65 research outputs found
Robot Manipulation Task Learning by Leveraging SE(3) Group Invariance and Equivariance
This paper presents a differential geometric control approach that leverages
SE(3) group invariance and equivariance to increase transferability in learning
robot manipulation tasks that involve interaction with the environment.
Specifically, we employ a control law and a learning representation framework
that remain invariant under arbitrary SE(3) transformations of the manipulation
task definition. Furthermore, the control law and learning representation
framework are shown to be SE(3) equivariant when represented relative to the
spatial frame. The proposed approach is based on utilizing a recently presented
geometric impedance control (GIC) combined with a learning variable impedance
control framework, where the gain scheduling policy is trained in a supervised
learning fashion from expert demonstrations. A geometrically consistent error
vector (GCEV) is fed to a neural network to achieve a gain scheduling policy
that remains invariant to arbitrary translation and rotations. A comparison of
our proposed control and learning framework with a well-known Cartesian space
learning impedance control, equipped with a Cartesian error vector-based gain
scheduling policy, confirms the significantly superior learning transferability
of our proposed approach. A hardware implementation on a peg-in-hole task is
conducted to validate the learning transferability and feasibility of the
proposed approach
Information-Theoretic Stochastic Optimal Control via Incremental Sampling-based Algorithms
This paper considers optimal control of dynamical systems which are
represented by nonlinear stochastic differential equations. It is well-known
that the optimal control policy for this problem can be obtained as a function
of a value function that satisfies a nonlinear partial differential equation,
namely, the Hamilton-Jacobi-Bellman equation. This nonlinear PDE must be solved
backwards in time, and this computation is intractable for large scale systems.
Under certain assumptions, and after applying a logarithmic transformation, an
alternative characterization of the optimal policy can be given in terms of a
path integral. Path Integral (PI) based control methods have recently been
shown to provide elegant solutions to a broad class of stochastic optimal
control problems. One of the implementation challenges with this formalism is
the computation of the expectation of a cost functional over the trajectories
of the unforced dynamics. Computing such expectation over trajectories that are
sampled uniformly may induce numerical instabilities due to the exponentiation
of the cost. Therefore, sampling of low-cost trajectories is essential for the
practical implementation of PI-based methods. In this paper, we use incremental
sampling-based algorithms to sample useful trajectories from the unforced
system dynamics, and make a novel connection between Rapidly-exploring Random
Trees (RRTs) and information-theoretic stochastic optimal control. We show the
results from the numerical implementation of the proposed approach to several
examples.Comment: 18 page
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