This thesis explores the field of legged robots with reduced degree-of-freedom (DOF) leg mechanisms. Multi-legged robots have drawn interest among researchers due to their high level of adaptability on unstructured terrains. However, conventional legged robots require multiple degrees of freedom and each additional degree of freedom increases the overall weight and complexity of the system. Additionally, the complexity of the control algorithms must be increased to provide mobility, stabilization, and maneuvering. Normally, robotic legs are designed with at least three degrees of freedom resulting in complex articulated mechanisms, which limits the applicability of such robots in real-world applications. However, reduced DOF leg mechanisms come with reduced tasking capabilities, such as maintaining constant body height and velocity during locomotion. To address some of the challenges, this thesis proposes a novel bipedal robot with reduced DOF leg mechanisms. The proposed leg mechanism utilizes the Reuleaux triangle to generate the foot trajectory to achieve a constant body height during locomotion while maintaining a constant velocity. By using a differential drive, the robot is also capable of steering. In addition to the analytical results of the trajectory profile of each leg, the thesis provides a trajectory function of the Reuelaux triangle cam with respect to time such that the robot can maintain a constant velocity and constant body height during walking. An experimental prototype of the bipedal robot was integrated and experiments were conducted to evaluate the walking capability of the robot. Ongoing future work of the proposed design is also outlined in the thesis. / Master of Science / Bipedal robots are a type of legged robots that use two legs to move. Legs require multiple degrees of freedom to provide propulsion, stabilization, and maneuvering. Additional degrees of freedom of the leg result in a heavier robot, more complex control method, and more energy consumption. However, reduced degree of freedom legs result in a tradeoff between certain tasking capabilities for easier controls and lower energy consumption. As an attempt to overcome these challenges, this thesis presents a robot design with a reduced degree of freedom leg mechanism. The design of the mechanism is described in detail with its preliminary analysis. In addition, this thesis presents experimental validation with the robot which validates that the robot is capable of moving with constant body height at constant velocity while being of capable of steering. The thesis concludes with a discussion of the future work.

Bipedal robots offer a uniquely flexible platform capable of navigating complex, human-centric environments. This makes them ideally suited for a variety of missions, including disaster response and relief, emergency scenarios, or exoskeleton systems for individuals with disabilities. This, however, requires significant advances in humanoid locomotion and control, as they are still slow, unnatural, inefficient, and relatively unstable. The work of this dissertation the state of the art with the aim was of increasing the robustness and efficiency of these bipedal walking platforms. We present a series of control improvements to enable reliable, robust, natural bipedal locomotion that was validated on a variety of bipedal robots using both hardware and simulation experiments. A huge part of reliable walking involves maximizing the robot's control authority. We first present the development of a model predictive controller to both control the ground reaction forces and perform step adjustment for walking stabilization using a mixed-integer quadratic program. This represents the first model predictive controller to include step rotation in the optimization and leverage the capabilities of the time-varying divergent component of motion for navigating rough terrain. We also analyze the potential capabilities of model predictive controllers for the control of bipedal walking. As an alternative to standard trajectory optimization-based model predictive controls, we present several optimization-based control schemes that leverage more traditional bipedal walking control approaches by embedding a proportional feedback controller into a quadratic program. This controller is capable of combining multiple feedback mechanisms: ground reaction feedback (the "ankle strategy"), angular momentum (the "hip strategy"), swing foot speed up, and step adjustment. This allows the robot to effectively shift its weight, pitch its torso, and adjust its feet to retain balance, while considering environmental constraints, when available. To enable the robot to walk with straightened legs, we present a strategy that insures that the dynamic plans are kinematically and dynamically feasible to execute using straight legs. The effects of timing on dynamic plans are typically ignored, resulting in them potentially requiring significantly bending the legs during execution. This algorithm modifies the step timings to insure the plan can be executed without bending the legs beyond certain angle, while leaving the desired footsteps unmodified. To then achieve walking with straight legs we then presented a novel approach for indirectly controlling the center of mass height through the leg angles. This avoids complicated height planning techniques that are both computationally expensive and often not general enough to consider variable terrain by effectively biasing the solution of the whole-body controller towards using straighter legs. To incorporate the toe-off motion that is essential to both natural and straight leg walking, we also present a strategy for toe-off control that allows it to be an emergent behavior of the whole-body controller. The proposed approach was demonstrated through a series of simulation and experimental results on a variety of platforms. Model predictive control for step adjustment and rough terrain is illustrated in simulation, while the other step adjustment strategies and straight leg walking approaches are presented recovering from external disturbances and walking over a variety of terrains in hardware experiments. We discuss many of the practical considerations and limitations required when porting simulation-based controller development to hardware platforms. Using the presented approaches, we also demonstrated a important concept: using whole-body control frameworks, not every desired motion need be directly commanded. Many of these motions, such as toe-off, may simply be emergent behaviors that result by attempting to satisfy other objectives, such as desired reaction forces. We also showed that optimization is a very powerful tool for walking control, able to determine both stabilizing inputs and joint torques. / Ph. D. / Bipedal robots offer a uniquely flexible platform capable of navigating the complex, humancentric environment that we live in. This makes them ideally suited for a variety of missions, including disaster response and relief, emergency scenarios, or exoskeleton systems for individuals with disabilities. This, however, requires significant advances in humanoid locomotion and control, as they are still slow, unnatural, inefficient, and relatively unstable. The work of this dissertation aims to increase the robustness and efficiency of these bipedal walking platforms. To increase the overall stability of the robot while walking, we aimed to develop new control schemes that incorporate more of the same balance strategies used by people. These include the adjustment of ground reaction forces (the “ankle strategy”, shifting weight), angular momentum (the “hip strategy”, pitching the torso and windmilling the arms), swing foot speed up, and step adjustment. Using these approaches, the robot is able to walk much more stably. With the ability to use human-like control strategies, the next step is to develop appropriate methods to allow it to walk with straighter legs. Without correct step timing, it may be necessary at times to significantly bend the knees to take the specified step. We develop an approach to adjust the step timing to decrease the required knee bend of the robot. We then present an approach for indirectly controlling the robot height through the knee angles. This avoids traditional complicated height planning techniques that are both computationally hard and not general enough to consider complex terrain. To incorporate the toe-off motion that is essential to both natural and straight leg walking, we also present a new strategy for toe-off that allows it to emerge natural from the controller. We present the proposed approach through a series of simulation and experimental results on several robots and in several environments. We discuss many of the practical considerations and limitations required when porting simulation-based controller development to hardware platforms. Using the presented approaches, we also demonstrated an important concept: using whole-body control frameworks, not every desired motion need be directly commanded. Many of these motions, such as toe-off, may simply be emergent behaviors that result by attempting to satisfy other objectives, such as desired reaction forces. We also showed that optimization is a very powerful tool for walking control, able to determine both stabilizing inputs and joint torques.

This thesis poses a feedback control method for obtaining humanlike bipedal walking on a human-inspired hybrid biped model. The end goal was to understand better the fundamental mechanisms that underlie bipedal walking in the hopes that this newfound understanding will facilitate better mechanical and control design for bipedal robots. Bipedal walking is hybrid in nature, characterized by periodic contact between a robot and the environment, i.e., the ground. Dynamic models derived from Lagrangians modeling mechanical systems govern the continuous dynamics while discrete dynamics were handed by an impact model using impulse-like forces and balancing angular momentum. This combination of continuous and discrete dynamics motivated the use of hybrid systems for modeling purposes. The framework of hybrid systems was used to model three-dimensional bipedal walking in a general setup for a robotic model with a hip, knees, and feet with the goal of obtaining stable walking. To achieve three-dimensional walking, functional Routhian reduction was used to decouple the sagittal and coronal dynamics. By doing so, it was possible to achieve walking in the two-dimensional sagittal plane on the three-dimensional model, restricted to operate in the sagittal plane. Imposing this restriction resulted in a reduced-order model, referred to as the sagittally-restricted model. Sagittal control in the form of controlled symmetries and additional control strategies was used to achieve stable walking on the sagittally-restricted model. Functional Routhian reduction was then applied to the full-order system. The sagittal control developed on the reduced-order model was used with reduction to achieve walking in three dimensions in simulation. The control schemes described resulted in walking which was remarkably anthropomorphic in nature. This observation is surprising given the simplistic nature of the controllers used. Moreover, the two-dimensional and three-dimensional dynamics were completely decoupled inasmuch as the dynamic models governing the sagittal motion were equivalent. Additionally, the reduction resulted in swaying in the lateral plane. This motion, which is generally present in human walking, was unplanned and was a side-effect of the decoupling process. Despite the approximate nature of the reduction, the motion was still almost completely decoupled with respect to the sagittal and coronal planes.

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This thesis presents an approach towards experimental realization of underactuated bipedal robotic walking using human data. Human-inspired control theory serves as the foundation for this work. As the name, "human-inspired control," suggests, by using human walking data, certain outputs (termed human outputs) are found which can be represented by simple functions of time (termed canonical walking functions). Then, an optimization problem is used to determine the best fit of the canonical walking function to the human data, which guarantees a physically realizable walking for a specific bipedal robot. The main focus of this work is to construct a control scheme which takes the optimization results as input and delivers human-like walking on the real-world robotic platform - AMBER. To implement the human-inspired control techniques experimentally on a physical bipedal robot AMBER, a simple voltage based control law is presented which utilizes only the human outputs and canonical walking function with parameters obtained from the optimization. Since this controller does not require model inversion, it can be implemented efficiently in software. Moreover, applying this methodology to AMBER, experimentally results in robust and efficient "human-like" robotic walking.

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No description available.

Military, Medical, Exploratory, and Commercial robots have much to gain from exchanging wheels for legs. However, the equations of motion of dynamic bipedal walker models are highly coupled and non-linear, making the selection of an appropriate control scheme difficult. A temporal difference reinforcement learning method known as Q-learning develops complex control policies through environmental exploration and exploitation. As a proof of concept, Q-learning was applied through simulation to a benchmark single pendulum swing-up/balance task; the value function was first approximated with a look-up table, and then an artificial neural network. We then applied Evolutionary Function Approximation for Reinforcement Learning to effectively control the swing-leg and torso of a 3 degree of freedom active dynamic bipedal walker in simulation. The model began each episode in a stationary vertical configuration. At each time-step the learning agent was rewarded for horizontal hip displacement scaled by torso altitude--which promoted faster walking while maintaining an upright posture--and one of six coupled torque activations were applied through two first-order filters. Over the course of 23 generations, an approximation of the value function was evolved which enabled walking at an average speed of 0.36 m/s. The agent oscillated the torso forward then backward at each step, driving the walker forward for forty-two steps in thirty seconds without falling over. This work represents the foundation for improvements in anthropomorphic bipedal robots, exoskeleton mechanisms to assist in walking, and smart prosthetics. / Master of Science

The work presented in this thesis was inspired by one of the most fascinating classes of naturally occurring molecules: bipedal motor proteins from the kinesin, dynein and myosin superfamilies walk along cellular tracks, carrying out essential tasks, such as vesicle transport, muscle contraction or force generation. Although a few synthetic mimicks based on DNA have been described, small-molecule analogues that exhibit the most important characteristics of the biological walkers were still missing until recently. In this thesis, the design, synthesis and operation of several small-molecule walker-track systems is described. All presented systems share a similar molecular architecture, featuring disulfide and hydrazone walker-track linkages, yet deviate fundamentally in the mechanism and energy input that is required for directional walker transport. Chapter I includes an overview of the biological walker proteins, as well as a comprehensive review of the DNA-based mimicks published to date. A set of fundamental walker characteristics is identified and special emphasis is given to the underlying physical mechanisms. Chapter II describes a series of experiments, which lay the groundwork for all smallmolecule walker systems presented in the following Chapters of this thesis. The mutually exclusive nature of disulfide and hydrazone exchange under basic and acidic reaction conditions, was demonstrated using an unprecedented type of macrocycle. The first small-molecule walker-track system is described in Chapter III. Due to the passive nature of both the track and the walker unit, an oscillation of acidic and basic reaction conditions led to a directionally un-biased, intramolecular ‘diffusion’ of the walker unit along the track. Using an irreversible redox-reaction for one of the foot-track exchange reactions conferred a certain degree of directionality to the walking sequence, with the oxidant iodine providing the chemical fuel for the underlying Brownian information ratchet mechanism. Chapter IV contains a comprehensive investigation of the dynamic properties of a series of walker-track conjugates derived from the walker-track conjugate presented in Chapter III. The most significant observation was that ring strain appears to be a requirement for the emergence of directional bias, a phenomenon that has also been found in biological walkers. In Chapter V a different type of walker-track conjugate is described, in which the track plays an active role and light is used as the fuel required for directional walker transport. The key for achieving directionality was the presence of a stilbene unit as part of the molecular track, through which ring strain could be induced in the isomer where the walker unit bridges the E-stilbene linkage. Significantly, the underlying Brownian energy ratchet mechanism allowed walker transport in either direction of the molecular track. Chapters II to V are presented in the form of articles that have recently been published or will be published in due course in peer-reviewed journals. No attempt has been made to re-write this work out of context, other than to avoid repetition, insert crossreferences to other Chapters (where appropriate) and to ensure consistency of presentation throughout this thesis. Chapters II, III, IV and V are reproduced in the Appendix, in their published formats. The Outlook contains closing remarks about the scope and significance of the presented work as well as ideas for the design and operation of a next generation of small-molecule walkers, some of which are well under way in the laboratory.

<p>U tezi je prikazan novi metod za sintezu i realizaciju dvonožnog<br />veštačkog hoda koji se zasniva na upotrebi jednostavnih pokreta čijim<br />je kombinovanjem moguće realizovati kompleksne pokrete kao što je<br />hod, a čiji se parametri mogu menjati tokom kretanja. Time je omogućeno<br />da se na osnovu informacija o nameravanom kretanju i stanja okoline<br />izvrši sinteza kretanja izborom i kombinacijom jednostavnih<br />bazičnih pokreta koje se nazivaju primitivi. Takođe je omogućeno da se,<br />tokom izvršavanja hoda bez njegovog prekida, menjaju parametri<br />kretanja kao što su brzina hoda, dužina koraka, pravac kretanja i<br />visina podizanja noge tokom prenosne faze. Potvrda je data kroz<br />eksperimentalne rezultate koji su sprovedeni simulacijom na<br />dinamičkom modelu humanoidnog robota.</p> / <p>This dissertation presents new method for the synthesis and realization of<br />biped artificial walk based on the use of simple movements that can be<br />combined in order to achieve complex movements such as walk, whereas it<br />is possible to change the motion parameters at any time. It means that,<br />based on the information about intended movement and current state of the<br />environment, it is possible to synthesize motion by selecting and tying simple<br />movements, i.e. motion primitives. It also enables the robot to change<br />walking parameters online such as walking speed, direction of walk, foot<br />length during swing phase and step length. Proof of this method is given by<br />experimental results obtained during the simulation on a dynamic model of<br />humanoid robot.</p>