29 research outputs found
Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations
We present a multi-contact walking pattern generator based on preview-control
of the 3D acceleration of the center of mass (COM). A key point in the design
of our algorithm is the calculation of contact-stability constraints. Thanks to
a mathematical observation on the algebraic nature of the frictional wrench
cone, we show that the 3D volume of feasible COM accelerations is a always a
downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D
points, for which optimal O(n log n) algorithms are readily available. This
reformulation brings a significant speedup compared to previous methods, which
allows us to compute time-varying contact-stability criteria fast enough for
the control loop. Next, we propose a conservative trajectory-wide
contact-stability criterion, which can be derived from COM-acceleration volumes
at marginal cost and directly applied in a model-predictive controller. We
finally implement this pipeline and exemplify it with the HRP-4 humanoid model
in multi-contact dynamically walking scenarios
Efficient Humanoid Contact Planning using Learned Centroidal Dynamics Prediction
Humanoid robots dynamically navigate an environment by interacting with it
via contact wrenches exerted at intermittent contact poses. Therefore, it is
important to consider dynamics when planning a contact sequence. Traditional
contact planning approaches assume a quasi-static balance criterion to reduce
the computational challenges of selecting a contact sequence over a rough
terrain. This however limits the applicability of the approach when dynamic
motions are required, such as when walking down a steep slope or crossing a
wide gap. Recent methods overcome this limitation with the help of efficient
mixed integer convex programming solvers capable of synthesizing dynamic
contact sequences. Nevertheless, its exponential-time complexity limits its
applicability to short time horizon contact sequences within small
environments. In this paper, we go beyond current approaches by learning a
prediction of the dynamic evolution of the robot centroidal momenta, which can
then be used for quickly generating dynamically robust contact sequences for
robots with arms and legs using a search-based contact planner. We demonstrate
the efficiency and quality of the results of the proposed approach in a set of
dynamically challenging scenarios
ZMP support areas for multi-contact mobility under frictional constraints
We propose a method for checking and enforcing multi-contact stability based
on the Zero-tilting Moment Point (ZMP). The key to our development is the
generalization of ZMP support areas to take into account (a) frictional
constraints and (b) multiple non-coplanar contacts. We introduce and
investigate two kinds of ZMP support areas. First, we characterize and provide
a fast geometric construction for the support area generated by valid contact
forces, with no other constraint on the robot motion. We call this set the full
support area. Next, we consider the control of humanoid robots using the Linear
Pendulum Mode (LPM). We observe that the constraints stemming from the LPM
induce a shrinking of the support area, even for walking on horizontal floors.
We propose an algorithm to compute the new area, which we call pendular support
area. We show that, in the LPM, having the ZMP in the pendular support area is
a necessary and sufficient condition for contact stability. Based on these
developments, we implement a whole-body controller and generate feasible
multi-contact motions where an HRP-4 humanoid locomotes in challenging
multi-contact scenarios.Comment: 14 pages, 10 figure
ZMP Support Areas for Multicontact Mobility Under Frictional Constraints
International audienceWe propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios
C-CROC: Continuous and Convex Resolution of Centroidal Dynamic Trajectories for Legged Robots in Multicontact Scenarios
International audienceSynthesizing legged locomotion requires planning one or several steps ahead (literally): when and where, and with which effector shouldthe next contact(s) be created between the robot and the environment? Validating a contact candidate implies \textit{a minima} the resolution of a slow, non-linear optimizationproblem, to demonstrate that a Center Of Mass (COM) trajectory, compatible with the contact transition constraints, exists. We propose a conservative reformulation of this trajectory generation problem as a convex 3D linear program, CROC. It results from the observation that if the COM trajectory is a polynomial with only one free variable coefficient, the non-linearity of the problem disappears. This has two consequences. On the positive side, in terms of computation times CROC outperforms the state of the art by at least one order of magnitude, and allows to consider interactive applications (with a planning time roughly equal to the motion time). On the negative side, in our experiments our approach finds a majority of the feasible trajectories found by a non-linear solver, but not all of them. Still, we demonstrate that the solution space covered by CROC is large enough to achieve the automated planning of a large variety of locomotion tasks for different robots, demonstrated in simulation and on the real HRP-2 robot, several of which were rarely seen before.Another significant contribution is the introduction of a Bezier curve representation of the problem, which guarantees that the constraints of the COM trajectory are verified continuously, and not only at discrete points as traditionally done. This formulation is lossless, and results in more robust trajectories. It is not restricted to CROC, but could rather be integrated with any method from the state of the art
An Efficient Paradigm for Feasibility Guarantees in Legged Locomotion
Developing feasible body trajectories for legged systems on arbitrary
terrains is a challenging task. Given some contact points, the trajectories for
the Center of Mass (CoM) and body orientation, designed to move the robot, must
satisfy crucial constraints to maintain balance, and to avoid violating
physical actuation and kinematic limits. In this paper, we present a paradigm
that allows to design feasible trajectories in an efficient manner. In
continuation to our previous work, we extend the notion of the 2D feasible
region, where static balance and the satisfaction of actuation limits were
guaranteed, whenever the projection of the CoM lies inside the proposed
admissible region. We here develop a general formulation of the improved
feasible region to guarantee dynamic balance alongside the satisfaction of both
actuation and kinematic limits for arbitrary terrains in an efficient manner.
To incorporate the feasibility of the kinematic limits, we introduce an
algorithm that computes the reachable region of the CoM. Furthermore, we
propose an efficient planning strategy that utilizes the improved feasible
region to design feasible CoM and body orientation trajectories. Finally, we
validate the capabilities of the improved feasible region and the effectiveness
of the proposed planning strategy, using simulations and experiments on the HyQ
robot and comparing them to a previously developed heuristic approach. Various
scenarios and terrains that mimic confined and challenging environments are
used for the validation.Comment: 17 pages, 13 figures, submitted to Transaction on Robotic