1,887 research outputs found
Safe Learning of Quadrotor Dynamics Using Barrier Certificates
To effectively control complex dynamical systems, accurate nonlinear models
are typically needed. However, these models are not always known. In this
paper, we present a data-driven approach based on Gaussian processes that
learns models of quadrotors operating in partially unknown environments. What
makes this challenging is that if the learning process is not carefully
controlled, the system will go unstable, i.e., the quadcopter will crash. To
this end, barrier certificates are employed for safe learning. The barrier
certificates establish a non-conservative forward invariant safe region, in
which high probability safety guarantees are provided based on the statistics
of the Gaussian Process. A learning controller is designed to efficiently
explore those uncertain states and expand the barrier certified safe region
based on an adaptive sampling scheme. In addition, a recursive Gaussian Process
prediction method is developed to learn the complex quadrotor dynamics in
real-time. Simulation results are provided to demonstrate the effectiveness of
the proposed approach.Comment: Submitted to ICRA 2018, 8 page
Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
Many modern nonlinear control methods aim to endow systems with guaranteed
properties, such as stability or safety, and have been successfully applied to
the domain of robotics. However, model uncertainty remains a persistent
challenge, weakening theoretical guarantees and causing implementation failures
on physical systems. This paper develops a machine learning framework centered
around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and
unmodeled dynamics in general robotic systems. Our proposed method proceeds by
iteratively updating estimates of Lyapunov function derivatives and improving
controllers, ultimately yielding a stabilizing quadratic program model-based
controller. We validate our approach on a planar Segway simulation,
demonstrating substantial performance improvements by iteratively refining on a
base model-free controller
Neural Lyapunov Control
We propose new methods for learning control policies and neural network
Lyapunov functions for nonlinear control problems, with provable guarantee of
stability. The framework consists of a learner that attempts to find the
control and Lyapunov functions, and a falsifier that finds counterexamples to
quickly guide the learner towards solutions. The procedure terminates when no
counterexample is found by the falsifier, in which case the controlled
nonlinear system is provably stable. The approach significantly simplifies the
process of Lyapunov control design, provides end-to-end correctness guarantee,
and can obtain much larger regions of attraction than existing methods such as
LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality
solutions for challenging control problems.Comment: NeurIPS 201
Data-Efficient Characterization of the Global Dynamics of Robot Controllers with Confidence Guarantees
This paper proposes an integration of surrogate modeling and topology to
significantly reduce the amount of data required to describe the underlying
global dynamics of robot controllers, including closed-box ones. A Gaussian
Process (GP), trained with randomized short trajectories over the state-space,
acts as a surrogate model for the underlying dynamical system. Then, a
combinatorial representation is built and used to describe the dynamics in the
form of a directed acyclic graph, known as {\it Morse graph}. The Morse graph
is able to describe the system's attractors and their corresponding regions of
attraction (\roa). Furthermore, a pointwise confidence level of the global
dynamics estimation over the entire state space is provided. In contrast to
alternatives, the framework does not require estimation of Lyapunov functions,
alleviating the need for high prediction accuracy of the GP. The framework is
suitable for data-driven controllers that do not expose an analytical model as
long as Lipschitz-continuity is satisfied. The method is compared against
established analytical and recent machine learning alternatives for estimating
\roa s, outperforming them in data efficiency without sacrificing accuracy.
Link to code: https://go.rutgers.edu/49hy35e
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