2,645 research outputs found
Robotic manipulation of a rotating chain
This paper considers the problem of manipulating a uniformly rotating chain:
the chain is rotated at a constant angular speed around a fixed axis using a
robotic manipulator. Manipulation is quasi-static in the sense that transitions
are slow enough for the chain to be always in "rotational" equilibrium. The
curve traced by the chain in a rotating plane -- its shape function -- can be
determined by a simple force analysis, yet it possesses complex multi-solutions
behavior typical of non-linear systems. We prove that the configuration space
of the uniformly rotating chain is homeomorphic to a two-dimensional surface
embedded in . Using that representation, we devise a manipulation
strategy for transiting between different rotation modes in a stable and
controlled manner. We demonstrate the strategy on a physical robotic arm
manipulating a rotating chain. Finally, we discuss how the ideas developed here
might find fruitful applications in the study of other flexible objects, such
as elastic rods or concentric tubes.Comment: 12 pages, 9 figure
Time-Optimal Path Tracking via Reachability Analysis
Given a geometric path, the Time-Optimal Path Tracking problem consists in
finding the control strategy to traverse the path time-optimally while
regulating tracking errors. A simple yet effective approach to this problem is
to decompose the controller into two components: (i)~a path controller, which
modulates the parameterization of the desired path in an online manner,
yielding a reference trajectory; and (ii)~a tracking controller, which takes
the reference trajectory and outputs joint torques for tracking. However, there
is one major difficulty: the path controller might not find any feasible
reference trajectory that can be tracked by the tracking controller because of
torque bounds. In turn, this results in degraded tracking performances. Here,
we propose a new path controller that is guaranteed to find feasible reference
trajectories by accounting for possible future perturbations. The main
technical tool underlying the proposed controller is Reachability Analysis, a
new method for analyzing path parameterization problems. Simulations show that
the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201
A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in
robotics and has a wide range of applications. There are two main families of
methods to address TOPP: Numerical Integration (NI) and Convex Optimization
(CO). NI-based methods are fast but difficult to implement and suffer from
robustness issues, while CO-based approaches are more robust but at the same
time significantly slower. Here we propose a new approach to TOPP based on
Reachability Analysis (RA). The key insight is to recursively compute reachable
and controllable sets at discretized positions on the path by solving small
Linear Programs (LPs). The resulting algorithm is faster than NI-based methods
and as robust as CO-based ones (100% success rate), as confirmed by extensive
numerical evaluations. Moreover, the proposed approach offers unique additional
benefits: Admissible Velocity Propagation and robustness to parametric
uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure
Uncountable families of prime z-ideals in C_0(R)
Denote by \continuum=2^{\aleph_0} the cardinal of continuum. We construct
an intriguing family (P_\alpha: \alpha\in\continuum) of prime -ideals in
\C_0(\reals) with the following properties:
If for some i_0\in\continuum, then for all but
finitely many i\in \continuum;
\bigcap_{i\neq i_0} P_i \nsubset P_{i_0} for each \i_0\in \continuum.
We also construct a well-ordered increasing chain, as well as a well-ordered
decreasing chain, of order type of prime -ideals in \C_0(\reals)
for any ordinal of cardinality \continuum.Comment: 12 page
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