316 research outputs found
Killing graphs over non-compact domains in 3-manifolds with a Killing vector field
Let be a connected and orientable Riemannian 3-manifold with a
non-singular Killing vector field whose
associated one-parameter group of the isometries of acts freely
and properly on . Then, there is a Killing submersion from
onto a connected and orientable surface whose fibers are the
integral curves of . We solve the Dirichlet problem for the minimal
surface equation over certain unbounded domains of , taking piecewise
continuous boundary values. In the particular case of the Heisenberg group, we
prove a uniqueness result for minimal Killing graphs with bounded boundary
values over a strip. We obtain Collin-Krust type estimates in arbitrary Killing
submersions with not necessary unitary Killing vector field. We also prove that
isolated singularities of Killing graphs with prescribed mean curvature are
removable.Comment: 25 pages, 8 figure
On Time Optimization of Centroidal Momentum Dynamics
Recently, the centroidal momentum dynamics has received substantial attention
to plan dynamically consistent motions for robots with arms and legs in
multi-contact scenarios. However, it is also non convex which renders any
optimization approach difficult and timing is usually kept fixed in most
trajectory optimization techniques to not introduce additional non convexities
to the problem. But this can limit the versatility of the algorithms. In our
previous work, we proposed a convex relaxation of the problem that allowed to
efficiently compute momentum trajectories and contact forces. However, our
approach could not minimize a desired angular momentum objective which
seriously limited its applicability. Noticing that the non-convexity introduced
by the time variables is of similar nature as the centroidal dynamics one, we
propose two convex relaxations to the problem based on trust regions and soft
constraints. The resulting approaches can compute time-optimized dynamically
consistent trajectories sufficiently fast to make the approach realtime
capable. The performance of the algorithm is demonstrated in several
multi-contact scenarios for a humanoid robot. In particular, we show that the
proposed convex relaxation of the original problem finds solutions that are
consistent with the original non-convex problem and illustrate how timing
optimization allows to find motion plans that would be difficult to plan with
fixed timing.Comment: 7 pages, 4 figures, ICRA 201
A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions
We develop a conformal duality for spacelike graphs in Riemannian and
Lorentzian three-manifolds that admit a Riemannian submersion over a Riemannian
surface whose fibers are the integral curves of a Killing vector field, which
is timelike in the Lorentzian case. The duality swaps mean curvature and bundle
curvature and sends the length of the Killing vector field to its reciprocal
while keeping invariant the base surface. We obtain two consequences of this
result. On the one hand, we find entire graphs in Lorentz-Minkowski space
with prescribed mean curvature a bounded function with bounded gradient. On the other hand, we obtain
conditions for existence and non existence of entire graphs which are related
to a notion of critical mean curvature.Comment: 20 pages, 2 figur
Multi-contact Stochastic Predictive Control for Legged Robots with Contact Locations Uncertainty
Trajectory optimization under uncertainties is a challenging problem for
robots in contact with the environment. Such uncertainties are inevitable due
to estimation errors, control imperfections, and model mismatches between
planning models used for control and the real robot dynamics. This induces
control policies that could violate the contact location constraints by making
contact at unintended locations, and as a consequence leading to unsafe motion
plans. This work addresses the problem of robust kino-dynamic whole-body
trajectory optimization using stochastic nonlinear model predictive control
(SNMPC) by considering additive uncertainties on the model dynamics subject to
contact location chance-constraints as a function of robot's full kinematics.
We demonstrate the benefit of using SNMPC over classic nonlinear MPC (NMPC) for
whole-body trajectory optimization in terms of contact location constraint
satisfaction (safety). We run extensive Monte-Carlo simulations for a quadruped
robot performing agile trotting and bounding motions over small stepping
stones, where contact location satisfaction becomes critical. Our results show
that SNMPC is able to perform all motions safely with 100% success rate, while
NMPC failed 48.3% of all motions
Receding-Constraint Model Predictive Control using a Learned Approximate Control-Invariant Set
In recent years, advanced model-based and data-driven control methods are
unlocking the potential of complex robotics systems, and we can expect this
trend to continue at an exponential rate in the near future. However, ensuring
safety with these advanced control methods remains a challenge. A well-known
tool to make controllers (either Model Predictive Controllers or Reinforcement
Learning policies) safe, is the so-called control-invariant set (a.k.a. safe
set). Unfortunately, for nonlinear systems, such a set cannot be exactly
computed in general. Numerical algorithms exist for computing approximate
control-invariant sets, but classic theoretic control methods break down if the
set is not exact. This paper presents our recent efforts to address this issue.
We present a novel Model Predictive Control scheme that can guarantee recursive
feasibility and/or safety under weaker assumptions than classic methods. In
particular, recursive feasibility is guaranteed by making the safe-set
constraint move backward over the horizon, and assuming that such set satisfies
a condition that is weaker than control invariance. Safety is instead
guaranteed under an even weaker assumption on the safe set, triggering a safe
task-abortion strategy whenever a risk of constraint violation is detected. We
evaluated our approach on a simulated robot manipulator, empirically
demonstrating that it leads to less constraint violations than state-of-the-art
approaches, while retaining reasonable performance in terms of tracking cost
and number of completed tasks.Comment: 7 pages, 3 figures, 3 tables, 2 pseudo-algo, conferenc
Efficient Reinforcement Learning for Jumping Monopods
In this work, we consider the complex control problem of making a monopod
reach a target with a jump. The monopod can jump in any direction and the
terrain underneath its foot can be uneven. This is a template of a much larger
class of problems, which are extremely challenging and computationally
expensive to solve using standard optimisation-based techniques. Reinforcement
Learning (RL) could be an interesting alternative, but the application of an
end-to-end approach in which the controller must learn everything from scratch,
is impractical. The solution advocated in this paper is to guide the learning
process within an RL framework by injecting physical knowledge. This expedient
brings to widespread benefits, such as a drastic reduction of the learning
time, and the ability to learn and compensate for possible errors in the
low-level controller executing the motion. We demonstrate the advantage of our
approach with respect to both optimization-based and end-to-end RL approaches
Nonlinear Stochastic Trajectory Optimization for Centroidal Momentum Motion Generation of Legged Robots
Generation of robust trajectories for legged robots remains a challenging
task due to the underlying nonlinear, hybrid and intrinsically unstable
dynamics which needs to be stabilized through limited contact forces.
Furthermore, disturbances arising from unmodelled contact interactions with the
environment and model mismatches can hinder the quality of the planned
trajectories leading to unsafe motions. In this work, we propose to use
stochastic trajectory optimization for generating robust centroidal momentum
trajectories to account for additive uncertainties on the model dynamics and
parametric uncertainties on contact locations. Through an alternation between
the robust centroidal and whole-body trajectory optimizations, we generate
robust momentum trajectories while being consistent with the whole-body
dynamics. We perform an extensive set of simulations subject to different
uncertainties on a quadruped robot showing that our stochastic trajectory
optimization problem reduces the amount of foot slippage for different gaits
while achieving better performance over deterministic planning
Inertial Parameter Identification Including Friction and Motor Dynamics
Identification of inertial parameters is fundamental for the implementation
of torque-based control in humanoids. At the same time, good models of friction
and actuator dynamics are critical for the low-level control of joint torques.
We propose a novel method to identify inertial, friction and motor parameters
in a single procedure. The identification exploits the measurements of the PWM
of the DC motors and a 6-axis force/torque sensor mounted inside the kinematic
chain. The partial least-square (PLS) method is used to perform the regression.
We identified the inertial, friction and motor parameters of the right arm of
the iCub humanoid robot. We verified that the identified model can accurately
predict the force/torque sensor measurements and the motor voltages. Moreover,
we compared the identified parameters against the CAD parameters, in the
prediction of the force/torque sensor measurements. Finally, we showed that the
estimated model can effectively detect external contacts, comparing it against
a tactile-based contact detection. The presented approach offers some
advantages with respect to other state-of-the-art methods, because of its
completeness (i.e. it identifies inertial, friction and motor parameters) and
simplicity (only one data collection, with no particular requirements).Comment: Pre-print of paper presented at Humanoid Robots, 13th IEEE-RAS
International Conference on, Atlanta, Georgia, 201
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