Robot dynamics are typically highly nonlinear and their control is a challenging research topic without a single overarching algorithm that demonstrates the best performance. In this thesis, I derive a nonlinear control algorithm that uses an analytical, closed-form solution to compute feedback with controllability-based guarantees for convergence. The proposed algorithm, based on needle variations, is computationally more efficient than alternative top-performing methods, while also \textit{a priori} guaranteeing convergence for dynamics that are controllable with first-order Lie brackets. The performance of the proposed algorithm is demonstrated on various systems and tasks, including a differential drive robot avoiding moving obstacles while converging to the target and a 3D underactuated robotic fish model tracking a target in the presence of fluid drift. The results highlight the ability of the feedback scheme to reject disturbances and run in real time, rendering it an attractive candidate nonlinear controller. As a second contribution, this thesis improves system identification methods via Koopman Operators. First, it introduces a generalizable methodology for data-driven identification of nonlinear dynamics using Koopman models that bound the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. The approach relies on synthesizing Koopman basis functions using the derivatives of general nonlinear dynamics that need not be known and can be computed numerically in real time. The error bounds are verified in different scenarios, including data-driven models learned from unknown dynamics of a pendulum with highly noisy measurements. The efficacy of the data-driven modeling approach is also validated with simulation and experimental results on the control of a tail-actuated robotic fish and is shown to outperform a well-tuned model-free PID (Proptional Integral Derivative) controller. When updated online, the data-driven model leads to significantly improved control performance in the presence of unmodeled fluid disturbance. Second, to improve learning of unknown dynamics with little data, this thesis leverages side information (i.e., general knowledge we have about the properties of a system, besides training data) and presents a new algorithm that imposes stability on the learned representation. The proposed algorithm, which is provably more memory efficient than top competing methods and achieves orders of magnitude lower modeling error, makes the learned model robust to the amount of training data and improves both prediction accuracy and control performance. The benefits of stability-constrained data-driven models are demonstrated in simulation and experiment, including the tasks of stabilizing a quadrotor in free-fall and learning the dynamics of a pusher-slider system. Conditions under which the learned dynamics of a controlled system can lead to an online certificate for stabilizing controllers, via control Lyapunov function analysis, are also discussed.

Creator

• Mamakoukas, Giorgos

DOI

• https://doi.org/10.21985/n2-t7h0-c573

Subject

• Robotics

Language

• en

Alternate Identifier

• etdadmin_upload_819790
• http://dissertations.umi.com/northwestern:15586

Keyword

• Obstacle avoidance
• Koopman operators
• Data-driven control
• Controllability-based control
• Sequential action control
• Stability

Date created

• 2021-01-01

Resource type

• Dissertation

Rights statement

• In Copyright