Hu et al. [1] suggested using uncrewed vehicles in civil infrastructure asset management. Similarly, Bechtsis et al. [2] propose using uncrewed ground vehicles (UGVs) in precision farming. One of the emerging areas where such vehicles can prove helpful is assisting in postdisaster evacuation. Natural disasters, including earthquakes, tsunamis, hurricanes, and volcanic eruptions, can severely damage the urban infrastructure, leading to considerable losses. Following such events, providing timely relief and disseminating crucial information, such as safe evacuation routes, becomes essential for affected individuals' safe and organized movement. Recently, among the advanced technologies integrated into disaster response missions include uncrewed aerial vehicles (UAVs) that have been crucial in assessing the state of critical infrastructure essential services, including telecommunications, transportation, and buildings, to facilitate efficient disaster response and evacuation [3]. UAV systems have proven to be increasingly valuable in disaster relief and emergency response (DRER) efforts by enhancing the capabilities of the first responders, offering advanced predictive insights, and enabling early warning systems [4]. UAVs have assisted in diverse tasks, including remote sensing, search and rescue, forest fire detection, survey and surveillance [5].

We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints, assuming that only zero-order information is available for both the objective and constraints, and that the objective is also subject to random sampling noise. Under this setting, we propose a Derivative-Free Stochastic Sequential Quadratic Programming (DF-SSQP) method. Due to the lack of derivative information, we adopt a simultaneous perturbation stochastic approximation (SPSA) technique to randomly estimate the gradients and Hessians of both the objective and constraints. This approach requires only a dimension-independent number of zero-order evaluations -- as few as eight -- at each iteration step. A key distinction between our derivative-free and existing derivative-based SSQP methods lies in the intricate random bias introduced into the gradient and Hessian estimates of the objective and constraints, brought by stochastic zero-order approximations. To address this issue, we introduce an online debiasing technique based on momentum-style estimators that properly aggregate past gradient and Hessian estimates to reduce stochastic noise, while avoiding excessive memory costs via a moving averaging scheme. Under standard assumptions, we establish the global almost-sure convergence of the proposed DF-SSQP method. Notably, we further complement the global analysis with local convergence guarantees by demonstrating that the rescaled iterates exhibit asymptotic normality, with a limiting covariance matrix resembling the minimax optimal covariance achieved by derivative-based methods, albeit larger due to the absence of derivative information. Our local analysis enables online statistical inference of model parameters leveraging DF-SSQP. Numerical experiments on benchmark nonlinear problems demonstrate both the global and local behavior of DF-SSQP.

Contemporary robots have become exceptionally skilled at achieving specific tasks in structured environments. However, they often fail when faced with the limitless permutations of real-world unstructured environments. This motivates robotics methods which learn from experience, rather than follow a pre-defined set of rules. In this thesis, we present a range of learning-based methods aimed at enabling robots, operating in dynamic and unstructured environments, to better understand their surroundings, anticipate the actions of others, and take informed actions accordingly. In the first part of the thesis, we investigate methods which leverage learning to represent the structure and motion in a robot's operating environment, in a continuous manner.