A Dynamical System Approach for Resource-Constrained Mobile Robotics

The revolution of autonomous vehicles has led to the development of robots with abundant sensors, actuators with many degrees of freedom, high-performance computing capabilities, and high-speed communication devices. These robots use a large volume of information from sensors to solve diverse problems. However, this usually leads to a significant modeling burden as well as excessive cost and computational requirements. Furthermore, in some scenarios, sophisticated sensors may not work precisely, the real-time processing power of a robot may be inadequate, the communication among robots may be impeded by natural or adversarial conditions, or the actuation control in a robot may be insubstantial. In these cases, we have to rely on simple robots with limited sensing and actuation, minimal onboard processing, moderate communication, and insufficient memory capacity. This reality motivates us to model simple robots such as bouncing and underactuated robots making use of the dynamical system techniques. In this dissertation, we propose a four-pronged approach for solving tasks in resource-constrained scenarios: 1) Combinatorial filters for bouncing robot localization; 2) Bouncing robot navigation and coverage; 3) Stochastic multi-robot patrolling; and 4) Deployment and planning of underactuated aquatic robots. First, we present a global localization method for a bouncing robot equipped with only a clock and contact sensors. Space-efficient and finite automata-based combinatorial filters are synthesized to solve the localization task by determining the robot\u27s pose (position and orientation) in its environment. Second, we propose a solution for navigation and coverage tasks using single or multiple bouncing robots. The proposed solution finds a navigation plan for a single bouncing robot from the robot\u27s initial pose to its goal pose with limited sensing. Probabilistic paths from several policies of the robot are combined artfully so that the actual coverage distribution can become as close as possible to a target coverage distribution. A joint trajectory for multiple bouncing robots to visit all the locations of an environment is incrementally generated. Third, a scalable method is proposed to find stochastic strategies for multi-robot patrolling under an adversarial and communication-constrained environment. Then, we evaluate the vulnerability of our patrolling policies by finding the probability of capturing an adversary for a location in our proposed patrolling scenarios. Finally, a data-driven deployment and planning approach is presented for the underactuated aquatic robots called drifters that creates the generalized flow pattern of the water, develops a Markov-chain based motion model, and studies the long- term behavior of a marine environment from a flow point-of-view. In a broad summary, our dynamical system approach is a unique solution to typical robotic tasks and opens a new paradigm for the modeling of simple robotics system