This thesis considers the problem of multi-robot task allocation with inter-agent distance constraints, e.g., due to the presence of physical tethers or communication requirements, that must be satisfied at all times. Specifically, three optimization-based formulations are explored: (i) a “Naive Method” that leverages the classical multiple traveling salesman (mTSP) formulation to find solutions that are then filtered out when the inter-agent distance constraints are violated, (ii) a “Timed Method” thatconstructs a new formulation that explicitly accounts for robot timings, including the inter-agent distance constraints, and (iii) an “Improved Naive Method” that reformulates the Naive Method with a novel graph-traversal algorithm to produce tours that, unlike the Naive Method, allow backtracking and also introduces a more systematic approach to filter out solutions that violate inter-agent distance constraints. The effectiveness of the approaches to return task allocations that satisfy the constraints are demonstrated and compared in simulation experiments.

The objective of this thesis is to propose two novel interval observer designs for different classes of linear and hybrid systems with nonlinear observations. The first part of the thesis presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations. The observer is constructed using mixed-monotone decompositions, which ensures correctness and positivity without additional constraints/assumptions. The proposed design also involves additional degrees of freedom that may improve the performance of the observer design. The proposed observer is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. The observer gains are computed using mixed-integer (linear) programs. The second part of the thesis addresses the problem of designing a novel asymptotically stable interval estimator design for hybrid systems with nonlinear dynamics and observations under the assumption of known jump times. The proposed architecture leverages mixed-monotone decompositions to construct a hybrid interval observer that is guaranteed to frame the true states. Moreover, using common Lyapunov analysis and the positive/cooperative property of the error dynamics, two approaches were proposed for constructing the observer gains to achieve uniform asymptotic stability of the error system based on mixed-integer semidefinite and linear programs, and additional degrees of freedom are incorporated to provide potential advantages similar to coordinate transformations. The effectiveness of both observer designs is demonstrated through simulation examples.

The introduction of assistive/autonomous features in cyber-physical systems, e.g., self-driving vehicles, have paved the way to a relatively new field of system analysis for safety-critical applications, along with the topic of controlling systems with performance and safety guarantees. The different works in this thesis explore and design methodologies that focus on the analysis of nonlinear dynamical systems via set-membership approximations, as well as the development of controllers and estimators that can give worst-case performance guarantees, especially when the sensor data containing information on system outputs is prone to data drops and delays. For analyzing the distinguishability of nonlinear systems, building upon the idea of set membership over-approximation of the nonlinear systems, a novel optimization-based method for multi-model affine abstraction (i.e., simultaneous set-membership over-approximation of multiple models) is designed. This work solves for the existence of set-membership over-approximations of a pair of different nonlinear models such that the different systems can be distinguished/discriminated within a guaranteed detection time under worst-case uncertainties and approximation errors. Specifically, by combining mesh-based affine abstraction methods with T-distinguishability analysis in the literature yields a bilevel bilinear optimization problem, whereby leveraging robust optimization techniques and a suitable change of variables result in a sufficient linear program that can obtain a tractable solution with T-distinguishability guarantees. Moreover, the thesis studied the designs of controllers and estimators with performance guarantees, and specifically, path-dependent feedback controllers and bounded-error estimators for time-varying affine systems are proposed that are subject to delayed observations or missing data. To model the delayed/missing data, two approaches are explored; a fixed-length language and an automaton-based model. Furthermore, controllers/estimators that satisfy the equalized recovery property (a weaker form of invariance with time-varying finite bounds) are synthesized whose feedback gains can be adapted based on the observed path, i.e., the history of observed data patterns up to the latest available time step. Finally, a robust kinodynamic motion planning algorithm is also developed with collision avoidance and probabilistic completeness guarantees. In particular, methods based on fixed and flexible invariant tubes are designed such that the planned motion/trajectories can reject bounded disturbances using noisy observations.

The need for autonomous cars has never been more vital, and for a vehicle to be completely autonomous, multiple components must work together, one of which is the capacity to park at the end of a mission. This thesis project aims to design and execute an automated parking assist system (APAS). Traditional Automated parking assist systems (APAS) may not be effective in some constrained urban parking environments because of the parking space dimension. The thesis proposes a novel four-wheel steering (4-WS) vehicle for automated parallel parking to overcome this kind of challenge. Then, benefiting from the maneuverability enabled by the 4WS system, the feasible initial parking area is vastly expanded from those for the conventional 2WS vehicles. In addition, the expanded initial area is divided into four areas where different paths are planned correspondingly. In the proposed novel APAS first, a suitable parking space is identified through ultra-sonic sensors, which are mounted around the vehicle, and then depending upon the vehicle's initial position, various compact and smooth parallel parking paths are generated. An optimization function is built to get the smoothest (i.e., the smallest steering angle change and the shortest path) parallel parking path. With the full utilization of the 4WS system, the proposed path planning algorithm can allow a larger initial parking area that can be easily tracked by the 4WS vehicles. The proposed APAS for 4WS vehicles makes the automatic parking process in restricted spaces efficient. To verify the feasibility and effectiveness of the proposed APAS, a 4WS vehicle prototype is applied for validation through both simulation and experiment results.

Soft robots provide an additional measure of safety and compliance over traditionalrigid robots. Generally, control and modelling experiments take place using a motion capture system for measuring robot configuration. While accurate, motion capture systems are expensive and require re-calibration whenever the cameras are adjusted. While advances in soft sensors contribute to a potential solution to sensing outside of a lab environment, most of these sensing methods require the sensors to be embedded into the soft robot arm. In this work, a more practical sensing method is proposed using off-the-shelf sensors and a Robust Extended Kalman Filter based sensor fusion method. Inertial measurement unit sensors and wire draw sensors are used to accurately estimate the state of the robot. An explanation for the need for sensor fusion is included in this work. The sensor fusion state estimate is compared to a motion capture measurement along with the raw inertial measurement unit reading to verify the accuracy of the results. The potential for this sensing system is further validated through Linear Quadratic Gaussian control of the soft robot. The Robust Extended Kalman Filter based sensor fusion shows an error of less than one degree when compared to the motion capture system.

Recent years, there has been many attempts with different approaches to the human-robot interaction (HRI) problems. In this paper, the multi-agent interaction is formulated as a differential game with incomplete information. To tackle this problem, the parameter estimation method is utilized to obtain the approximated solution in a real time basis. Previous studies in the parameter estimation made the assumption that the human parameters are known by the robot; but such may not be the case and there exists uncertainty in the modeling of the human rewards as well as human's modeling of the robot's rewards. The proposed method, empathetic estimation, is tested and compared with the ``non-empathetic'' estimation from the existing works. The case studies are conducted in an uncontrolled intersection with two agents attempting to pass efficiently. Results have shown that in the case of both agents having inconsistent belief of the other agent's parameters, the empathetic agent performs better at estimating the parameters and has higher reward values, which indicates the scenarios when empathy is essential: when agent's initial belief is mismatched from the true parameters/intent of the agents.

As technological advancements in silicon, sensors, and actuation continue, the development of robotic swarms is shifting from the domain of science fiction to reality. Many swarm applications, such as environmental monitoring, precision agriculture, disaster response, and lunar prospecting, will require controlling numerous robots with limited capabilities and information to redistribute among multiple states, such as spatial locations or tasks. A scalable control approach is to program the robots with stochastic control policies such that the robot population in each state evolves according to a mean-field model, which is independent of the number and identities of the robots. Using this model, the control policies can be designed to stabilize the swarm to the target distribution. To avoid the need to reprogram the robots for different target distributions, the robot control policies can be defined to depend only on the presence of a “leader” agent, whose control policy is designed to guide the swarm to a particular distribution. This dissertation presents a novel deep reinforcement learning (deep RL) approach to designing control policies that redistribute a swarm as quickly as possible over a strongly connected graph, according to a mean-field model in the form of the discrete-time Kolmogorov forward equation. In the leader-based strategies, the leader determines its next action based on its observations of robot populations and shepherds the swarm over the graph by probabilistically repelling nearby robots. The scalability of this approach with the swarm size is demonstrated with leader control policies that are designed using two tabular Temporal-Difference learning algorithms, trained on a discretization of the swarm distribution. To improve the scalability of the approach with robot population and graph size, control policies for both leader-based and leaderless strategies are designed using an actor-critic deep RL method that is trained on the swarm distribution predicted by the mean-field model. In the leaderless strategy, the robots’ control policies depend only on their local measurements of nearby robot populations. The control approaches are validated for different graph and swarm sizes in numerical simulations, 3D robot simulations, and experiments on a multi-robot testbed.