrated for updating spatial relations of novel environments.</p> / Doctor of Philosophy (PhD)

No-vision walking is supported in the central nervous system (CNS) by a spatial updating process. This process involves the iterative updating of a mental representation of the environment using estimates of distance traveled gleaned from locomotive kinematic activity. An effective means of examining the online regulation of this process is a continuous pointing task, which requires performers to walk along a straight-line forward trajectory while keeping their right arm straight and index finger fixated on a stationary ground-level target beside the walking path. In the current thesis, no-vision continuous pointing was examined in typically calibrated and recalibrated perceptual-motor states. Shoulder and trunk joint angles provided the basis for perceptual measures that reflected spatial updating performance and kinematic measures that reflected its underlying CNS online regulation. In the typically calibrated conditions, no-vision walking demonstrated a slight perceptual underestimation of distance traveled (Study 1). In the recalibrated conditions, no-vision walking demonstrated: a) perceptual underestimation and overestimation following adaptation periods involving walking with low and high visual gains, respectively (Study 2); and b) partial recalibration following exposures to vision and arm gains (Study 3). The latter was suggested as being impacted by task specific changes in CNS multisensory integration resulting from the development of a robust task prior and/or the altering of sensory cue weights. Importantly, this thesis used a novel trajectory parsing procedure to quantify discrete CNS perceptual updating units in the shoulder plane of elevation trajectory. The starts and ends of these updating units were consistently timed to the late left-to-early right foot swing phase of the step-cycle, regardless of perceptual-motor state. This was suggested to reflect perceptual units that were purposely timed, but indirectly mapped, to this kinematic event. The perceptual differences in Studies 1 and 2 were at least partially reflected in these units. / Thesis / Doctor of Philosophy (PhD) / It is well understood that humans can effectively walk without vision to environmental locations up to 15 metres away. However, less is known about how these walking movements are controlled during the course of forward progression. This thesis fills this knowledge gap using a task that requires participants to walk forward along a straight path while keeping their right index finger pointed toward a ground-level target beside the walking path. The patterns of arm movements performed during this task are indicative of the control strategies used by the performer to mentally update their positions in space. One of the key contributions of this work is showing that humans perform this mental updating in a repetitive manner, and that these repetitions are consistently linked to early forward movements of the right leg. This pattern is maintained when walking without vision is performed in a variety of different contexts.

No / There is an increasing interest in modelling of agents interacting as crowd and a simulation of such scenarios that map to real-life situations. This paper presents a generic state-based abstract model for crowd behaviour that can be mapped onto different agent-based systems. In particular, the abstract model is mapped into the simulation framework NetLogo. We have used the model to simulate a real-life case study of high density diverse crowd such as the Hajj ritual at the mosque in Mecca (Makkah). The computational model is based on real data extracted from videos of the ritual. We also present a methodology for extracting significant data, parameters, and patterns of behaviour from real-world videos that has been used as an early stage validation to demonstrate that the obtained simulations are realistic.

This thesis synthesizes general and scalable distributed nonlinear control algorithms with application to legged robots. It explores both naturally decentralized problems in legged locomotion, such as the collaborative control of human-lower extremity prosthesis and the decomposition of high-dimensional controllers of a naturally centralized problem into a net- work of low-dimensional controllers while preserving equivalent performance. In doing so, strong nonlinear interaction forces arise, which this thesis considers and sufficiently addresses. It generalizes to both symmetric and asymmetric combinations of subsystems. Specifically, this thesis results in two distinct distributed control algorithms based on the decomposition approach. Towards synthesizing the first algorithm, this thesis presents a formal foundation based on de- composition, Hybrid Zero Dynamics (HZD), and scalable optimization to develop distributed controllers for hybrid models of collaborative human-robot locomotion. This approach con- siders a centralized controller and then decomposes the dynamics and parameterizes the feedback laws to synthesize local controllers. The Jacobian matrix of the Poincaré map with local controllers is studied and compared with the centralized ones. An optimization problem is then set up to tune the parameters of the local controllers for asymptotic stability. It is shown that the proposed approach can significantly reduce the number of controller parameters to be optimized for the synthesis of distributed controllers, deeming the method computationally tractable. To evaluate the analytical results, we consider a human amputee with the point of separation just above the knee and assume the average physical parameters of a human male. For the lower-extremity prosthesis, we consider the PRleg, a powered knee-ankle prosthetic leg, and together, they form a 19 Degrees of Freedom (DoF) model. A multi-domain hybrid locomotion model is then employed to rigorously assess the performance of the afore-stated control algorithm via numerical simulations. Various simulations involving the application of unknown external forces and altering the physical parameters of the human model unbeknownst to the local controllers still result in stable amputee loco- motion, demonstrating the inherent robustness of the proposed control algorithm. In the later part of this thesis, we are interested in developing distributed algorithms for the real-time control of legged robots. Inspired by the increasing popularity of Quadratic programming (QP)-based nonlinear controllers in the legged locomotion community due to their ability to encode control objectives subject to physical constraints, this thesis exploits the idea of distributed QPs. In particular, this thesis presents a formal foundation to systematically decompose QP-based centralized nonlinear controllers into a network of lower-dimensional local QPs. The proposed approach formulates a feedback structure be- tween the local QPs and leverages a one-step communication delay protocol. The properties of local QPs are analyzed, wherein it is established that their steady-state solutions on periodic orbits (representing gaits) coincide with that of the centralized QP. The asymptotic convergence of local QPs' solutions to the steady-state solution is studied via Floquet theory. Subsequently, to evaluate the effectiveness of the analytical results, we consider an 18 DoF quadrupedal robot, A1, as a representative example. The network of distributed QPs mentioned earlier is condensed to two local QPs by considering a front-hind decomposition scheme. The robustness of the distributed QP-based controller is then established through rigorous numerical simulations that involve exerting unmodelled external forces and intro- ducing unknown ground height variations. It is further shown that the proposed distributed QPs have reduced sensitivity to noise propagation when compared with the centralized QP. Finally, to demonstrate that the resultant distributed QP-based nonlinear control algorithm translates equivalently well to hardware, an extensive set of blind locomotion experiments on the A1 robot are undertaken. Similar to numerical simulations, unknown external forces in the form of aggressive pulls and pushes were applied, and terrain uncertainties were introduced with the help of arbitrarily displaced wooden blocks and compliant surfaces. Additionally, outdoor experiments involving a wide range of terrains such as gravel, mulch, and grass at various speeds up to 1.0 (m/s) reiterate the robust locomotion observed in numerical simulations. These experiments also show that the computation time is significantly dropped when the distributed QPs are considered over the centralized QP. / Doctor of Philosophy / Inspiration from animals and human beings has long driven the research of legged loco- motion and the subsequent design of the robotic counterparts: bipedal and quadrupedal robots. Legged robots have also been extended to assist human amputees with the help of powered prostheses and aiding people with paraplegia through the development of exoskeleton suits. However, in an effort to capture the same robustness and agility demonstrated by nature, our design abstractions have become increasingly complicated. As a result, the en- suing control algorithms that drive and stabilize the robot are equivalently complicated and subjected to the curse of dimensionality. This complication is undesirable as failing to compute and prescribe a control action quickly destabilizes and renders the robot uncontrollable. This thesis addresses this issue by seeking nature for inspiration through a different perspective. Specifically, through some earlier biological studies on cats, it was observed that some form of locality is implemented in the control of animals. This thesis extends this observation to the control of legged robots by advocating an unconventional solution. It proposes that a high-dimensional, single-legged agent be viewed as a virtual composition of multiple, low-dimensional subsystems. While this outlook is not new and forms precedent to the vast literature of distributed control, the focus has always been on large-scale systems such as power networks or urban traffic networks that preserve sparsity, mathematically speaking. On the contrary, legged robots are underactuated systems with strong interaction forces acting amongst each subsystem and dense mathematical structures. This thesis considers this problem in great detail and proposes developments that provide theoretical stability guarantees for the distributed control of interconnected legged robots. As a result, two distinctly different distributed control algorithms are formulated. We consider a naturally decentralized structure appearing in the form of a human-lower extremity prosthesis to synthesize distributed controllers using the first control algorithm. Subsequently, the resultant local controllers are rigorously validated through extensive full- order simulations. In order to validate the second algorithm, this thesis considers the problem of quadrupedal locomotion as a representative example. It assumes for the purposes of control synthesis that the quadruped is comprised of two subsystems separated at the geometric center, resulting in a front and hind subsystem. In addition to rigorous validation via numerical simulations, in the latter part of this thesis, to demonstrate that distributed controllers preserve practicality, rigorous and extensive experiments are undertaken in indoor and outdoor settings on a readily available quadrupedal robot A1.

This study focuses on developing a better comprehension of the mobility of lightweight autonomous vehicles with varying locomotion platforms on sand. This research involves four segments. The first segment is a review of military criteria for the development of lightweight unmanned ground vehicles, followed by a review a review of current methodologies for evaluating the terramechanic (vehicle-ground interaction) mobility measures of heavyweight wheeled and tracked vehicles, and ending with a review of the defining properties of deformable terrain with specific emphasis on sand. These present a basis for understanding what currently defines mobility and how mobility is quantified for traditional heavyweight wheeled and tracked vehicles, as well as an understanding of the environment of operation (sandy terrain) for the lightweight vehicles in this study. The second segment involves the identification of key properties associated with the mobility and operation of lightweight vehicles on sand as related to given mission criteria, so as to form a quantitative assessment system to compare lightweight vehicles of varying locomotion platforms. A table based on the House of Quality shows the relationships&#8212;high, low, or adverse&#8212;between mission profile requirements and general performance measures and geometries of vehicles under consideration for use. This table, when combined with known values for vehicle metrics, provides information for an index formula used to quantitatively compare the mobility of a user-chosen set of vehicles, regardless of their methods of locomotion. This table identifies several important or fundamental terramechanics properties that necessitate model development for robots with novel locomotion platforms and testing for lightweight wheeled and tracked vehicles so as to consider the adaptation of counterpart heavyweight terramechanics models for use. The third segment is a study of robots utilizing novel forms of locomotion, emphasizing the kinematics of locomotion (gait and foot placement) and proposed starting points for the development of terramechanics models so as to compare their mobility and performance with more traditional wheeled and tracked vehicles. In this study several new autonomous vehicles&#8212;bipedal, self-excited dynamic tripedal, active spoke-wheel&#8212;that are currently under development are explored. The final segment involves experimentation of several lightweight vehicles and robots on sand. A preliminary experimentation was performed evaluating a lightweight autonomous tracked vehicle for its performance and operation on sand. A bipedal robot was then tested to study the foot-ground interaction with and sinkage into a medium-grade sand, utilizing a one of the first-developed walking gaits. Finally, a comprehensive set of experiments was performed on a lightweight wheeled vehicle. While the terramechanics properties of wheeled and tracked vehicles, such as the contact patch pressure distribution, have been understood and models have been developed for heavy vehicles, the feasibility of extrapolating them to the analysis of light vehicles is still under analysis. A wheeled all-terrain vehicle was tested for effects of sand gradation, vehicle speed, and vehicle payload on measures of pressure and sinkage in the contact patch, and preliminary analysis is presented on the sinkage of the wheeled all-terrain vehicle. These four segments&#8212;review of properties of sandy terrain and measures of and criteria for the mobility of lightweight vehicles operating on sandy terrain, the development of the comparison matrix and indexing function, modeling and development of novel forms of locomotion, and physical experimentation of lightweight tracked and wheeled vehicles as well as a bipedal robot&#8212;combine to give an overall picture of mobility that spans across different forms of locomotion. / Master of Science

Biological systems offer novel and efficient solutions to many engineering applications, including marine propulsion. It is of interest to determine how fish interact with the water around them, and how best to utilize the potential their methods offer. A stingray-like fin was chosen for analysis due to the maneuverability and versatility of stingrays. The stingray fin was modeled in 2D as a sinusoidal wave with an amplitude increasing from zero at the leading edge to a maximum at the trailing edge. Using this model, a parametric study was performed to examine the effects of the fin on surrounding water in computational fluid dynamics (CFD) simulations. The results were analyzed both qualitatively, in terms of the pressure contours on the fin and vorticity in the trailing wake, and quantitatively, in terms of the resultant forces and the mechanical power requirements to actuate the desired fin motion. The average thrust was shown to depend primarily on the relationship between the swimming speed and the frequency and wavelength (which both are directly proportional to the wavespeed of the fin), although amplitude can be used to augment thrust production as well. However, acceleration was shown to significantly correlate with a large variation in lift and moment, as well as with greater power losses. Using results from the parametric study, the potential for power regeneration was also examined. Relationships between frequency, velocity, drag, and power input were determined using nonlinear regression that explained more than 99.8% of the data. The actuator for a fin was modeled as a single DC motor-shaft system, allowing the combination of the energetic effects of the motor with the fin-fluid system. When combined, even a non-ideal fin model was able to regenerate more power at a given flow speed than was required to swim at the same speed. Even in a more realistic setting, this high proportion of regenerative power suggests that regeneration and energy harvesting could be both feasible and useful in a mission setting. / Master of Science / Animals interact with the world much differently than engineered systems, and can offer new and efficient ways to solve engineering problems, including underwater vehicles. To learn how to move an underwater vehicle in an environmentally conscious way, it is useful to study how a fish’s movements affect the manner in which it moves through the water. Through careful study, the principles involved can be implemented for an efficient, low-disturbance underwater vehicle. The particular fish chosen for in-depth study was the stingray, due to its maneuverability and ability to travel close to the seafloor without disturbing the sediment and creatures around it. In this work, computational analysis was performed on a model of a single stingray fin to determine how the motion of the fin affects the water around it, and how the water affects the fin in turn. The results were analyzed both in terms of the wake behind the fin and in terms of how much power was required to make the fin move in a particular way. The speed of the fin motion was found to have the strongest effect in controlling swimming speed, although the lateral motion of the fin also helped with accelerating faster. Additionally, the potential for a robotic stingray fin to harness power from the water around it was examined. Based on results from simulations of the fin, a mathematical model was formulated to relate energy harvesting with the flow speed past the fin. This model was used to determine how worthwhile it was to use energy harvesting. Analysis of the model showed that harvesting energy from the water was quite efficient, and would likely be a worthwhile investment for an exploration mission.

The impressive kinematic capabilities and structural adaptations presented by bio-locomotion continue to inspire some of the advancements in today's small-scaled flying and swimming vehicles. These vehicles operate in a low Reynolds number flow regime where viscous effects dominate flow interactions, which makes it challenging to generate lift and thrust. Overcoming these challenges means utilizing non-conventional lifting and flow control mechanisms generated by unsteady flapping body motion. Understanding and characterizing the aerodynamic phenomena associated with the unsteady motion is vital to predict the unsteady fluid loads generated, to implement control methodologies, and to assess the dynamic stability and control authority of airborne and underwater vehicles. This dissertation presents experimental results for forced oscillations on multi-element airfoils and hydrofoils for Reynolds numbers between Re=104 and Re=106. The document divides the work into four main sections: The first topic presents wind tunnel measurements of lift forces generated by an oscillating trailing edge flap on a NACA-0012 airfoil to illustrate the effects that frequency and pitching amplitude have on lift enhancement. The results suggest that this dynamic trailing edge flap enhances the mean lift by up to 20% in the stalled flow regime. Using frequency response approach, it is determined that the maximum enhancement in circulatory lift amplitude occurs at stalled angles of attack for lower pitching amplitudes. The second topic presents wind tunnel measurements for lift and drag generated by a sinusoidal and non-sinusoidal oscillations of a NACA-0012 airfoil. The results show that 'trapezoidal' pitching enhances the mean lift and the RMS lift by up to 50% and 35% in the pre-stall flow regime, respectively, whereas the 'reverse sawtooth' and sinusoidal pitching generate the most substantial increase of the lift-to-drag ratio in stall and post-stall flow regimes, respectively. The third topic involves a study on the role of fish-tail flexibility on thrust and propulsive efficiency. Flexible tails enhance thrust production in comparison to a rigid ones of the same size and under the same operating conditions. Further analysis indicates that varying the tail's aspect ratio has a more significant effect on propulsive efficiency and the thrust-to-power ratio at zero freestream flow. On the other hand, changing the material's property has the strongest impact on propulsive efficiency at non-zero freestream flow. The results also show that the maximum thrust peaks correspond to the maximum passive tail amplitudes only for the most flexible case. The final topic aims to assess the unsteady hydrodynamic forces and moments generated by a three-link swimming prototype performing different swimming gaits, swimming speeds, and oscillatory frequencies. We conclude that the active actuation of the tail's first mode bending produces the most significant thrust force in the presence of freestream flow. In contrast, the second mode bending kinematics provides the most significant thrust force in a zero-freestream flow. / Doctor of Philosophy / It is by no surprise that animal locomotion continues to inspire the design of flying and swimming vehicles. Although nature produces complex kinematics and highly unsteady flow characteristics, simplified approximations to model bio-inspired locomotion in fluid flows are experimentally achievable using low degrees of freedom motion, such as pitching airfoils and trailing edge flaps. The contributions of this dissertation are divided into four primary foci: (a) wind tunnel force measurements on a flapped NACA-0012 airfoil undergoing forced pitching, (b) wind tunnel measurements of aerodynamic forces generated by sinusoidal and non-sinusoidal pitching of a NACA-0012 airfoil, (c) towing tank measurements of thrust forces and torques generated by a one-link swimming prototype with varying tail flexibilities, and (d) towing tank measurements of hydrodynamic forces and moments generated by active tail actuation of a multi-link swimming prototype. From our wind tunnel measurements, we determine that lift enhancement by a trailing edge flap is achieved under certain flow regimes and oscillating conditions. Additionally, we assess the aerodynamic forces for a sinusoidal and non-sinusoidal pitching of an airfoil and show that 'trapezoidal' pitching produces the largest lift coefficient amplitude whereas the sinusoidal and 'reverse sawtooth' pitching achieve the best lift to drag ratios. From our towing tank experiments, we note that the role of tail flexibility enhances thrust generation on a swimming device. Finally, we conclude that different kinematics on an articulating body strongly affect the hydrodynamic forces and moments. The results of the towing tank measurements are accessible from an online public database to encourage research and contribution in underwater vehicle design through physics-based low-order models that can accommodate hydrodynamic principles and geometric control concepts.

This thesis addresses two important issues when operating the novel three legged mobile robot STriDER (Self-excited Tripedal Dynamic Experimental Robot); how to stand up after falling down while minimizing the motor torques at the joints and considerations for gait planning. STriDER uses a unique tripedal gait to walk with high energy efficiency and has the ability to change directions. In the first version of STriDER, the concept of passive dynamic locomotion was emphasized; however, for the new version, all joints are actively controlled for robustness. The robot is inherently stable when all three feet are on the ground due to its tripod stance, but it can still fall down if it trips while taking a step or if unexpected external forces act on it. The unique structure of STriDER makes the simple task of standing up challenging for a number of reasons; the high height of the robot and long limbs require high torque at the actuators due to its large moment arms; the joint configuration and length of the limbs limit the workspace where the feet can be placed on the ground for support; the compact design of the joints allows limited joint actuation motor output torque; three limbs do not allow extra support and stability in the process of standing up. This creates a unique problem and requires novel strategies to make STriDER stand up. This thesis examines five standing up strategies unique to STriDER: three feet pushup, two feet pushup, one foot pushup, spiral pushup, and feet slipping pushup. Each strategy was analyzed and evaluated considering constraints such as static stability, friction at the feet, kinematic configuration and joint motor torque limits to determine optimal design and operation parameters. Using the findings from the analysis, experiments were conducted for all five standing up strategies to determine the most efficient standing up strategy for a given prototype using the same design and operation parameters for each method. Also, a literature review was conducted for human standing from a chair and human pushup exercises and the conclusions were compared to the analysis presented in this thesis. Many factors contribute to the development of STriDER's gait. Several considerations for gait planning as the robot takes a step are investigated, including: stability, dynamics, the body's maximum and minimum allowable heights, the swing legs foot clearance to the ground, and the range of the subsequent swing foot contact positions. A static stability margin was also developed to asses the stability of STriDER. This work will lay the foundation for future gait generation research for STriDER. Additionally, guidelines for future work on single step gait generation based on kinematics and dynamics are discussed. The findings presented will advance the capabilities and adaptability of the novel robot STriDER. By studying standing up strategies and gait planning issues, the most efficient control methods can be implement for standing up and preparing to take a step and lay out the foundations for future research and development on STriDER. / Master of Science

The ability of fish to deform their bodies in steady swimming action is gaining from robotic designers. While bound by the same physical laws, fish have evolved to move in ways that often outperform artificial systems in critical measures such as efficiency, agility, and stealth through thousands of years of natural selection. As we expand our presence in the ocean with deep-sea exploration or offshore drilling for petroleum and natural gas, the demand for prolonging underwater operations is growing significantly. Therefore, it is critical for robotic designers to understand the physics of pisciform (fish-like) locomotion and learn how to effectively implement the propulsive mechanisms into their designs to create the next generation of aquatic robots. Aiming to assist this process, this thesis presents an experimental apparatus called Towed Biolocomotion Emulator (TBE), which is capable of imitating the undulating action of different fish species in steady swimming and can be quickly adapted to different configurations with modular modules. Using the TBE device, an experiment is performed to test its hydrodynamic performance and evaluate the effectiveness of the bio-inspired locomotion implemented on such a mechanical system. The analysis of hydrodynamic data collected from the experiment shows that there exists a small range of kinematic parameters where the undulating motion of the device produces the optimal performance. This result confirms the benefits of utilizing pisciform locomotion for small-scale underwater vehicles. In addition, this thesis also proposes a reduced-order flow model using the unsteady vortex lattice method (UVLM) to predict the hydrodynamic performance of such a system. The proposed model is then validated with the experimental data collected earlier. The tool developed can be employed to quickly explore the possible design space early in the conceptual design stage for such a bio-mimetic vehicle. / Master of Science / It is no surprise that through thousands of years of natural evolution, marine species possess incredible ability to navigate through water. As we expand our presence in the sea, more and more tasks require underwater operations such as ocean exploration, oil-rig maintenance, etc. Yet, most of the underwater robotic vehicles still utilize propellers as the primary propulsive mechanism. In many cases, the bio-inspired propulsion system that mimics the swimming action of fish offers many advantages in agility, maneuverability, and stealth. With the rising interest in the field, the works presented in this thesis aim to expand our understanding of how to implement the bio-inspired propulsive mechanism to robotic design. To achieve this, a mechanical device is designed to mimic the swimming action of different fish species. Then, an experiment is performed to subject the device to different fish-like motions and test their effectiveness. In addition, a reduced-ordered model is also introduced as an alternative method to predict the hydrodynamic performance of this propulsive mechanism. The works presented in this thesis help to expand the toolbox available for the engineer to design the next generation of the underwater robotic vehicle.

Bipedal locomotion in humanoid robots is a very challenging problem within the field of robot locomotion. In this thesis, we propose and demonstrate an omni-directional walking engine that achieves stable walking using feedback from an inertial measurement unit. Our walking engine generates gaits for which the zero moment point is on the center of the supporting foot. The mechanical structure of CHARLI-L, a humanoid robot used as our test platform in this thesis, is first introduced by describing the inverse kinematics of its legs. The principles of the omni-directional gait generator that creates walking motions and overcomes the robot's mechanical deficiencies is discussed. We develop and implement two kinds of feedback controllers; one is the gait feedback controller and the other is the joint feedback controller. Both feedback controllers use proportional-derivative of the angle of the pelvis from an inertial measurement unit. The results of the experiments are presented the efficacy of our proposed walking engine. / Master of Science