Gaussian Processes Model-Based Control of Underactuated Balance Robots

Abstract

Ranging from cart-pole systems and autonomous bicycles to bipedal robots, control of these underactuated balance robots aims to achieve both external (actuated) subsystem trajectory tracking and internal (unactuated) subsystem balancing tasks with limited actuation authority. This paper proposes a learning model-based control framework for underactuated balance robots. The key idea to simultaneously achieve tracking and balancing tasks is to design control strategies in slow-and fast-time scales, respectively. In slow-time scale, model predictive control (MPC) is used to generate the desired internal subsystem trajectory that encodes the external subsystem tracking performance and control input. In fast-time scale, the actual internal trajectory is stabilized to the desired internal trajectory by using an inverse dynamics controller. The coupling effects between the external and internal subsystems are captured through the planned internal trajectory profile and the dual structural properties of the robotic systems. The control design is based on Gaussian processes (GPs) regression model that are learned from experiments without need of priori knowledge about the robot dynamics nor successful balance demonstration. The GPs provide estimates of modeling uncertainties of the robotic systems and these uncertainty estimations are incorporated in the MPC design to enhance the control robustness to modeling errors. The learning-based control design is analyzed with guaranteed stability and performance. The proposed design is demonstrated by experiments on a Furuta pendulum and an autonomous bikebot.

Nonlinear UGV Identification Methods via the Gaussian Process Regression Model for Control System Design

“…The combination with a MPC strategy results in safe and stable control under changing friction road conditions. In [31], a learning-based control approach for underactuated balance robots was considered and a GP regression model was incorporated to enhance robustness to modeling errors.…”

Kernel-Based Hamilton–Jacobi Equations for Data-Driven Optimal and H-Infinity Control

“…While practical systems may not be completely described by (13), kernel functions have recently become popular and promising for representing unknown nonlinear systems in fields of system identification and machine learning [32]. Indeed, the kernel-based drift term model f (x) in (13) includes several functions, such as kernel ridge regression models [4], GP models [5], and GP-based state-dependent coefficient models [8].…”

“…Such kernel-based models include kernel ridge regression models [4], Gaussian processes (GPs) [5]- [7], and GP-based state-dependent coefficient models [8]. Successful utilization of the GPs can be seen in control systems [9]- [13]. This study focuses on data-driven methods using kernel-based models to design controllers for unknown systems.…”

On-Line Learning for Planning and Control of Underactuated Robots With Uncertain Dynamics

“…The control design is tailored to this specific system, and cannot be easily extended to generic underactuated robots. In [28], a learning scheme is proposed to realize trajectory tracking of underactuated balance robots (e.g., a Furuta pendulum); because of the simpler balancing task, the reference trajectory of the active joints is not replanned and stabilization in the large is never addressed.…”