182 research outputs found
Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas
While humans are highly capable of recovering from external disturbances and
uncertainties that result in large tracking errors, humanoid robots have yet to
reliably mimic this level of robustness. Essential to this is the ability to
combine traditional "ankle strategy" balancing with step timing and location
adjustment techniques. In doing so, the robot is able to step quickly to the
necessary location to continue walking. In this work, we present both a new
swing speed up algorithm to adjust the step timing, allowing the robot to set
the foot down more quickly to recover from errors in the direction of the
current capture point dynamics, and a new algorithm to adjust the desired
footstep, expanding the base of support to utilize the center of pressure
(CoP)-based ankle strategy for balance. We then utilize the desired centroidal
moment pivot (CMP) to calculate the momentum rate of change for our
inverse-dynamics based whole-body controller. We present simulation and
experimental results using this work, and discuss performance limitations and
potential improvements
Frequency-Aware Model Predictive Control
Transferring solutions found by trajectory optimization to robotic hardware
remains a challenging task. When the optimization fully exploits the provided
model to perform dynamic tasks, the presence of unmodeled dynamics renders the
motion infeasible on the real system. Model errors can be a result of model
simplifications, but also naturally arise when deploying the robot in
unstructured and nondeterministic environments. Predominantly, compliant
contacts and actuator dynamics lead to bandwidth limitations. While classical
control methods provide tools to synthesize controllers that are robust to a
class of model errors, such a notion is missing in modern trajectory
optimization, which is solved in the time domain. We propose frequency-shaped
cost functions to achieve robust solutions in the context of optimal control
for legged robots. Through simulation and hardware experiments we show that
motion plans can be made compatible with bandwidth limits set by actuators and
contact dynamics. The smoothness of the model predictive solutions can be
continuously tuned without compromising the feasibility of the problem.
Experiments with the quadrupedal robot ANYmal, which is driven by
highly-compliant series elastic actuators, showed significantly improved
tracking performance of the planned motion, torque, and force trajectories and
enabled the machine to walk robustly on terrain with unmodeled compliance
3LP: a linear 3D-walking model including torso and swing dynamics
In this paper, we present a new model of biped locomotion which is composed
of three linear pendulums (one per leg and one for the whole upper body) to
describe stance, swing and torso dynamics. In addition to double support, this
model has different actuation possibilities in the swing hip and stance ankle
which could be widely used to produce different walking gaits. Without the need
for numerical time-integration, closed-form solutions help finding periodic
gaits which could be simply scaled in certain dimensions to modulate the motion
online. Thanks to linearity properties, the proposed model can provide a
computationally fast platform for model predictive controllers to predict the
future and consider meaningful inequality constraints to ensure feasibility of
the motion. Such property is coming from describing dynamics with joint torques
directly and therefore, reflecting hardware limitations more precisely, even in
the very abstract high level template space. The proposed model produces
human-like torque and ground reaction force profiles and thus, compared to
point-mass models, it is more promising for precise control of humanoid robots.
Despite being linear and lacking many other features of human walking like CoM
excursion, knee flexion and ground clearance, we show that the proposed model
can predict one of the main optimality trends in human walking, i.e. nonlinear
speed-frequency relationship. In this paper, we mainly focus on describing the
model and its capabilities, comparing it with human data and calculating
optimal human gait variables. Setting up control problems and advanced
biomechanical analysis still remain for future works.Comment: Journal paper under revie
A Reactive and Efficient Walking Pattern Generator for Robust Bipedal Locomotion
Available possibilities to prevent a biped robot from falling down in the
presence of severe disturbances are mainly Center of Pressure (CoP) modulation,
step location and timing adjustment, and angular momentum regulation. In this
paper, we aim at designing a walking pattern generator which employs an optimal
combination of these tools to generate robust gaits. In this approach, first,
the next step location and timing are decided consistent with the commanded
walking velocity and based on the Divergent Component of Motion (DCM)
measurement. This stage which is done by a very small-size Quadratic Program
(QP) uses the Linear Inverted Pendulum Model (LIPM) dynamics to adapt the
switching contact location and time. Then, consistent with the first stage, the
LIPM with flywheel dynamics is used to regenerate the DCM and angular momentum
trajectories at each control cycle. This is done by modulating the CoP and
Centroidal Momentum Pivot (CMP) to realize a desired DCM at the end of current
step. Simulation results show the merit of this reactive approach in generating
robust and dynamically consistent walking patterns
Real-Time Planning with Primitives for Dynamic Walking over Uneven Terrain
We present an algorithm for receding-horizon motion planning using a finite
family of motion primitives for underactuated dynamic walking over uneven
terrain. The motion primitives are defined as virtual holonomic constraints,
and the special structure of underactuated mechanical systems operating subject
to virtual constraints is used to construct closed-form solutions and a special
binary search tree that dramatically speed up motion planning. We propose a
greedy depth-first search and discuss improvement using energy-based
heuristics. The resulting algorithm can plan several footsteps ahead in a
fraction of a second for both the compass-gait walker and a planar
7-Degree-of-freedom/five-link walker.Comment: Conference submissio
An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion
We describe a whole-body dynamic walking controller implemented as a convex
quadratic program. The controller solves an optimal control problem using an
approximate value function derived from a simple walking model while respecting
the dynamic, input, and contact constraints of the full robot dynamics. By
exploiting sparsity and temporal structure in the optimization with a custom
active-set algorithm, we surpass the performance of the best available
off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We
describe applications to balancing and walking tasks using the simulated Atlas
robot in the DARPA Virtual Robotics Challenge.Comment: 6 pages, published at ICRA 201
Impact-Aware Online Motion Planning for Fully-Actuated Bipedal Robot Walking
The ability to track a general walking path with specific timing is crucial
to the operational safety and reliability of bipedal robots for avoiding
dynamic obstacles, such as pedestrians, in complex environments. This paper
introduces an online, full-body motion planner that generates the desired
impact-aware motion for fully-actuated bipedal robotic walking. The main
novelty of the proposed planner lies in its capability of producing desired
motions in real-time that respect the discrete impact dynamics and the desired
impact timing. To derive the proposed planner, a full-order hybrid dynamic
model of fully-actuated bipedal robotic walking is presented, including both
continuous dynamics and discrete lading impacts. Next, the proposed
impact-aware online motion planner is introduced. Finally, simulation results
of a 3-D bipedal robot are provided to confirm the effectiveness of the
proposed online impact-aware planner. The online planner is capable of
generating full-body motion of one walking step within 0.6 second, which is
shorter than a typical bipedal walking step
Imprecise dynamic walking with time-projection control
We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller
When and Where to Step: Terrain-Aware Real-Time Footstep Location and Timing Optimization for Bipedal Robots
Online footstep planning is essential for bipedal walking robots, allowing
them to walk in the presence of disturbances and sensory noise. Most of the
literature on the topic has focused on optimizing the footstep placement while
keeping the step timing constant. In this work, we introduce a footstep planner
capable of optimizing footstep placement and step time online. The proposed
planner, consisting of an Interior Point Optimizer (IPOPT) and an optimizer
based on Augmented Lagrangian (AL) method with analytical gradient descent,
solves the full dynamics of the Linear Inverted Pendulum (LIP) model in real
time to optimize for footstep location as well as step timing at the rate of
200~Hz. We show that such asynchronous real-time optimization with the AL
method (ARTO-AL) provides the required robustness and speed for successful
online footstep planning. Furthermore, ARTO-AL can be extended to plan
footsteps in 3D, allowing terrain-aware footstep planning on uneven terrains.
Compared to an algorithm with no footstep time adaptation, our proposed ARTO-AL
demonstrates increased stability in simulated walking experiments as it can
resist pushes on flat ground and on a ramp up to 120 N and 100 N
respectively. For the video, see https://youtu.be/ABdnvPqCUu4. For code, see
https://github.com/WangKeAlchemist/ARTO-AL/tree/master.Comment: 32 pages, 15 figures. Submitted to Robotics and Autonomous System
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