13,972 research outputs found
Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion
Underactuation is ubiquitous in human locomotion and should be ubiquitous in
bipedal robotic locomotion as well. This chapter presents a coherent theory for
the design of feedback controllers that achieve stable walking gaits in
underactuated bipedal robots. Two fundamental tools are introduced, virtual
constraints and hybrid zero dynamics. Virtual constraints are relations on the
state variables of a mechanical model that are imposed through a time-invariant
feedback controller. One of their roles is to synchronize the robot's joints to
an internal gait phasing variable. A second role is to induce a low dimensional
system, the zero dynamics, that captures the underactuated aspects of a robot's
model, without any approximations. To enhance intuition, the relation between
physical constraints and virtual constraints is first established. From here,
the hybrid zero dynamics of an underactuated bipedal model is developed, and
its fundamental role in the design of asymptotically stable walking motions is
established. The chapter includes numerous references to robots on which the
highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte
Dynamically Stable 3D Quadrupedal Walking with Multi-Domain Hybrid System Models and Virtual Constraint Controllers
Hybrid systems theory has become a powerful approach for designing feedback
controllers that achieve dynamically stable bipedal locomotion, both formally
and in practice. This paper presents an analytical framework 1) to address
multi-domain hybrid models of quadruped robots with high degrees of freedom,
and 2) to systematically design nonlinear controllers that asymptotically
stabilize periodic orbits of these sophisticated models. A family of
parameterized virtual constraint controllers is proposed for continuous-time
domains of quadruped locomotion to regulate holonomic and nonholonomic outputs.
The properties of the Poincare return map for the full-order and closed-loop
hybrid system are studied to investigate the asymptotic stabilization problem
of dynamic gaits. An iterative optimization algorithm involving linear and
bilinear matrix inequalities is then employed to choose stabilizing virtual
constraint parameters. The paper numerically evaluates the analytical results
on a simulation model of an advanced 3D quadruped robot, called GR Vision 60,
with 36 state variables and 12 control inputs. An optimal amble gait of the
robot is designed utilizing the FROST toolkit. The power of the analytical
framework is finally illustrated through designing a set of stabilizing virtual
constraint controllers with 180 controller parameters.Comment: American Control Conference 201
Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot
This paper presents three feedback controllers that achieve an asymptotically
stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot
consisting of a torso, two legs, and passive (unactuated) point feet. The
contact between the robot and the walking surface is assumed to inhibit yaw
rotation. The studied robot has 8 DOF in the single support phase and 6
actuators. The interest of studying robots with point feet is that the robot's
natural dynamics must be explicitly taken into account to achieve balance while
walking. We use an extension of the method of virtual constraints and hybrid
zero dynamics, in order to simultaneously compute a periodic orbit and an
autonomous feedback controller that realizes the orbit. This method allows the
computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model.
The stability of the walking gait under closed-loop control is evaluated with
the linearization of the restricted Poincar\'e map of the hybrid zero dynamics.
Three strategies are explored. The first strategy consists of imposing a
stability condition during the search of a periodic gait by optimization. The
second strategy uses an event-based controller. In the third approach, the
effect of output selection is discussed and a pertinent choice of outputs is
proposed, leading to stabilization without the use of a supplemental
event-based controller
Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops
Impedance control is a well-established technique to control interaction
forces in robotics. However, real implementations of impedance control with an
inner loop may suffer from several limitations. Although common practice in
designing nested control systems is to maximize the bandwidth of the inner loop
to improve tracking performance, it may not be the most suitable approach when
a certain range of impedance parameters has to be rendered. In particular, it
turns out that the viable range of stable stiffness and damping values can be
strongly affected by the bandwidth of the inner control loops (e.g. a torque
loop) as well as by the filtering and sampling frequency. This paper provides
an extensive analysis on how these aspects influence the stability region of
impedance parameters as well as the passivity of the system. This will be
supported by both simulations and experimental data. Moreover, a methodology
for designing joint impedance controllers based on an inner torque loop and a
positive velocity feedback loop will be presented. The goal of the velocity
feedback is to increase (given the constraints to preserve stability) the
bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016
Analytical and experimental stability investigation of a hardware-in-the-loop satellite docking simulator
The European Proximity Operation Simulator (EPOS) of the DLR-German Aerospace
Center is a robotics-based simulator that aims at validating and verifying a
satellite docking phase. The generic concept features a robotics tracking
system working in closed loop with a force/torque feedback signal. Inherent
delays in the tracking system combined with typical high stiffness at contact
challenge the stability of the closed-loop system. The proposed concept of
operations is hybrid: the feedback signal is a superposition of a measured
value and of a virtual value that can be tuned in order to guarantee a desired
behavior. This paper is concerned with an analytical study of the system's
closed-loop stability, and with an experimental validation of the hybrid
concept of operations in one dimension (1D). The robotics simulator is modeled
as a second-order loop-delay system and closed-form expressions for the
critical delay and associated frequency are derived as a function of the
satellites' mass and the contact dynamics stiffness and damping parameters. A
numerical illustration sheds light on the impact of the parameters on the
stability regions. A first-order Pade approximation provides additional means
of stability investigation. Experiments were performed and tests results are
described for varying values of the mass and the damping coefficients. The
empirical determination of instability is based on the coefficient of
restitution and on the observed energy. There is a very good agreement between
the critical damping values predicted by the analysis and observed during the
tests...Comment: 16 page
Mobility of bodies in contact. I. A 2nd-order mobility index formultiple-finger grasps
Using a configuration-space approach, the paper develops a 2nd-order mobility theory for rigid bodies in contact. A major component of this theory is a coordinate invariant 2nd-order mobility index for a body, B, in frictionless contact with finger bodies A1,...A k. The index is an integer that captures the inherent mobility of B in an equilibrium grasp due to second order, or surface curvature, effects. It differentiates between grasps which are deemed equivalent by classical 1st-order theories, but are physically different. We further show that 2nd-order effects can be used to lower the effective mobility of a grasped object, and discuss implications of this result for achieving new lower bounds on the number of contacting finger bodies needed to immobilize an object. Physical interpretation and stability analysis of 2nd-order effects are taken up in the companion pape
Structural dynamics branch research and accomplishments to FY 1992
This publication contains a collection of fiscal year 1992 research highlights from the Structural Dynamics Branch at NASA LeRC. Highlights from the branch's major work areas--Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are included in the report as well as a listing of the fiscal year 1992 branch publications
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