The aim of this dissertation is to systematically construct a hierarchical framework that allows for robust multi-agent collaborative legged locomotion. More specifically, this work provides a detailed derivation of a torque controller that is theoretically justifiable in the context of Hybrid Zero Dynamics at the lowest level of control to produce highly robust locomotion, even when subject to uncertainty. The torque controller is based on virtual constraints and partial feedback linearization and is cast into the form of a strictly convex quadratic program. This partial feedback linearization is then relaxed through the use of a defect variable, where said defect variable is allowed only to change in a manner that is consistent with rapidly exponentially stable output dynamics through the use of a Control Lyapunov Function. The torque controller is validated in both simulation and on hardware to demonstrate the efficacy of the approach. In particular, the robot is subject to payload and push disturbances and is still able to remain stable. Furthermore, the continuity of the torque controller, in addition to robustness analysis of the periodic orbit, is also provided. At the next level of control, we consider emulating the Single Rigid Body model through the use of Behavioral Systems Theory, resulting in a data-driven model that adequately describes a quadruped at the reduced-order level. Still, due to the complexity and a considerable number of variables in the problem, the model further undergoes a $2$-norm approximation, resulting in a model that is computationally efficient enough to be used in a real-time manner for trajectory planning. In order to test the method rigorously, we consider a series of experiments to examine how the planner works when using different gait parameters than that which was used during data collection. Furthermore, the planner is compared to the traditional Single Rigid Body model to test its efficacy for reference tracking. This data-driven model is then extended to the multi-agent case, where each agent is rigidly holonomically constrained to one another. In this case, the model is used in a distributed manner using a one-step communication delay such that the coupling between agents can be adequately considered while spreading the computational demand. The trajectory planner is evaluated through various hardware experiments with three agents, and simulations are also used to display the scalability of the approach by considering five robots. Finally, this dissertation examines how traditional reduced-order models can be used in tandem with data-based models to reap the benefits of both methods. More specifically, an interconnected Single Rigid Body model is considered, where the interaction forces are described via a data-driven model. Simulations are provided to display the efficacy of this approach at the reduced order level and show that the interaction forces can be reduced by considering them in the trajectory planner. As in the previous cases, this is followed by experimental evaluation subject to external forces and different terrains. / Doctor of Philosophy / The goal of this dissertation is to create a layered control scheme for teams of quadrupeds that results in stable and robust locomotion, including a high-level trajectory planner and a low-level controller. More specifically, this work outlines an optimal torque-based whole-body controller that operates at the joint level to track desired trajectories. These trajectories are obtained by a high-level trajectory planner, which utilizes a data-driven predictive controller to create an optimal trajectory without explicitly requiring knowledge of a model. The hierarchical control scheme is then extended to consider collaborative locomotion. Namely, this work considers teams of quadrupeds that are rigidly connected to one another such that there is no relative motion between them. There are potentially large interaction forces that are applied between the robots that cannot be measured, which can result in instability. Furthermore, the models used to describe the interconnected system are prohibitively complex when being used for trajectory planning. For this reason, the data-driven model considered for a single robot is extended to create a centralized model that encapsulates not only the motion of a single robot but also its connection constraints. The resulting model is very large, making it difficult to use in a real-time manner. Therefore, this work outlines how to distribute the model such that each robot can locally plan for its own motion while also considering the coupling between them. Finally, this work provides one additional extension that combines a traditional physics-based model with a data-driven model to capitalize on the strengths of each. In particular, a physics-based model is considered as a baseline, while a data-driven model is used to describe the interaction forces between robots. In using this final extension, both improved solve times and smoother locomotion are achieved. Each of the aforementioned methods is tested thoroughly through both simulations and experiments.

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