9 research outputs found
Gait generation for underactuated compass-like robots using dissipative forces in the controller
This work addresses the problem of gait generation in underactuated compass-like biped robots using dissipative forces in the controller. Three different controllers are presented. The first one is a simultaneous interconnection and damping assignment passivity-based control with dissipative forces. The second one is an energy pumping-and-damping control, while the third one is an energy pumping or damping control action. Numerical case studies, comparisons, and critical discussions evaluate the performance of the proposed approaches
Energy pumping-and-damping for gait robustification of underactuated planar biped robots within the hybrid zero dynamics framework
This paper addresses the robust gait control for planar and passive biped robots using approaches based on energy properties. Energy pumping-and-damping passivity-based control is used to increase the robustness against uncertainties on the initial conditions of the passive gait exhibited by planar biped robots. The stability analysis is carried out by exploiting the system’s passivity and the hybrid zero dynamics method. Besides, the proposed approach is applied to new gaits that are generated using interconnection and damping assignment passivity-based control. The performance of the proposed design is evaluated through numerical simulations and compared with an existing technique
Energy Shaping of Underactuated Systems via Interconnection and Damping Assignment Passivity-Based Control with Applications to Planar Biped Robots
The sought goal of this thesis is to show that total energy shaping is an effective and versatile tool to control underactuated mechanical systems. The performance of several approaches, rooted in the port-Hamiltonian formalism, are analyzed while tackling distinct control
problems: i) equilibrium stabilization; ii) gait generation; iii) gait robustication. Firstly, a constructive solution to deal with interconnection
and damping assignment passivity-based control (IDA-PBC) for underactuated two-degree-of-freedom mechanical systems is proposed. This strategy does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending
on generalized momenta are introduced by the controller. The methodology is applied to the stabilization of a translational oscillator with a rotational actuator system, as well as, to the gait generation for
an underactuated compass-like biped robot (CBR). Then, the problem of gait generation is addressed using dissipative forces in the controller. In this sense, three distinct controllers are presented, namely simultaneous
interconnection and damping assignment passivity-based control
with dissipative forces, energy pumping-and-damping passivity-based control (EPD-PBC), and energy pumping-or-damping control. Finally, EPD-PBC is used to increase the robustness of the gait exhibited by the CBR over uncertainties on the initial conditions. The passivity of the system is exploited, as well as, its hybrid nature (using the hybrid zero dynamics method) to carry out the stability analysis. Besides, such an approach is applied to new gaits that are generated using IDA-PBC.
Numerical case studies, comparisons, and critical discussions evaluate the performance of the proposed approaches
Immersion and invariance orbital stabilization of underactuated mechanical systems with collocated pre-feedback
In this note we study the generation of attractive oscillations of a class of
mechanical systems with underactuation one. The proposed design consists of two
terms, i.e., a partial linearizing state feedback, and an immersion and
invariance orbital stabilization controller. The first step is adopted to
simplify analysis and design, however, bringing an additional difficulty that
the model loses its Euler-Lagrange structure after the collocated pre-feedback.
To address this, we propose a constructive solution to the orbital
stabilization problem via a smooth controller in an analytic form, and the
model class identified in the paper is characterized via some easily apriori
verifiable assumptions on the inertia matrix and the potential energy function
Simultaneous Position-and-Stiffness Control of Underactuated Antagonistic Tendon-Driven Continuum Robots
Continuum robots have gained widespread popularity due to their inherent
compliance and flexibility, particularly their adjustable levels of stiffness
for various application scenarios. Despite efforts to dynamic modeling and
control synthesis over the past decade, few studies have focused on
incorporating stiffness regulation in their feedback control design; however,
this is one of the initial motivations to develop continuum robots. This paper
aims to address the crucial challenge of controlling both the position and
stiffness of a class of highly underactuated continuum robots that are actuated
by antagonistic tendons. To this end, the first step involves presenting a
high-dimensional rigid-link dynamical model that can analyze the open-loop
stiffening of tendon-driven continuum robots. Based on this model, we propose a
novel passivity-based position-and-stiffness controller adheres to the
non-negative tension constraint. To demonstrate the effectiveness of our
approach, we tested the theoretical results on our continuum robot, and the
experimental results show the efficacy and precise performance of the proposed
methodology
On the equivalence of contraction and Koopman approaches for nonlinear stability and control
In this paper we prove new connections between two frameworks for analysis
and control of nonlinear systems: the Koopman operator framework and
contraction analysis. Each method, in different ways, provides exact and global
analyses of nonlinear systems by way of linear systems theory. The main results
of this paper show equivalence between contraction and Koopman approaches for a
wide class of stability analysis and control design problems. In particular:
stability or stablizability in the Koopman framework implies the existence of a
contraction metric (resp. control contraction metric) for the nonlinear system.
Further in certain cases the converse holds: contraction implies the existence
of a set of observables with which stability can be verified via the Koopman
framework. We provide results for the cases of autonomous and time-varying
systems, as well as orbital stability of limit cycles. Furthermore, the
converse claims are based on a novel relation between the Koopman method and
construction of a Kazantzis-Kravaris-Luenberger observer. We also provide a
byproduct of the main results, that is, a new method to learn contraction
metrics from trajectory data via linear system identification
Unknown Piecewise Constant Parameters Identification with Exponential Rate of Convergence
The scope of this research is the identification of unknown piecewise
constant parameters of linear regression equation under the finite excitation
condition. Compared to the known methods, to make the computational burden
lower, only one model to identify all switching states of the regression is
used in the developed procedure with the following two-fold contribution. First
of all, we propose a new truly online estimation algorithm based on a
well-known DREM approach to detect switching time and preserve time alertness
with adjustable detection delay. Secondly, despite the fact that a switching
signal function is unknown, the adaptive law is derived that provides global
exponential convergence of the regression parameters to their true values in
case the regressor is finitely exciting somewhere inside the time interval
between two consecutive parameters switches. The robustness of the proposed
identification procedure to the influence of external disturbances is
analytically proved. Its effectiveness is demonstrated via numerical
experiments, in which both abstract regressions and a second-order plant model
are used.Comment: 31 pages, 12 figure
Orbital stabilization of nonlinear systems via Mexican sombrero energy shaping and pumping-and-damping injection
International audienceIn this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method – originally proposed for stabilization of equilibria of nonlinear systems – allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes “sign” according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control