Hierarchical Control of Constrained Multi-Agent Legged Locomotion: A Data-Driven Approach

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.