3,441 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
On Advanced Mobility Concepts for Intelligent Planetary Surface Exploration
Surface exploration by wheeled rovers on Earth's Moon (the two Lunokhods) and Mars (Nasa's Sojourner and the two MERs) have been followed since many years already very suc-cessfully, specifically concerning operations over long time. However, despite of this success, the explored surface area was very small, having in mind a total driving distance of about 8 km (Spirit) and 21 km (Opportunity) over 6 years of operation. Moreover, ESA will send its ExoMars rover in 2018 to Mars, and NASA its MSL rover probably this year. However, all these rovers are lacking sufficient on-board intelligence in order to overcome longer dis-tances, driving much faster and deciding autonomously on path planning for the best trajec-tory to follow. In order to increase the scientific output of a rover mission it seems very nec-essary to explore much larger surface areas reliably in much less time. This is the main driver for a robotics institute to combine mechatronics functionalities to develop an intelligent mo-bile wheeled rover with four or six wheels, and having specific kinematics and locomotion suspension depending on the operational terrain of the rover to operate. DLR's Robotics and Mechatronics Center has a long tradition in developing advanced components in the field of light-weight motion actuation, intelligent and soft manipulation and skilled hands and tools, perception and cognition, and in increasing the autonomy of any kind of mechatronic systems. The whole design is supported and is based upon detailed modeling, optimization, and simula-tion tasks. We have developed efficient software tools to simulate the rover driveability per-formance on various terrain characteristics such as soft sandy and hard rocky terrains as well as on inclined planes, where wheel and grouser geometry plays a dominant role. Moreover, rover optimization is performed to support the best engineering intuitions, that will optimize structural and geometric parameters, compare various kinematics suspension concepts, and make use of realistic cost functions like mass and consumed energy minimization, static sta-bility, and more. For self-localization and safe navigation through unknown terrain we make use of fast 3D stereo algorithms that were successfully used e.g. in unmanned air vehicle ap-plications and on terrestrial mobile systems. The advanced rover design approach is applica-ble for lunar as well as Martian surface exploration purposes. A first mobility concept ap-proach for a lunar vehicle will be presented
Bipedal Hopping: Reduced-order Model Embedding via Optimization-based Control
This paper presents the design and validation of controlling hopping on the
3D bipedal robot Cassie. A spring-mass model is identified from the kinematics
and compliance of the robot. The spring stiffness and damping are encapsulated
by the leg length, thus actuating the leg length can create and control hopping
behaviors. Trajectory optimization via direct collocation is performed on the
spring-mass model to plan jumping and landing motions. The leg length
trajectories are utilized as desired outputs to synthesize a control Lyapunov
function based quadratic program (CLF-QP). Centroidal angular momentum, taking
as an addition output in the CLF-QP, is also stabilized in the jumping phase to
prevent whole body rotation in the underactuated flight phase. The solution to
the CLF-QP is a nonlinear feedback control law that achieves dynamic jumping
behaviors on bipedal robots with compliance. The framework presented in this
paper is verified experimentally on the bipedal robot Cassie.Comment: 8 pages, 7 figures, accepted by IROS 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
Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model
A Hybrid passive Linear Inverted Pendulum (H-LIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Period-l (P1) and Period -2 (P2) orbits are geometrically characterized in the state space of the H-LIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Spring-loaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a stepping-in-place motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots
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