We propose a collection of formal definitions for problems and solutions, and study the relationships between the two. Problems and solutions can be represented as morphisms in two categories, and the structure of problem reduction and problem-solving has the properties of a heteromorphic twisted arrow category (a generalization of the twisted arrow category) defined on them. Lagado, a compositional computational system built on a type-theoretic foundation that accounts for the resources required for computation is provided as an example.
This thesis furthermore provides the universal conditions for defining any compositional computational system. We argue that any problem can be represented as a function from the product of hom-sets of two semicategories to a rig (a kinded function) and that any procedure can also be represented as a similar kinded function. Combining all problems and procedures defined over the same subcategory of SemiCat via a solution judgment map results in a heteromorphic twisted arrow category called Laputa, which automatically provides problem-reducing and problem-solving properties.
The thesis illustrates the practical application of the theory of compositional computations systems by studying the representation of co-design problems from the theory of mathematical co-design as part of several different compositional computations systems. In the process, new results on the conditions for the solvability of co-design problems and their compositional category-theoretical properties are also presented.

As robotics matures and increases in complexity, it is more necessary than ever for robot autonomy research to be “reproducible”. Compared to other sciences, there are specific challenges to benchmarking autonomy, such as the complexity of the software stacks, the variability of the hardware and the reliance on data-driven techniques, amongst others. In this paper we describe a new concept for reproducible research, in which development and benchmarking are integrated, so that reproducibility is obtained “by design” from the beginning of the research/development processes. We provide the overall conceptual objectives to achieve this goal and then provide a concrete instance that we have built, the DUCKIENet. One of the central components of this setup is the Duckietown Autolab, a remotely accessible standardized setup that is itself also relatively low cost and reproducible. When evaluating agents, careful definition of interfaces allows users to choose among local vs. remote evaluation using simulation, logs, or the remote automated hardware setups. We validate the system by analyzing the repeatability of experiments run using the infrastructure and show that there is low variance across different robot hardware and across different remote labs.

Self-diagnosis and self-repair are some of the key challenges in deploying robotic platforms for long-term real-world applications. One of the issues that can occur to a robot is miscalibration of its sensors due to aging, environmental transients, or external disturbances. Precise calibration lies at the core of a variety of applications, due to the need to accurately perceive the world. However, while a lot of work has focused on calibrating the sensors, not much has been done towards identifying when a sensor needs to be recalibrated. This paper focuses on a data-driven approach to learn the detection of miscalibration in vision sensors, specifically RGB cameras. Our contributions include a proposed miscalibration metric for RGB cameras and a novel semi-synthetic dataset generation pipeline based on this metric. Additionally, by training a deep convolutional neural network, we demonstrate the effectiveness of our pipeline to identify whether a recalibration of the camera's intrinsic parameters is required or not.

Multi-rendezvous spacecraft trajectory optimization problems are notoriously difficult to solve. For this reason, the design space is usually pruned by using heuristics and past experience. As an alternative, the current research explores some properties of ΔV matrices which provide the minimum ΔV values for a transfer between two celestial bodies for various times of departure and transfer duration values. These can assist in solving multi-rendezvous problems in an automated way. The paper focuses on the problem of, given a set of candidate objects, how to find the sequence of N objects to rendezvous with that minimizes the total ΔV required. Transfers are considered as single algebraic objects corresponding to ΔV matrices, which allow intuitive concatenation via a generalized summation. Waiting times, both due to mission requirements and prospects for cheaper and faster future transfers, are also incorporated in the ΔV matrices. A transcription of the problem as a shortest path search on a graph can utilize a range of available efficient shortest path solvers. Given an efficient ΔV matrix estimator, the new paradigm proposed here is believed to offer an alternative to the pruning techniques currently used.