We introduce a novel method to estimate the essential matrix for two-view Structure from Motion (SfM). We show that every 3 × 3 essential matrix can be embedded in a 4 × 4 rotation having its bottom right entry fixed to zero; we call the latter the quintessential matrix. This embedding leads to rich relations with the space of 4-D rotations, quaternions, and the classical twisted-pair ambiguity in two-view SfM. We use this structure to derive a succession of semidefinite relaxations that require fewer parameters than the existing non-minimal solvers and yield faster convergence with certifiable optimality. We then exploit the low-rank geometry of these relaxations to reduce them to an equivalent optimization on a Riemannian manifold and solve them via the Riemannian Staircase method. The experimental evaluation confirms that our algorithm always finds the globally optimal solution and outperforms the existing non-minimal methods. We make our implementations open source .1.

In this paper we introduce a novel SLAM system for 2-D indoor environments that relies only on limited sensing. Our fully autonomous system uses only the trajectory of the robot around walls and objects in the environment as landmarks and is capable of robust and long-term exploration and mapping of a broad range of household floor plans. Rank-deficient and full-rank factors are created when the robot observes existing trajectory-based landmarks, and they are filtered and added in a pose graph, which is optimized periodically. The mission space is mapped by efficient adaptive local mapping algorithms. The proposed SLAM system has been extensively tested in various scenarios, and experimental results show its robustness and accuracy.

Search and Rescue (SAR) is an important part of several applications of national and social interest. Existing solutions for search missions in both terrestrial and aerial domains are mostly limited to single agent and specific environments; however, search missions can significantly benefit from the use of multiple agents that can quickly adapt to new environments. In this paper, we propose a framework based on Multi-Agent Deep Reinforcement Learning (MADRL) that realizes the actor-critic framework in a distributed manner for coordinating multiple Unmanned Aerial Vehicles (UAVs) in the exploration of unknown regions. One of the original aspects of our work is that the actors represent simulated or actual UAVs exploring the environment in parallel instead of traditional computer threads. Also, we propose addition of Long Short Term Memory (LSTM) neural network layers to the actor and critic architectures to handle imperfect communication and partial observability scenarios. The proposed approach has been evaluated in a grid world and has been compared against other competing algorithms such as Multi-Agent Q-Learning, Multi-Agent Deep Q-Learning to show its advantages. More generally, our approach could be extended to image-based/continuous action space environments as well.