Maneuvering through 3D structures nimbly is pivotal to the advancement of legged locomotion. However, few methods have been developed that can generate 3D gaits in those terrains and fewer if none can be generalized to control dynamic maneuvers. In this thesis, foot placement planning for dynamic locomotion traversing irregular terrains is explored in three dimensional space. Given boundary values of the center of mass' apexes during the gait, sagittal and lateral Phase Plane trajectories are predicted based on multi-contact and inverted pendulum dynamics. To deal with the nonlinear dynamics of the contact motions and their dimensionality, we plan a geometric surface of motion beforehand and rely on numerical integration to solve the models. In particular, we combine multi-contact and prismatic inverted pendulum models to resolve feet transitions between steps, allowing to produce trajectory patterns similar to those observed in human locomotion. Our contributions lay in the following points: (1) the introduction of non planar surfaces to characterize the center of mass' geometric behavior; (2) an automatic gait planner that simultaneously resolves sagittal and lateral feet placements; (3) the introduction of multi-contact dynamics to smoothly transition between steps in the rough terrains. Data driven methods are powerful approaches in absence of accurate models. These methods rely on experimental data for trajectory regression and prediction. Here, we use regression tools to plan dynamic locomotion in the Phase Space of the robot's center of mass and we develop nonlinear controllers to accomplish the desired plans with accuracy and robustness. In real robotic systems, sensor noise, simplified models and external disturbances contribute to dramatic deviations of the actual closed loop dynamics with respect to the desired ones. Moreover, coming up with dynamic locomotion plans for bipedal robots and in all terrains is an unsolved problem. To tackle these challenges we propose here two robust mechanisms: support vector regression for data driven model fitting and contact planning, and trajectory based sliding mode control for accuracy and robustness. First, support vector regression is utilized to learn the data set obtained through numerical simulations, providing an analytical solution to the nonlinear locomotion dynamics. To approximate typical Phase Plane behaviors that contain infinite slopes and loops, we propose to use implicit fitting functions for the regression. Compared to mainstream explicit fitting methods, our regression method has several key advantages: 1) it models high dimensional Phase Space states by a single unified implicit function; 2) it avoids trajectory over-fitting; 3) it guarantees robustness to noisy data. Finally, based on our regression models, we develop contact switching plans and robust controllers that guarantee convergence to the desired trajectories. Overall, our methods are more robust and capable of learning complex trajectories than traditional regression methods and can be easily utilized to develop trajectory based robust controllers for locomotion. Various case studies are analyzed to validate the effectiveness of our methods including single and multi step planning in a numerical simulation and swing foot trajectory control on our Hume bipedal robot. / text

Dynamics in locomotion is highly useful, as can be seen in animals and is becomingapparent in robots. For instance, chimpanzees are dynamic climbers that canreach virtually any part of a tree and even move to neighboring trees, while sloths arequasistatic climbers confined only to a few branches. Although dynamic maneuversare undoubtedly beneficial, only a few engineered systems use them, most of whichlocomote horizontally. This is because the design and control are often extremelycomplicated.This thesis explores a family of dynamic climbing robots which extend roboticdynamic legged locomotion from horizontal motions such as walking, hopping, andrunning, to vertical motions such as leaping maneuvers. The motion of these dynamicrobots resembles the motion of an athlete jumping and climbing inside achute. Whereas this environment might be an unnavigable obstacle for a slow, quasistaticclimber, it is an invaluable source of reaction forces for a dynamic climber.The mechanisms described here achieve dynamic, vertical motions while retainingsimplicity in design and control.The first mechanism called DSAC, for Dynamic Single Actuated Climber, comprisesonly two links connected by a single oscillating actuator. This simple, openlooposcillation, propels the robot stably between two vertical walls. By rotating theaxis of revolution of the single actuator by 90 degrees, we also developed a simplerrobot that can be easily miniaturized and can be used to climb inside tubes.The DTAR, for Dynamic Tube Ascending Robot, uses a single continuously rotatingmotor, unlike the oscillating DSAC motor. This continuous rotation even furthersimplifies and enables the miniaturization of the robot to enable robust climbinginside small tubes. The last mechanism explored in this thesis is the ParkourBot,which sacrifices some of the simplicity shown in the first two mechanism in favorof efficiency and more versatile climbing. This mechanism comprises two efficientspringy legs connected to a body.We use this family of dynamic climbers to explore a minimalist approach to locomotion.We first analyze the open-loop stability characteristics of all three mechanisms.We show how an open-loop, sensorless control, such as the fixed oscillationof the DSAC’s leg can converge to a stable orbit. We also show that a change inthe mechanism’s parameters not only changes the stability of the system but alsochanges the climbing pattern from a symmetric climb to a limping, non-symmetricclimb. Corresponding analyses are presented for the DTAR and ParkourBot mechanisms.We finally show how the open-loop behavior can be used to traverse morecomplex terrains by incrementally adding feedback. We are able to achieve climbinginside a chute with wall width changes without the need for precise and fast sensingand control.

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With the ability to navigate natural and man-made environments and utilize standard human tools, humanoid robots have the potential to transform emergency response and disaster relief applications by serving as first responders in hazardous scenarios. Such applications will require major advances in humanoid control, enabling robots to traverse difficult, cluttered terrain with both speed and stability. To advance the state of the art, this dissertation presents a complete dynamic locomotion and whole-body control framework for compliant (torque-controlled) humanoids. We develop low-level, mid-level, and high-level controllers to enable low-impedance balancing and walking on compliant and uneven terrain. For low-level control, we present a cascaded joint impedance controller for series elastic humanoids with parallel actuation. A distributed controller architecture is implemented using a dual-axis motor controller that computes desired actuator forces and motor currents using simple models of the joint mechanisms and series elastic actuators. An inner-loop force controller is developed using feedforward and PID control with a model-based disturbance observer, enabling naturally compliant behaviors with low joint impedance. For mid-level control, we implement an optimization-based whole-body control strategy assuming a rigid body model of the robot. Joint torque setpoints are computed using an efficient quadratic program (QP) given desired joint accelerations, spatial accelerations, and momentum rates of change. Constraints on the centroidal dynamics, contact forces, and joint limits ensure admissibility of the optimized setpoints. Using this approach, we develop compliant standing and stepping behaviors based on simple feedback controllers. For high-level control, we present a dynamic planning and control approach for humanoid locomotion using a novel time-varying extension of the Divergent Component of Motion (DCM). By varying the natural frequency of the DCM, we are able to achieve generic vertical center of mass (CoM) trajectories during walking. Complementary reverse-time integration and model predictive control (MPC) strategies are proposed to generate dynamically feasible DCM plans over a multi-step preview window, supporting locomotion on uneven terrain. The proposed approach is validated through experimental results obtained using THOR, a 34 degree of freedom (DOF) series elastic humanoid. Rough terrain locomotion is demonstrated in simulation, and compliant locomotion and push recovery are demonstrated in hardware. We discuss practical considerations that led to a successful implementation on the THOR hardware platform and conclude with an application of the presented control framework for humanoid firefighting onboard the ex-USS Shadwell, a decommissioned Navy ship. / Ph. D.