4 research outputs found
Control of Magnetic Microrobot Teams for Temporal Micromanipulation Tasks
In this paper, we present a control framework that allows magnetic microrobot
teams to accomplish complex micromanipulation tasks captured by global Linear
Temporal Logic (LTL) formulas. To address this problem, we propose an optimal
control synthesis method that constructs discrete plans for the robots that
satisfy both the assigned tasks as well as proximity constraints between the
robots due to the physics of the problem. Our proposed algorithm relies on an
existing optimal control synthesis approach combined with a novel
sampling-based technique to reduce the state-space of the product automaton
that is associated with the LTL specifications. The synthesized discrete plans
are executed by the microrobots independently using local magnetic fields.
Simulation studies show that the proposed algorithm can address large-scale
planning problems that cannot be solved using existing optimal control
synthesis approaches. Moreover, we present experimental results that also
illustrate the potential of our method in practice. To the best of our
knowledge, this is the first control framework that allows independent control
of teams of magnetic microrobots for temporal micromanipulation tasks
Multirobot Coordination with Counting Temporal Logics
In many multirobot applications, planning trajectories in a way to guarantee
that the collective behavior of the robots satisfies a certain high-level
specification is crucial. Motivated by this problem, we introduce counting
temporal logics---formal languages that enable concise expression of multirobot
task specifications over possibly infinite horizons. We first introduce a
general logic called counting linear temporal logic plus (cLTL+), and propose
an optimization-based method that generates individual trajectories such that
satisfaction of a given cLTL+ formula is guaranteed when these trajectories are
synchronously executed. We then introduce a fragment of cLTL+, called counting
linear temporal logic (cLTL), and show that a solution to planning problem with
cLTL constraints can be obtained more efficiently if all robots have identical
dynamics. In the second part of the paper, we relax the synchrony assumption
and discuss how to generate trajectories that can be asynchronously executed,
while preserving the satisfaction of the desired cLTL+ specification. In
particular, we show that when the asynchrony between robots is bounded, the
method presented in this paper can be modified to generate robust trajectories.
We demonstrate these ideas with an experiment and provide numerical results
that showcase the scalability of the method.Comment: Under submission for a journa
STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems
This paper proposes a new highly scalable and asymptotically optimal control
synthesis algorithm from linear temporal logic specifications, called
for large-Scale optimal Temporal Logic Synthesis, that is
designed to solve complex temporal planning problems in large-scale multi-robot
systems. Existing planning approaches with temporal logic specifications rely
on graph search techniques applied to a product automaton constructed among the
robots. In our previous work, we have proposed a more tractable sampling-based
algorithm that builds incrementally trees that approximate the state-space and
transitions of the synchronous product automaton and does not require
sophisticated graph search techniques. Here, we extend our previous work by
introducing bias in the sampling process which is guided by transitions in the
Bchi automaton that belong to the shortest path to the
accepting states. This allows us to synthesize optimal motion plans from
product automata with hundreds of orders of magnitude more states than those
that existing optimal control synthesis methods or off-the-shelf model checkers
can manipulate. We show that is probabilistically complete
and asymptotically optimal and has exponential convergence rate. This is the
first time that convergence rate results are provided for sampling-based
optimal control synthesis methods. We provide simulation results that show that
can synthesize optimal motion plans for very large
multi-robot systems which is impossible using state-of-the-art methods
An Abstraction-Free Method for Multi-Robot Temporal Logic Optimal Control Synthesis
The majority of existing Linear Temporal Logic (LTL) planning methods rely on
the construction of a discrete product automaton, that combines a discrete
abstraction of robot mobility and a Bchi automaton that
captures the LTL specification. Representing this product automaton as a graph
and using graph search techniques, optimal plans that satisfy the LTL task can
be synthesized. However, constructing expressive discrete abstractions makes
the synthesis problem computationally intractable. In this paper, we propose a
new sampling-based LTL planning algorithm that does not require any discrete
abstraction of robot mobility. Instead, it incrementally builds trees that
explore the product state-space, until a maximum number of iterations is
reached or a feasible plan is found. The use of trees makes data storage and
graph search tractable, which significantly increases the scalability of our
algorithm. To accelerate the construction of feasible plans, we introduce bias
in the sampling process which is guided by transitions in the
Bchi automaton that belong to the shortest path to the
accepting states. We show that our planning algorithm, with and without bias,
is probabilistically complete and asymptotically optimal. Finally, we present
numerical experiments showing that our method outperforms relevant temporal
logic planning methods.Comment: 21 pages, 10 figure