  We develop an algorithm for the motion and task planning of a system
comprised of multiple robots and unactuated objects under tasks expressed as
Linear Temporal Logic (LTL) constraints. The robots and objects evolve subject
to uncertain dynamics in an obstacle-cluttered environment. The key part of the
proposed solution is the intelligent construction of a coupled transition
system that encodes the motion and tasks of the robots and the objects. We
achieve such a construction by designing appropriate adaptive control protocols
in the lower level, which guarantee the safe robot navigation/object
transportation in the environment while compensating for the dynamic
uncertainties. The transition system is efficiently interfaced with the
temporal logic specification via a sampling-based algorithm to output a
discrete path as a sequence of synchronized actions of the robots; such actions
satisfy the robots' as well as the objects' specifications. The robots execute
this discrete path by using the derived low level control protocol. Simulation
results verify the proposed framework.
