931 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
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
Push recovery with stepping strategy based on time-projection control
In this paper, we present a simple control framework for on-line push
recovery with dynamic stepping properties. Due to relatively heavy legs in our
robot, we need to take swing dynamics into account and thus use a linear model
called 3LP which is composed of three pendulums to simulate swing and torso
dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use
a particular time-projection method to adjust the next footstep location
on-line during the motion continuously. This adjustment, which is found based
on both pelvis and swing foot tracking errors, naturally takes the swing
dynamics into account. Suggested adjustments are added to the Cartesian 3LP
gaits and converted to joint-space trajectories through inverse kinematics.
Fixed and adaptive foot lift strategies also ensure enough ground clearance in
perturbed walking conditions. The proposed structure is robust, yet uses very
simple state estimation and basic position tracking. We rely on the physical
series elastic actuators to absorb impacts while introducing simple laws to
compensate their tracking bias. Extensive experiments demonstrate the
functionality of different control blocks and prove the effectiveness of
time-projection in extreme push recovery scenarios. We also show self-produced
and emergent walking gaits when the robot is subject to continuous dragging
forces. These gaits feature dynamic walking robustness due to relatively soft
springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our
proposed architecture.Comment: 20 pages journal pape
Dynamic Walking: Toward Agile and Efficient Bipedal Robots
Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient
Optimal Walking of an Underactuated Planar Biped with Segmented Torso
Recently, underactuated bipeds with pointed feet have been studied to achieve dynamic and energy efficient robot walking patterns. However, these studies usually simplify a robot torso as one link, which is different from a human torsos containing 33 vertebrae. In this paper, therefore, we study the optimal walking of a 6-link planar biped with a segmented torso derived from its 5-link counterpart while ensuring that two models are equivalent when the additional torso joint is locked. For the walking, we suppose that each step is composed of a single support phase and an instantaneous double support phase, and two phases are connected by a plastic impact mapping. In addition, the controlled outputs named symmetry outputs capable of generating exponentially stable orbits using hybrid zero dynamics, are adopted to improve physical interpretation. The desired outputs are parameterized by BÂŽezier functions, with 5-link robot having 16 parameters to optimize and 6-link robot having 19 parameters. According to our energy criterion, the segmented torso structure may reduce energy consumption up to 8% in bipedal walking, and the maximum energy saving is achieved at high walking speeds, while leaving the criteria at low walking speeds remain similar for both robots.China CSC LCF
Deep Kernels for Optimizing Locomotion Controllers
Sample efficiency is important when optimizing parameters of locomotion
controllers, since hardware experiments are time consuming and expensive.
Bayesian Optimization, a sample-efficient optimization framework, has recently
been widely applied to address this problem, but further improvements in sample
efficiency are needed for practical applicability to real-world robots and
high-dimensional controllers. To address this, prior work has proposed using
domain expertise for constructing custom distance metrics for locomotion. In
this work we show how to learn such a distance metric automatically. We use a
neural network to learn an informed distance metric from data obtained in
high-fidelity simulations. We conduct experiments on two different controllers
and robot architectures. First, we demonstrate improvement in sample efficiency
when optimizing a 5-dimensional controller on the ATRIAS robot hardware. We
then conduct simulation experiments to optimize a 16-dimensional controller for
a 7-link robot model and obtain significant improvements even when optimizing
in perturbed environments. This demonstrates that our approach is able to
enhance sample efficiency for two different controllers, hence is a fitting
candidate for further experiments on hardware in the future.Comment: (Rika Antonova and Akshara Rai contributed equally
Bayesian Optimization Using Domain Knowledge on the ATRIAS Biped
Controllers in robotics often consist of expert-designed heuristics, which
can be hard to tune in higher dimensions. It is typical to use simulation to
learn these parameters, but controllers learned in simulation often don't
transfer to hardware. This necessitates optimization directly on hardware.
However, collecting data on hardware can be expensive. This has led to a recent
interest in adapting data-efficient learning techniques to robotics. One
popular method is Bayesian Optimization (BO), a sample-efficient black-box
optimization scheme, but its performance typically degrades in higher
dimensions. We aim to overcome this problem by incorporating domain knowledge
to reduce dimensionality in a meaningful way, with a focus on bipedal
locomotion. In previous work, we proposed a transformation based on knowledge
of human walking that projected a 16-dimensional controller to a 1-dimensional
space. In simulation, this showed enhanced sample efficiency when optimizing
human-inspired neuromuscular walking controllers on a humanoid model. In this
paper, we present a generalized feature transform applicable to non-humanoid
robot morphologies and evaluate it on the ATRIAS bipedal robot -- in simulation
and on hardware. We present three different walking controllers; two are
evaluated on the real robot. Our results show that this feature transform
captures important aspects of walking and accelerates learning on hardware and
simulation, as compared to traditional BO.Comment: 8 pages, submitted to IEEE International Conference on Robotics and
Automation 201
Input to State Stability of Bipedal Walking Robots: Application to DURUS
Bipedal robots are a prime example of systems which exhibit highly nonlinear
dynamics, underactuation, and undergo complex dissipative impacts. This paper
discusses methods used to overcome a wide variety of uncertainties, with the
end result being stable bipedal walking. The principal contribution of this
paper is to establish sufficiency conditions for yielding input to state stable
(ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and
phase-based uncertainties. In particular, it will be shown formally that
exponential input to state stabilization (e-ISS) of the continuous dynamics,
and hybrid invariance conditions are enough to realize stable walking in the
23-DOF bipedal robot DURUS. This main result will be supported through
successful and sustained walking of the bipedal robot DURUS in a laboratory
environment.Comment: 16 pages, 10 figure
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