Recently, there has been an increasing interest in robotics related to multi-robot applications. Such systems can be involved in several tasks such as collaborative search and rescue, aerial transportation, surveillance, and monitoring, to name a few. There are two possible architectures for the autonomous control of multi-robot systems. In the centralized architecture, a master controller communicates with all the robots to collect information. It uses this information to make decisions for the entire system and then sends commands to each robot. In contrast, in the distributed architecture, each robot makes its own decision independent from a central authority. While distributed architecture is a more portable solution, it comes at the expense of extensive information exchange (communication). The extensive communication between robots can result in decision delays because of which distributed architecture is often impractical for systems with strict real-time constraints, e.g. when decisions have to be taken in the order of milliseconds. In this thesis, we propose a distributed framework that strikes a balance between limited communicated information and reasonable system-wide performance while running in real-time. We implement the proposed approach in a game setting of two competing teams of drones, defenders and attackers. Defending drones execute a proposed linear program algorithm (using only onboard computing modules) to obstruct attackers from infiltrating a defense zone while having minimal local message passing. Another main contribution is that we developed a realistic simulation environment as well as lab and outdoor hardware setups of customized drones for testing the system in realistic scenarios. Our software is completely open-source and fully integrated with the well-known Robot Operating System (ROS) in hopes to make our work easily reproducible and for rapid future improvements.

This thesis aims to address the real-time planning and nonlinear control of quadrupedal locomotion such that the resulting gaits are robust to various kinds of disturbances. Specifically, this work addresses two scenarios. Namely, a quasi-static formulation in which an inertial appendage (i.e., a tail) is used to assist the quadruped in negating external push disturbances, and an agile formulation which is derived in a manner such that an appendage could easily be added in future work to examine the affect of tails on agile and high-speed motions. Initially, this work presents a unified method in which bio-inspired articulated serpentine robotic tails may be integrated with walking robots, specifically quadrupeds, in order to produce stable and highly robust locomotion. The design and analysis of a holonomically constrained 2 degree of freedom (DOF) tail is shown and its accompanying nonlinear dynamic model is presented. The model created is used to develop a hierarchical control scheme which consists of a high-level path planner and a full-order nonlinear low-level controller. The high-level controller is based on model predictive control (MPC) and acts on a linear inverted pendulum (LIP) model which has been extended to include the forces produced by the tail by augmenting the LIP model with linearized tail dynamics. The MPC is used to generate center of mass (COM) and tail trajectories and is subject to the net ground reaction forces of the system, tail shape, and torque saturation of the tail in order to ensure overall feasibility of locomotion. At the lower level, a full-order nonlinear controller is implemented to track the generated trajectories using quadratic program (QP) based input-output (I-O) feedback linearization which acts on virtual constraints. The analytical results of the proposed approach are verified numerically through simulations using a full-order nonlinear model for the quadrupedal robot, Vision60, augmented with a tail, totaling at 20 DOF. The simulations include a variety of disturbances to show the robustness of the presented hierarchical control scheme. The aforementioned control scheme is then extended in the latter portion of this thesis to achieve more dynamic, agile, and robust locomotion. In particular, we examine the use of a single rigid body model as the template model for the real-time high-level MPC, which is linearized using variational based linearization (VBL) and is solved at 200 Hz as opposed to an event-based manner. The previously defined virtual constraints controller is also extended so as to include a control Lyapunov function (CLF) which contributes to both numerical stability of the QP and aids in stability of the output dynamics. This new hierarchical scheme is validated on the A1 robot, with a total of 18 DOF, through extensive simulations to display agility and robustness to ground height variations and external disturbances. The low-level controller is then further validated through a series of experiments displaying the ability for this algorithm to be readily transferred to hardware platforms. / Master of Science / This thesis aims to address the real-time planning and nonlinear control of four legged walking robots such that the resulting gaits are robust to various kinds of disturbances. Initially, this work presents a method in which a robotic tail can be integrated with legged robots to produce very stable walking patterns. A model is subsequently created to develop a multi-layer control scheme which consists of a high-level path planner, based on a reduced-order model and model predictive control techniques, that determines the trajectory for the quadruped and tail, followed by a low-level controller that considers the full-order dynamics of the robot and tail for robust tracking of the planned trajectory. The reduced-order model considered here enforces quasi-static motions which are slow but generally stable. This formulation is validated numerically through extensive full-order simulations of the Vision60 robot. This work then proceeds to develop an agile formulation using a similar multi-layer structure, but uses a reduced-order model which is more amenable to dynamic walking patterns. The low-level controller is also augmented slightly to provide additional robustness and theoretical guarantees. The latter control algorithm is extensively numerically validated in simulation using the A1 robot to show the large increase in robustness compared to the quasi-static formulation. Finally, this work presents experimental validation of the low-level controller formulated in the latter half of this work.

Robotic motion planning aspires to match the ease and efficiency with which humans move through and interact with their environment. Yet state of the art robotic planners fall short of human abilities; they are slower in computation, and the results are often of lower quality. One stumbling block in traditional motion planning is that points and paths are often considered in isolation. Many planners fail to recognize that substantial shared information exists among path alternatives. Exploitation of the geometric and topological relationships among path alternatives can therefore lead to increased efficiency and competency. These benefits include: better-informed path sampling, dramatically faster collision checking, and a deeper understanding of the trade-offs in path selection. In path sampling, the principle of locality is introduced as a basis for constructing an adaptive, probabilistic, geometric model to influence the selection of paths for collision test. Recognizing that collision testing consumes a sizable majority of planning time and that only collision-free paths provide value in selecting a path to execute on the robot, this model provides a significant increase in efficiency by circumventing collision testing paths that can be predicted to collide with obstacles. In the area of collision testing, an equivalence relation termed local path equivalence, is employed to discover when the work of testing a path has been previously performed. The swept volumes of adjoining path alternatives frequently overlap, implying that a continuum of intermediate paths exists as well. By recognizing such neighboring paths with related shapes and outcomes, up to 90% of paths may be tested implicitly in experiments, bypassing the traditional, expensive collision test and delivering a net 300% boost in collision test performance. Local path equivalence may also be applied to the path selection problem in order to recognize higher-level navigation options and make smarter choices. This thesis presents theoretical and experimental results in each of these three areas, as well as inspiration on the connections to how humans reason about moving through spaces.

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.