Analytical Modeling, Control, Energy Analysis, and Path Planning of Spherical Robots

Abstract

A spherical shell and an internal actuation unit are the most common components of spherical robots. When compared with other rolling systems, they offer some distinct features such as: omnidirectional movement, high maneuverability, ease of rolling on uneven terrains, capability of recovery after collisions, and low friction. A protective shell around these robots allows operation in hazardous environments. These robots have a wide range of applications ranging from exploration to agriculture. Various sources of actuation including propellers, control moment gyroscopes, and inverted pendulums are used to mobilize these robots. Equipping these lightweight robots with propellers allows flying in order to negotiate obstacles. These benefits make spherical robots a good candidate for operating in rough environments such as search and rescue, confined spaces, mines, exploration, and planetary missions.Hybrid rolling/flying robots can address the drawbacks of aerial-only and terrestrial-only systems. Terrestrial-only systems (such as rovers and legged robots) have limitations in terms of negotiating obstacles and maneuverability on rough terrains. Additionally, getting tipped over could significantly damage the system and end the mission. Aerial-only systems are limited by their short operating time (due to constantly defying gravity) and their inability to operate in tight spaces and in the proximity of objects. Safety is another limitation for aerial-only systems. The hybrid rolling/flying system proposed in this work uses rolling to save energy and flying in order to avoid obstacles. By using the rolling mode, the system can save up to 90 percent energy compared to flying, thus addressing one the main challenges facing unmanned robots: energy consumption. Despite the fact that one of the key advantages of spherical robots is their capability to operate on uneven surfaces, control, energy analysis, and path planning of these systems have only been researched for flat terrains. Lack of accurate analytical models and reliable control algorithms on uneven terrains has delayed the implication of spherical robots. It should be mentioned that the current work on spherical robots that considers uneven surfaces, assumes that the analytical equation of the surface is known. This is not a valid assumption in a real application. The models developed in this work can be used when either an analytical equation of the terrain is accessible or the empirical data (such as a point cloud) is available. Since the flying motion of spherical robots is a well-studied subject, this work focuses on the terrestrial mode of motion. The work developed in this dissertation can be summarized as: Evaluating the dynamic equations of the proposed spherical robots on a generic terrain; Introducing a control algorithm for trajectory tracking of the proposed spherical robots on uneven terrains; Evaluating the energy required to take the proposed systems from an initial point to a desired point; Developing an optimal path to take the proposed systems from an initial point to a desired point; Providing an algorithm that evaluates traversability, separation, and energy/power consumption of the proposed spherical robots; Performing the aforementioned items above when either the analytical equation of the surface is available or the empirical information of the terrain is accessible. Additionally, a dynamics and control model for all terrains is developed. Finally, the dissertation discusses the contribution of this research and the future work.