In this article we design a backstepping control law based on geometric principles to swing up a spherical pendulum mounted on a moving quadrotor. The available degrees of freedom in the control vector also permit us to position the plane of the quadrotor parallel to the ground. The problem addressed here is, indeed, novel and has many practical applications which arise during the transport of a payload mounted on top of a quadrotor. The modeling and control law are coordinate-free and thus avoid singularity issues. The geometric treatment of the problem greatly simplifies both the modeling and control law for the system. The control action is verified and supported by numerical experiments for aggressive manoeuvres starting very close to the downward stable equilibrium position of the pendulum.
The lack of stability guarantee restricts the practical use of learning-based methods in core control problems in robotics. We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free reinforcement learning (RL) setting. We use sample-based approaches and the Almost Lyapunov function conditions to estimate the region of attraction and invariance properties through the learned Lyapunov critic functions. The methods enhance stability of neural controllers for various nonlinear systems including automobile and quadrotor control.
The energy shaping method, Controlled Lagrangian, is a well-known approach to stabilize the under-actuated Euler Lagrange (EL) systems. In this approach, to construct a control rule, some nonlinear, nonhomogeneous partial differential equations (PDEs), which are called matching conditions, must be solved. In this paper, a method is proposed to obtain an approximate solution of these matching conditions for a class of under-actuated EL systems. To develop the method, the potential energy matching condition is transformed to a set of linear PDEs using an approximation of inertia matrices. So the…
Real-Time Nonlinear MPC via Sequential Quadratic Programming with Structure-Exploiting ADMM and Interior-Point Methods for Underactuated Double-Pendulum Swing-Up
University of California at Los Angeles（加利福尼亚大学洛杉矶分校）
In this paper, we revisit the problem of learning a stabilizing controller from a finite number of demonstrations by an expert. By first focusing on feedback linearizable systems, we show how to combine expert demonstrations into a stabilizing controller, provided that demonstrations are sufficiently long and there are at least $n+1$ of them, where $n$ is the number of states of the system being controlled. When we have more than $n+1$ demonstrations, we discuss how to optimally choose the best $n+1$ demonstrations to construct the stabilizing controller. We then extend these results to a clas…
This paper introduces a framework for learning a minimum-norm stabilizing controller for a system with unknown dynamics using model-free policy optimization methods. The approach begins by first designing a Control Lyapunov Function (CLF) for a (possibly inaccurate) dynamics model for the system, along with a function which specifies a minimum acceptable rate of energy dissipation for the CLF at different points in the state-space. Treating the energy dissipation condition as a constraint on the desired closed-loop behavior of the real-world system, we use penalty methods to formulate an uncon…
The design of robust orbitally stabilizing feedback is considered. From a known orbitally stabilizing controller for a nominal, disturbance-free system, a robustifying feedback extension is designed utilizing the sliding-mode control (SMC) methodology. The main contribution of the paper is to provide a constructive procedure for designing the time-invariant switching function used in the SMC synthesis. More specifically, its zero-level set (the sliding manifold) is designed using a real Floquet-Lyapunov transformation to locally correspond to an invariant subspace of the Monodromy matrix of a …
This paper presents a method to design a min-norm Control Lyapunov Function (CLF)-based stabilizing controller for a control-affine system with uncertain dynamics using Gaussian Process (GP) regression. In order to estimate both state and input-dependent model uncertainty, we propose a novel compound kernel that captures the control-affine nature of the problem. Furthermore, by the use of GP Upper Confidence Bound analysis, we provide probabilistic bounds of the regression error, leading to the formulation of a CLF-based stability chance constraint which can be incorporated in a min-norm optim…
Adaptive control is a critical component of reliable robot autonomy in rapidly changing operational conditions. Adaptive control designs benefit from a disturbance model, which is often unavailable in practice. This motivates the use of machine learning techniques to learn disturbance features from training data offline, which can subsequently be employed to compensate the disturbances online. This paper develops geometric adaptive control with a learned disturbance model for rigid-body systems, such as ground, aerial, and underwater vehicles, that satisfy Hamilton's equations of motion over t…
