skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Model reference adaptive control for nonlinear time‐varying hybrid dynamical systems
Summary This paper presents the first model reference adaptive control system for nonlinear, time‐varying, hybrid dynamical plants affected by matched and parametric uncertainties, whose resetting events are unknown functions of time and the plant's state. In addition to a control law and an adaptive law, which resemble those of the classical model reference adaptive control framework for continuous‐time dynamical systems, the proposed framework allows imposing instantaneous variations in the reference model's trajectory to rapidly steer the trajectory tracking error to zero, while retaining the closed‐loop system's ability to follow a user‐defined signal. These results are enabled by the first extension of the classical LaSalle–Yoshizawa theorem to time‐varying hybrid dynamical systems, which is presented in this paper as well. A numerical simulation shows the key features of the proposed adaptive control system and highlights its ability to reduce both the control effort and the trajectory tracking error over a classical model reference adaptive control system applied to the same problem.  more » « less
Award ID(s):
2137159
PAR ID:
10497897
Author(s) / Creator(s):
Corporate Creator(s):
Editor(s):
M. Grimble
Publisher / Repository:
Wiley
Date Published:
Journal Name:
International Journal of Adaptive Control and Signal Processing
Edition / Version:
37/8
Volume:
37
Issue:
8
ISSN:
0890-6327
Page Range / eLocation ID:
2162 to 2183
Subject(s) / Keyword(s):
Dynamics, Control
Format(s):
Medium: X Size: 1MB Other: PDF
Size(s):
1MB
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; (, SciTech)
    AIAA (Ed.)
    In this paper, a novel model reference adaptive control (MRAC) architecture for nonlinear, time-varying, hybrid dynamical systems is applied for the first time to design the control system of a multi-rotor unmanned aerial vehicle (UAV). The proposed control system is specifically designed to address problems of practical interests involving autonomous UAVs transporting unknown, unsteady payloads and subject to instantaneous variations both in their state and in their dynamics. These variations can be due, for instance, to the payload’s dynamics, impacts between the payload and its casing, and sudden payload dropping and pickup. The proposed hybrid MRAC architecture improves the UAV’s trajectory tracking performance over classical MRAC also in the presence of motor failures. The applicability of the proposed framework is validated numerically through the first use of the high-fidelity simulation environment PyChrono for autonomous UAV control system testing. 
    more » « less
  2. ; (, 2018 Annual American Control Conference (ACC))
    We model a three-link fully actuated biped as a hybrid system and propose a prediction-based control algorithm for global tracking of reference trajectories. The proposed control strategy consists of a reference system that generates the desired periodic gait, a virtual system that generates a suitable reference trajectory using prediction, and a tracking control law that steers the biped to the virtual trajectory. The proposed algorithms achieves, in finite time, tracking in two steps. We present mathematical properties that define the main elements in the hybrid predictive controller for achieving convergence to the reference within the first two steps. The results are validated through numerical simulations. 
    more » « less
  3. ; ; ; (, Journal of Dynamic Systems, Measurement, and Control)
    Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 
    more » « less
  4. ; ; (, American Control Conference)
    We develop an optimization-based framework for joint real-time trajectory planning and feedback control of feedback-linearizable systems. To achieve this goal, we define a target trajectory as the optimal solution of a time-varying optimization problem. In general, however, such trajectory may not be feasible due to , e.g., nonholonomic constraints. To solve this problem, we design a control law that generates feasible trajectories that asymptotically converge to the target trajectory. More precisely, for systems that are (dynamic) full-state linearizable, the proposed control law implicitly transforms the nonlinear system into an optimization algorithm of sufficiently high order. We prove global exponential convergence to the target trajectory for both the optimization algorithm and the original system. We illustrate the effectiveness of our proposed method on multi-target or multi-agent tracking problems with constraints. 
    more » « less
  5. ; ; ; (, Journal of Dynamic Systems, Measurement, and Control)
    Abstract Accurate control of a humanoid robot's global position (i.e., its three-dimensional (3D) position in the world) is critical to the reliable execution of high-risk tasks such as avoiding collision with pedestrians in a crowded environment. This paper introduces a time-based nonlinear control approach that achieves accurate global-position tracking (GPT) for multi-domain bipedal walking. Deriving a tracking controller for bipedal robots is challenging due to the highly complex robot dynamics that are time-varying and hybrid, especially for multi-domain walking that involves multiple phases/domains of full actuation, over actuation, and underactuation. To tackle this challenge, we introduce a continuous-phase GPT control law for multi-domain walking, which provably ensures the exponential convergence of the entire error state within the full and over actuation domains and that of the directly regulated error state within the underactuation domain. We then construct sufficient multiple-Lyapunov stability conditions for the hybrid multi-domain tracking error system under the proposed GPT control law. We illustrate the proposed controller design through both three-domain walking with all motors activated and two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3 bipedal humanoid robot demonstrate the satisfactory accuracy and convergence rate of the proposed control approach under two different cases of multi-domain walking as well as various walking speed and desired paths. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email