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Biped walking remains a difficult problem and robot models can greatly {facilitate} our understanding of the underlying biomechanical principles as well as their neuronal control. The goal of this study is to specifically demonstrate that stable biped walking can be achieved by combining the physical properties of the walking robot with a small, reflex-based neuronal network, which is governed mainly by local sensor signals. This study shows that human-like gaits emerge without {specific} position or trajectory control and that the walker is able to compensate small disturbances through its own dynamical properties. The reflexive controller used here has the following characteristics, which are different from earlier approaches: (1) Control is mainly local. Hence, it uses only two signals (AEA=Anterior Extreme Angle and GC=Ground Contact) which operate at the inter-joint level. All other signals operate only at single joints. (2) Neither position control nor trajectory tracking control is used. Instead, the approximate nature of the local reflexes on each joint allows the robot mechanics itself (e.g., its passive dynamics) to contribute substantially to the overall gait trajectory computation. (3) The motor control scheme used in the local reflexes of our robot is more straightforward and has more biological plausibility than that of other robots, because the outputs of the motorneurons in our reflexive controller are directly driving the motors of the joints, rather than working as references for position or velocity control. As a consequence, the neural controller and the robot mechanics are closely coupled as a neuro-mechanical system and this study emphasises that dynamically stable biped walking gaits emerge from the coupling between neural computation and physical computation. This is demonstrated by different walking experiments using two real robot as well as by a Poincar\' map analysis applied on a model of the robot in order to assess its stability. In addition, this neuronal control structure allows the use of a policy gradient reinforcement learning algorithm to tune the parameters of the neurons in real-time, during walking. This way the robot can reach a record-breaking walking speed of 3.5 leg-lengths per second after only a few minutes of online learning, which is even comparable to the fastest relative speed of human walking.

Passive dynamic walking is a manner of walking developed, partially or in whole, by the energy provided by gravity. Studying passive dynamic walking provides insight into human walking and is an invaluable tool for designing energy efficient biped robots. The objective of this research was to develop a new mathematical model of passive dynamic walking that modeled the ground reaction forces. A physical passive walker was built to validate the proposed mathematical model. The stability of the gait was analyzed using the proposed model. A novel method was created to determine the stability region of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of the gait was examined. The proposed model matched the gait of the physical passive walker exceptionally well, both in trend and magnitude. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

Passive dynamic walking is a manner of walking developed, partially or in whole, by the energy provided by gravity. Studying passive dynamic walking provides insight into human walking and is an invaluable tool for designing energy efficient biped robots. The objective of this research was to develop a new mathematical model of passive dynamic walking that modeled the ground reaction forces. A physical passive walker was built to validate the proposed mathematical model. The stability of the gait was analyzed using the proposed model. A novel method was created to determine the stability region of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of the gait was examined. The proposed model matched the gait of the physical passive walker exceptionally well, both in trend and magnitude. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

Current state-of-the-art walking controllers for humanoid robots use simple models, such as Linear Inverted Pendulum Mode (LIPM), to approximate Center of Mass(CoM) dynamics of a robot. These models are then used to generate CoM trajectories that keep the robot balanced while walking. Such controllers need prior information of foot placements, which is generated by a walking pattern generator. While the robot is walking, any change in the goal position leads to aborting the existing foot placement plan and re-planning footsteps, followed by CoM trajectory generation. This thesis proposes a tightly coupled walking pattern generator and a reactive balancing controller to plan and execute one step at a time. Walking is an emergent behavior from such a controller which is achieved by applying a virtual force in the direction of the goal. This virtual force, along with external forces acting on the robot, is used to compute desired CoM acceleration and the footstep parameters for only the next step. Step location is selected based on the capture point, which is a point on the ground at which the robot should step to stay balanced. Because each footstep location is derived as needed based on the capture point, it is not necessary to compute a complete set of footsteps. Experiments show that this approach allows for simpler inputs, results in faster operation, and is inherently immune to external perturbing and other reaction forces from the environment. Experiments are performed on Boston Dynamic's Atlas robot and NASA's Valkyrie R5 robot in simulation, and on Atlas hardware.

Current state-of-the-art walking controllers for humanoid robots use simple models, such as Linear Inverted Pendulum Mode (LIPM), to approximate Center of Mass(CoM) dynamics of a robot. These models are then used to generate CoM trajectories that keep the robot balanced while walking. Such controllers need prior information of foot placements, which is generated by a walking pattern generator. While the robot is walking, any change in the goal position leads to aborting the existing foot placement plan and re-planning footsteps, followed by CoM trajectory generation. This thesis proposes a tightly coupled walking pattern generator and a reactive balancing controller to plan and execute one step at a time. Walking is an emergent behavior from such a controller which is achieved by applying a virtual force in the direction of the goal. This virtual force, along with external forces acting on the robot, is used to compute desired CoM acceleration and the footstep parameters for only the next step. Step location is selected based on the capture point, which is a point on the ground at which the robot should step to stay balanced. Because each footstep location is derived as needed based on the capture point, it is not necessary to compute a complete set of footsteps. Experiments show that this approach allows for simpler inputs, results in faster operation, and is inherently immune to external perturbing and other reaction forces from the environment. Experiments are performed on Boston Dynamic's Atlas robot and NASA's Valkyrie R5 robot in simulation, and on Atlas hardware.

Teaching simulated biped robots to walk is a popular problem in machine learning. However, until this thesis, evolving a biped controller has not been attempted through an indirect encoding, i.e. a compressed representation of the solution, despite the fact that natural bipeds such as humans evolved through such an indirect encoding (i.e. DNA). Thus the promise for indirect encoding is to evolve gaits that rival those seen in nature. In this thesis, an indirect encoding called HyperNEAT evolves a controller for a biped robot in a computer simulation. To most effectively explore the deceptive behavior space of biped walkers, novelty search is applied as a fitness metric. The result is that although the indirect encoding can evolve a stable bipedal gait, the overall neural architecture is brittle to small mutations. This result suggests that some capabilities might be necessary to include beyond indirect encoding, such as lifetime adaptation. Thus this thesis provides fresh insight into the requisite ingredients for the eventual achievement of fluid bipedal walking through artificial evolution.

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