Alexander Ivanov

Alexander Ivanov, Gleb Nosovskiy, Alexey Chekunov et al.

Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and semi-supervised learning. Here we present new approach to manifold hypothesis checking and underlying manifold dimension estimation. In order to do it we use two very different methods simultaneously - one geometric, another probabilistic - and check whether they give the same result. Our geometrical method is a modification for sparse data of a well-known box-counting algorithm for Minkowski dimension calculation. The probabilistic method is new. Although it exploits standard nearest neighborhood distance, it is different from methods which were previously used in such situations. This method is robust, fast and includes special preliminary data transformation. Experiments on real datasets show that the suggested approach based on two methods combination is powerful and effective.

Alexander Ivanov, Mark Campbell

Cyber Physical Systems (CPS) are becoming ubiquitous and affect the physical world, yet security is seldom at the forefront of their design. This is especially true of robotic control algorithms which seldom consider the effect of a cyber attack on mission objectives and success. This work presents a secure optimal control algorithm in the face of a cyber attack on a robot's knowledge of the environment. This work focuses on cyber attack, but the results generalize to incomplete or outdated information of an environment. This work fuses ideas from robust control, optimal control, and sensor based planning to provide a generalization of stopping distance in 3D. The planner is implemented in simulation and its properties are analyzed.

Alexander Ivanov, Mark Campbell

Autonomous exploration and multi-object tracking by a team of agents have traditionally been considered as two separate, yet related, problems which are usually solved in two phases: an exploration phase then a tracking phase. The exploration problem is usually viewed through an information theoretic framework where a robotic agent attempts to gather as much information about the environment or an Object of Interest (OI). Conversely, the tracking problem attempts to maintain precise location information about an OI over time. This work proposes a single framework which enables the multi-robot multi-object problem to be solved simultaneously. A hierarchical architecture is used to coordinate robotic agents in the tracking of multiple OIs while simultaneously allowing the task to remain computationally efficient. The primary contributions of this work are a probabilistic constraint on the tracked OIs' covariances guarantees tracking performance throughout the entire mission. The automatic discovery of new OIs, a seamless transition to guaranteed tracking of discovered OIs, and the automatic balancing of exploration with the requirements of tracking.

Alexander Ivanov, Mark Campbell

Efficient robotic exploration of unknown, sensor limited, global-information-deficient environments poses unique challenges to path planning algorithms. In these difficult environments, no deterministic guarantees on path completion and mission success can be made in general. Integrated Exploration (IE), which strives to combine localization and exploration, must be solved in order to create an autonomous robotic system capable of long term operation in new and challenging environments. This paper formulates a probabilistic framework which allows the creation of exploration algorithms providing probabilistic guarantees of success. A novel connection is made between the Hamiltonian Path Problem and exploration. The Guaranteed Probabilistic Information Explorer (G-PIE) is developed for the IE problem, providing a probabilistic guarantee on path completion, and asymptotic optimality of exploration. A receding horizon formulation, dubbed RH-PIE, is presented which addresses the exponential complexity present in G-PIE. Finally, RH-PIE planner is verified via autonomous, hardware-in-the-loop experiments.