Dynamics modeling and control of mechanical systems using machine learning approaches and their applications to a quadrotor UAV

Abstract

In the majority of engineering problems, modeling a dynamic system usually concerned with estimating the motion of a rigid body on a Euclidean space by means of Newtonian mechanics. In Newtonian mechanics, as far as we can keep track of all the forces acting on entire bodies, we can estimate the motion of the bodies, which means the dynamic characteristics of the system can be explicitly understandable. When the system configuration is just a bit more complicated, however, it is difficult to analyze the relationship between the forces acting between the objects, and the Newtonian approach cannot easily applicable. In the field of aerospace engineering, for example, a single aircraft can be easily modeled as a rigid body. Yet, simple applications such as controlling an object suspended from an aircraft, designing a slung load transportation system with multiple UAVs, and stabilizing an inverted pendulum on top of a multi-rotor aircraft are considered to be difficult problems from the Newtonian perspective. Therefore, in this dissertation, we propose machine learning approaches in modeling and control of a dynamic system, to which the analytic solution cannot be easily achievable. To this end, we exploit differential geometry and Lagrangian mechanics to fit the problem into a differentiable program, which is far from the previous approaches that train a neural network with supervised learning by simulating given dynamics. Simply speaking, we get the next state from an automatic differentiation of a Lagrangian, which is a scalar Energy-related function. We also exploit the reinforcement learning approach to control the auto-generated system in a single machine learning pipeline. As an example, to verify the feasibility of the proposed method, the attitude dynamics of the multi-rotor UAV, which evolves on the special orthogonal group SO(3) is simulated. In addition, by designing an attitude controller with a geometric control and reinforcement learning approaches, we describe a series of processes required in dynamic modeling and control of a mechanical system.